# Online Appendix Feedback Effects, Asymmetric Trading, and the Limits to Arbitrage

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 Online Appendix Feedback Effects, Asymmetric Trading, and the Limits to Arbitrage Alex Edmans LBS, NBER, CEPR, and ECGI Itay Goldstein Wharton Wei Jiang Columbia May 8, 05 A Proofs of Propositions and Corollaries in the Paper Proof of Proposition This proof only provides material supplementary to what is in the main text. No Trade Equilibrium NT. The order flows of X = and X = are off the equilibrium path and the posteriors are given by 0 and, respectively, as these are the only posteriors that satisfy the Intuitive Criterion (as stated in the main text). The order flows of X {, 0, } are on the equilibrium path and so the posteriors can be calculated by Bayes rule: We thus have: q( ) = q(x) = Pr(H X) = Pr(X H) Pr(X H) + Pr(X L). λ(/) + ( λ)(/) λ(/) + ( λ)(/) + λ(/) + ( λ)(/) =, and q (0) and q () are calculated in exactly the same way. Sequential rationality leads to the

2 decisions d and prices p as given by the Table in the proof in the main text. We now turn to calculating the speculator s payoff (gross of the transaction cost κ) under different trading strategies, which comprises of the value of her final stake (of, 0, or share), plus (minus) the price received (paid) for any share sold (bought). Under the positively-informed speculator s equilibrium strategy of not trading, we have X {, 0, } and so her payoff is 0. If she deviates to buying: With probability (w.p.), X =, and she is fully revealed. Her payoff is 0. W.p., X {0, }, and she pays R H + R L per share. Her payoff is R H ( R H + R L) = (R H R L ). Thus, her expected gross gain from deviating to buying is given by: (R H R L ) κ NT. () A similar calculation shows that, if the negatively-informed speculator sells, her expected gross gain is also given by (). Thus, if and only if κ κ NT, the no-trade equilibrium is sustainable. The above calculations apply both in the case of feedback ( λ > γ and λ λ < γ ) and no feedback ( λ γ and λ λ γ ). Partial Trade Equilibrium BNS. The order flow of X = is off the equilibrium path and the posterior is given by 0. The posteriors of the other order flows are given as follows: q ( ) = q (0) = q() = ( λ)(/) ( λ)(/) + λ(/) + ( λ)(/) = λ λ, λ(/) + ( λ)(/) λ(/) + ( λ)(/) + λ(/) + ( λ)(/) =, λ(/) + ( λ)(/) λ(/) + ( λ)(/) + λ(/) + ( λ)(/) =, q() = λ (/) λ (/) =. Under the positively-informed speculator s equilibrium strategy of buying: W.p., X =, and she is fully revealed. Her payoff is 0. W.p., X {0, }, and she pays R H + R L per share. Her payoff is R H ( R H + R L) = (R H R L ).

3 If she deviates to not trading, her payoff is 0. Thus, her expected gross gain from deviating to not trading is κ NT (as given by ()) in the cases of both feedback and no feedback. Under the positively-informed speculator s equilibrium strategy of not trading, her payoff is 0. If she deviates to selling: W.p., X =, and she is fully revealed. Her payoff is 0. W.p. λ, X =. In the case of feedback, she receives (R λ H x c)+ (R λ L + x c) per share, and so her payoff is (R L + x c) + ( λ λ (R H x) + λ (R L + x) c) = λ (R λ H R L x). In the case of no feedback, she receives λr λ H + R λ L per share, and so her payoff is R L + ( λ λ R H + λ R L) = λ λ (R H R L ). W.p., X = 0, and she receives R H + R L per share. Her payoff is R L +( R H + R L) = (R H R L ). Thus, her expected gross gain from deviating to selling is given by: in the case of feedback, and in the case of no feedback. [ λ λ (R H R L x) + ] (R H R L ) κ T () [ λ λ + ] (R H R L ) κ NF () Thus, the BNS equilibrium is sustainable if and only if κ T κ < κ NT in the case of feedback, and κ NF κ < κ NT in the case of no feedback. Partial Trade Equilibrium SNB. The order flow of X = is off the equilibrium path and the posterior is given by. The posteriors of the other order flows are given as follows: 0 q( ) = λ (/) = 0, λ(/) + ( λ)(/) q ( ) = λ(/) + ( λ)(/) + λ(/) + ( λ)(/) =, λ(/) + ( λ)(/) q (0) = λ(/) + ( λ)(/) + λ(/) + ( λ)(/) =, λ(/) + ( λ)(/) q() = λ(/) + ( λ)(/) + ( λ)(/) = λ.

4 Under the negatively-informed speculator s equilibrium strategy of selling: W.p., X =, and she is fully revealed. Her payoff is 0. W.p., X {, 0}, and she receives R H + R L per share. Her payoff is R L + ( R H + R ) L = (R H R L ). If she deviates to not trading, her payoff is 0. Thus, her expected gross gain from deviating to not trading is κ NT (as given by ()) in the cases of both feedback and no feedback. Under the positively-informed speculator s equilibrium strategy of not trading, her payoff is 0. If she deviates to buying: W.p., X =, and she is fully revealed. Her payoff is 0. W.p., X =. In the case of feedback, she pays λ (R H + x) + λ λ (R L x) c per share, and so her payoff is (R H + x c) ( λ (R H + x) + λ λ (R L x) c) = λ (R λ H R L + x). In the case of no feedback, she pays R λ H + λr λ L per share, and so her payoff is R H ( λ R H + λ λ R L) = λ λ (R H R L ). W.p., X = 0, and she pays R H + R L per share. Her payoff is R H ( R H + R L) = (R H R L ). Thus, her expected gross gain from deviating to buying is given by: [ λ λ (R H R L + x) + ] (R H R L ) κ SNB in the case of feedback, and κ NF (as given by ()) in the case of no feedback. Thus, the SNB equilibrium is sustainable if and only if κ SNB κ < κ NT feedback, and κ NF κ < κ NT in the case of no feedback. in the case of Trade Equilibrium T. All order flows are on the equilibrium path and so the posteriors are 4

5 given as follows: 0 q( ) = λ (/) = 0, ( λ)(/) q ( ) = ( λ)(/) + λ(/) + ( λ)(/) = λ λ, λ(/) + ( λ)(/) q (0) = λ(/) + ( λ)(/) + λ(/) + ( λ)(/) =, λ(/) + ( λ)(/) q() = λ(/) + ( λ)(/) + ( λ)(/) = λ, q() = λ (/) λ (/) =. Under the negatively-informed speculator s equilibrium strategy of selling: W.p., X =, and she is fully revealed. Her payoff is 0. λ W.p., X =. In the case of feedback, she receives (R λ H x) + (R λ L + x) c per share, and so her payoff is (R L + x c) + ( λ λ (R H x) + λ (R L + x) c) = λ (R λ H R L x). In the case of no feedback, she receives λr λ H + R λ L per share, and so her payoff is R L + ( λ λ R H + λ R L) = λ λ (R H R L ). W.p., X = 0, and she receives R H + R L per share. Her payoff is R L +( R H + R L) = (R H R L ). If she deviates to not trading, her payoff is 0. Thus, her expected gross gain from deviating to not trading is κ T (as given by ()) in the case of feedback, and κ NF (as given by ()) in the case of no feedback. A similar calculation shows that, if the positively-informed speculator deviates to not trading, her gross gain is κ SNB (κ SNB > κ T ) in the case of feedback and κ NF no feedback. Thus, the trade equilibrium is sustainable if and only if κ < κ T feedback, and κ < κ NF in the case of no feedback. in the case of in the case of We now turn to the range of parameter values in which BNS is the only pure-strategy equilibrium in the case of feedback. If κ T κ < κ NT, then the conditions for both the NT and T equilibrium to exist are violated. In addition, this is also the range where BNS equilibrium exists. We thus must derive conditions under which the SN B equilibrium does not hold, so that BNS is the unique equilibrium. There are two cases to consider. (i) If κ SNB κ NT, the 5

6 SNB equilibrium never exists, and so κ T κ < κ NT is suffi cient for BNS to be the unique equilibrium. (ii) If κ T < κ SNB κ NT, the SNB equilibrium exists unless κ < κ SNB. Thus, BNS is the unique equilibrium if κ T κ < κ SNB. Combining the two cases gives the range κ T κ < min(κ SNB, κ NT ) in the Proposition. Proof of Lemma For part (i), if θ = H, the expected posterior is given by: We have: [ q H = ( λ) q ( ) + q (0) + ] ( q () + λ q (0) + q () + ) q () = λ q ( ) + q (0) + q () + λ q () ( λ) = 6 λ + + λ. (4) q H λ = + [ ] ( λ)( λ) + ( λ) ( λ) [ = ( ) ] λ + λ λ λ = [ ( )] λ λ > 0. The expected posterior is increasing in λ: if the speculator is more likely to be present, she is more likely to impound her information into prices by trading. Moving to part (ii), if θ = L, we have: q L = (q ( ) + q (0) + q ()) = λ 6 λ +. (5) This quantity is decreasing in λ. Even though the speculator does not trade upon θ = L if she is present, her information is still partially incorporated into prices. With θ = L, there is a probability that the order flow is X =. This is consistent with the speculator being absent (in which case the state may be either H or L) or her being present and observing θ = L; it 6

7 is not consistent with the speculator observing θ = H. The greater the likelihood that the speculator is present, the greater the likelihood that X = stems from θ = L, and thus the greater the decrease in the market maker s posterior. Part (iii) follows from simple calculations. Proof of Proposition For parts (i) and (ii), we have: q H,spec = (q (0) + q () + q ()) =, (6) q L,spec = (q ( ) + q (0) + q ()) = λ 6 λ +. (7) Note that q H,spec is independent of λ, but q L,spec is decreasing in λ. The variable λ can affect the expected posterior in two ways: first, it can change the relative likelihood of the different order flows, and second, it can change the actual posterior given a certain order flow. Since we are conditioning on the speculator being present, the first channel is ruled out: conditional on the speculator being present and θ = H, X {0,, } with uniform probability regardless of λ; conditional on the speculator being present and θ = L, X {, 0, } with uniform probability regardless of λ. Turning to the second channel, the only posterior that depends on λ is q ( ): since X = is inconsistent with the speculator being present and seeing θ = H, it has a particularly negative impact on the likelihood of θ = H if the speculator is more likely to be present. In contrast, X {, } is fully revealing and so the posterior is independent of λ; X {0, } is completely uninformative and so the posterior is again independent of λ. Since X = can only occur in the presence of a speculator if she has received bad news, only q L,spec depends on λ but q H,spec does not. Part (iii) follows from simple calculations. Proof of Lemma We start by calculating p 0. With probability, the state will be θ = L and there is no trade, regardless of whether the speculator is present. Thus, X {, 0, } with equal probability. With probability, the state will be θ = H. If the speculator is absent (w.p. ( λ)), there is no trade and we again have X {, 0, }. If the speculator is present, X {0,, }. Letting p (X) denote the stock price set by the market maker after observing order flow X at t =, 7

8 the price at t = 0 will be the expectation over all possible future prices at t =, and is given as follows: p 0 = λ ( p (0) + p () + ) ( p () + λ ) ( p ( ) + p (0) + ) p () = (( λ ) p ( ) + p (0) + p () + λ ) p () = 6 [R H + R L c + λx]. (8) Even though the initial belief y is independent of λ, the initial stock price p 0 is increasing in λ, because the speculator provides information to improve the manager s decision. For part (i), if θ = H is realized, the expected price at t = is given by: Note that: [ p H = ( λ) p ( ) + p (0) + ] ( p () + λ p (0) + p () + ) p () = λ p ( ) + p (0) + p () + λ p () = ( λ)r H + ( λ)(r L + λx) c ( λ). (9) p H λ = p() p( ) + λ p( ) λ = R H R L + ( 4λ + λ )x > 0, ( λ) i.e., p H is increasing in λ, since the speculator impounds information about the high state into prices. Turning to part (ii), if θ = L is realized, the expected price at t = is given by: p L = (p ( ) + p (0) + p ()). (0) We have pl = R L R H +x λ ( λ). If the speculator is more likely to be present, then X = is more likely to result from θ = L. Thus, the price is higher if and only if firm value is higher in this state, i.e., R L + x > R H x (Case ). The calculations of p H p 0 and p L p 0 follow automatically. Proof of Proposition 8

9 For part (i), if the speculator receives positive information, she will buy one share and so the expected price becomes: p H,spec = (p (0) + p () + p ()). () Unlike p H (equation (9)), this quantity is independent of λ, for the same reasons that q H,spec (equation (6)) is independent of λ. The stock return realized when the speculator receives good information is thus given by: p H,spec p 0 = (p (0) + p () + p ()) = ( λ ) (p () p ( )) (( λ ) p ( ) + p (0) + p () + λ ) p () = 6 (R H R L + ( λ)x) > 0, () and we have ( p H,spec p 0 ) λ = x < 0. Equation () is decreasing in λ, whereas the stock return not conditioning on the speculator s presence, p H p 0, was increasing in λ. This reversal is because p 0 is increasing in λ, but p H,spec is independent of λ. For part (ii), if the speculator is present and receives negative information, we have: p L,spec = (p ( ) + p (0) + p ()) = pl, () and p L,spec p 0 = (p ( ) + p (0) + p ()) (( λ ) p ( ) + p (0) + p () + λ ) p () = λ 6 (p ( ) p ()) = pl p 0 < 0. Parts (iii) and (iv) follow from simple calculations. Dropping constants, both equation (4) (the asymmetry between the price impact of good and bad news) and equation (5) (the average return, conditional on the speculator being present) 9

11 and so we have p spec p spec = 6 λ λ (R L R H + x), which is positive if we are in Case and negative if we are in Case. B Full Analyses and Proofs of Alternative Models B. Equilibria when firm value is non-monotonic in states: Full analysis In this subsection, we consider the case where, if the firm disinvests, its value is higher in state θ = L (R H x < R L + x). Hence, disinvestment is suffi ciently powerful to outweigh the effect of the state on firm value and lead to a higher value in the low state. The analysis of equilibrium outcomes becomes more complicated in the case of non-monotonicity. In the core model, where firm value is monotone in the state, a positively-informed speculator always loses money by selling and a negatively-informed speculator always loses money by buying, since firm value is always higher in state H than in state L. However, now that firm value may be higher in state L, a positively-informed speculator may find it optimal to sell and a negatively-informed speculator may find it optimal to buy. Hence, there are nine possible pure-strategy equilibria (each type of speculator positively-informed and negatively-informed may either buy, sell, or not trade). The following Lemma simplifies the equilibrium analysis, moving us closer to the analysis conducted in the core model. Lemma (No equilibrium with trading against information). Suppose that R H x < R L + x. Then: (i) The trading game has no pure-strategy equilibrium where the speculator sells when she knows that θ = H. (ii) The trading game has no pure-strategy equilibrium where the speculator buys when she knows that θ = L. Proof. See Appendix B.. Following the Lemma, there are four possible pure-strategy equilibria, just as in the previous subsection: NT, T, SNB, and BNS. However, the conditions for these equilibria to hold are now tighter. The reason that the positively-informed speculator never sells in equilibrium is

12 that if the market maker and the manager believe that she sells, she cannot make a profit from selling. However, she still might be tempted to deviate to selling in any of the four equilibria mentioned above. When she sells, she potentially misleads the market maker and the manager to believe that the negatively-informed speculator is present, and so to disinvest. Since disinvestment is suboptimal if θ = H, this decision reduces firm value and causes the speculator to make a profit on her short position. Hence, for any of the above four equilibria to hold, an additional condition must be satisfied to ensure that the positively-informed speculator does not have an incentive to deviate to selling. Interestingly, the same issue does not arise with the negatively-informed speculator, as she never has an incentive to deviate to buying. If she does so, she misleads the market maker and the manager to believe that the positively-informed speculator is present, and so to (incorrectly) take the investment. This decision reduces firm value, causing the speculator to incur a loss from selling. In analyzing deviations from the equilibrium, another issue that arises in this subsection is the specification of off-equilibrium beliefs. In Case, due to monotonicity, the only assumption that satisfied the Intuitive Criterion was that an off-equilibrium order flow of X = is due to the positively-informed speculator (and so the posterior is q = ), while an off-equilibrium order flow of X = is due to the negatively-informed speculator (and so the posterior is q = 0). In this subsection, however, the Intuitive Criterion is not suffi cient to rule out other off-equilibrium beliefs. We nevertheless retain this assumption regarding off-equilibrium beliefs, which is reasonable given the possible equilibria in our model. Our results remain the same for any other off-equilibrium beliefs that are monotone in the order flow. Proposition 4 provides the characterization of equilibrium outcomes. Proposition 4 (Equilibrium, firm value is non-monotone in the state). Suppose that R H x < R L + x, and suppose that the belief of the market maker and the manager is that an offequilibrium order flow of X = (X = ) is associated with the presence of negatively-informed (positively-informed) speculator. Then, if R H R L is suffi ciently high compared to x (formally, R H R L > 4 x), the characterization of equilibrium outcomes is identical to that in Lemma for the case of feedback and Proposition for the case of no feedback. Goldstein and Guembel (008) also derive conditions to ensure that the speculator does not deviate from the equilibrium to trade against her information. Other papers that use similar monotonicity assumptions for off-equilibrium beliefs include Gul and Sonnenschein (988) and Bikhchandani (99).

14 information. This loss occurs at the X = node. As in the core model, the key to this result is λ <. Even though both the speculator and market maker know that disinvestment will occur if X =, they have differing views on firm value conditional on disinvestment. The speculator knows that disinvestment will occur, and that disinvestment is desirable for firm value (since she knows that θ = L), and so firm value is R L + x c. In contrast, the market maker knows the disinvestment will occur but is not certain that it is optimal, because she is unsure of the underlying state θ. Order flow X = is consistent with a negatively-informed speculator, but also with an absent speculator and selling by the noise trader. Hence, it is possible that θ = H, in which case disinvestment is undesirable, leading to firm value of R H x c. Therefore, the price set by the market maker is only λ λ (R H x) + λ (R L + x) c, since he puts weight on the possibility that disinvestment may be undesirable, and so the speculator loses λ (R λ H R L x) before transaction costs. Moreover, Proposition 4 also shows that the feedback effect generates an additional force in this subsection: the desire of the positively-informed speculator to deviate and manipulate the price by selling. She can potentially profit from leading the manager to divest incorrectly, which enables her to gain on her short position. The manipulation incentive is not strong enough to interfere with equilibrium conditions as long as R H R L is suffi ciently high relative to x; a suffi cient condition is R H R L > 4 x. In this case, the loss from trading against good news (which is proportional to R H R L ) is high relative to the benefit from manipulation (which is proportional to x, the value destroyed by inducing the manager to divest incorrectly). Otherwise, additional conditions are required to sustain the various possible equilibria. B. Positive initial position: Full analysis We now assume that the speculator starts off with a stake of α and can trade s {, 0, }. Thus, her final position becomes {α, α, α + }. Our main result from the core model is that, under feedback, the range of κ that supports the BNS equilibrium is strictly greater than that which supports the SN B equilibrium. Thus, for conciseness, we consider the case of feedback ( λ > γ = + c x rather than the T and NT equilibria. Buy Not Sell Equilibrium BNS. λ < γ λ = c ) and analyze only the BNS and SNB equilibria, x Under the positively-informed speculator s equilibrium strategy of buying: 4

15 W.p., X =, and she is fully revealed. Her payoffis (α+) (R H + x c) (R H + x c) = α (R H + x c). W.p., X {0, }, and she pays R H + R L per share. Her payoff is (α + )R H ( R H + R L) = αr H + (R H R L ). If she deviates to not trading: W.p., X {0, }, and her payoff is αr H. W.p., X =, and her payoff is α (R H x c). Her expected gross gain from deviating to not trading is: [αx + (R H R L )] κ α NT. Under the negatively-informed speculator s equilibrium strategy of not trading: W.p., X {0, }, and her payoff is αr L. W.p., X = and her payoff is α (R L + x c). If she deviates to selling: W.p., X = and she is fully revealed. Thus her payoff is (α ) (R L + x c) + (R L + x c) = α (R L + x c). λ W.p., X = and she receives (R λ H x c) + (R λ L + x c) per share. Her payoff is (α ) (R L + x c) + ( λ λ (R H x) + λ (R L + x) c) = α (R L + x c) + λ (R λ H R L x). W.p., X = 0, and she receives R H + R L per share. Her payoff is (α )R L + ( R H + R L) = αr L + (R H R L ). Her expected gross gain from deviating to selling is: [ α(x c) + λ λ (R H R L x) + ] (R H R L ) κ α T. 5

16 The BNS equilibrium holds for κ [κ α T, κα NT ]. Sell Not Buy Equilibrium SNB. Under the positively-informed speculator s equilibrium strategy of not trading: W.p., X = and her payoff is α (R H + x c). W.p., X {, 0} and her payoff is αr H. If she deviates to buying: W.p., X =, and she is fully revealed. Her payoffis (α+) (R H + x c) (R H + x c) = α (R H + x c). W.p., X =, and she pays λ (R H + x) + λ λ (R L x) c per share. Her payoff is (α + ) (R H + x c) ( λ (R H + x) + λ λ (R L x) c) = α (R H + x c) + λ (R λ H R L + x) W.p., X = 0, and she pays R H + R L per share. Her payoff is (α + )R H ( R H + R L) = αr H + (R H R L ). Thus, her expected gross gain from deviating to buying is: [ α (x c) + λ λ (R H R L + x) + ] (R H R L ) κ α SNB. Under the negatively-informed speculator s equilibrium strategy of selling: W.p., X =, and she is fully revealed. Her payoff is (α ) (R L + x c) + (R L + x c) = α (R L + x c). W.p., X {, 0}, and she receives R H + R L per share. Her payoff is (α )R L + ( R H + R ) L = αrl + (R H R L ). If she deviates to not selling: W.p., X =, and her payoff is α (R L x c). W.p., X {, 0}, and her payoff is αr L. 6

17 Thus, her expected gross gain from deviating to not trading is: [αx + (R H R L )] κ α NT. The SNB equilibrium holds for κ [κ α SNB, κα NT ]. The maximum value of κ that supports the BNS and SNB equilibria is the same for both equilibria (κ α NT ). The transaction cost must be suffi ciently small to deter the positively-informed speculator from deviating to not trading in BN S, and the negatively-informed speculator from deviating to not trading in SN B. Under BN S, the positively-informed speculator s motive to play her equilibrium strategy of buying is that doing so leads to correct investment. Under BN S, the negatively-informed speculator s motive to play her equilibrium strategy of selling is that doing so leads to correct disinvestment. Since the value created by correct investment equals the value created by correct disinvestment, these motives are equally strong, thus leading to the same threshold. While the maximum value of κ must be suffi ciently low not to deter the positively-informed speculator from deviating to not buying (under BN S) and the negatively-informed speculator from deviating not selling (under SNB), the minimum value of κ must be suffi ciently high to deter the negatively-informed speculator from deviating to selling (under BNS) and positivelyinformed speculator from deviating to buying (under SNB). While this minimum is is κ α T for BNS, it is κ α SNB for SNB. We have κ α SNB κ α T = { α[(x c) (x c)] + λ } λ [(R H R L + x) (R H R L x)] = λ λ 4x > 0 (4) Thus, the minimum value is strictly smaller for BNS, and so the range of κ that support BNS is a strict superset of the range that supports SNB just as in the core model where the speculator has a zero initial stake. To understand the intuition, the first term in the difference (4) is zero, since the value created by correct investment equals the value created by correct disinvestment. The second term is positive due to the feedback effect: investment increases the sensitivity of firm value to the state of nature (which becomes now R H R L + x), and disinvestment decreases the sensitivity of firm value to the state of nature (which becomes now R H R L x). Due to the 7

19 Proof of Proposition 4 This proof only provides material supplementary to Appendix B.. As discussed in the main text, it is straightforward to show that the negatively-informed speculator will not deviate to buying. Here, we calculate the profits made if the positively-informed speculator deviates to selling, to derive the necessary conditions to prevent such a deviation. No Trade Equilibrium NT. Under the positively-informed speculator s equilibrium strategy of not trading, her payoff is 0. If she deviates to selling: W.p., X =, and her (gross) payoff is (R H x c)+(r L + x c) = R L R H +x. W.p., X {, 0}, and she receives R H + R L per share. Her payoff is R H + R H + R L = (R L R H ). Thus, her overall gross gain from deviating to selling is given by: (R L R H + x) κ M NT. Thus, if and only if κ κ M NT, she will not deviate to selling. The above calculations apply both in the case of feedback and no feedback. The suffi cient condition R H R L > 4 x implies R L R H + x < 0, and hence the additional equilibrium condition is satisfied. Partial Trade Equilibrium BNS. Under the positively-informed speculator s equilibrium strategy of buying: W.p., X =, and she is fully revealed. Her payoff is 0. W.p., X {0, }, and she pays R H + R L per share. Her payoff is R H ( R H + R L) = (R H R L ). If she deviates to selling: W.p., X =, and her payoff is (R H x c) + R L + x c = R L R H + x. W.p., X =, and her payoff is (R H x c) + λ λ (R H x) + λ (R L + x) c = (R λ L R H + x) in the case of feedback and R H + λr λ H + R λ L = (R λ L R H ) in the case of no feedback. 9

20 W.p., X = 0, and her payoff is R H + R H + R L = (R L R H ). Thus, she will not deviate if 6 λ 5λ x < λ 4 λ (R H R L ) in the case of feedback and 5λ x < 6λ (R H R L ) in the case of no feedback. In the case of feedback, the condition is equivalent to R H R L > 4λ 5λ x. It is straightforward to show that 4 > 4λ 5λ, and hence the suffi cient condition R H R L > 4 x implies the additional equilibrium condition in the case of feedback. A similar argument shows that the additional equilibrium condition is also satisfied in the case of no feedback. Partial Trade Equilibrium SNB. Under the positively-informed speculator s equilibrium strategy of not trading, her payoff is 0. If she deviates to selling: W.p., X =, and her payoff is (R H x c) + R L + x c = R L R H + x. W.p., X {, 0}, and her payoff is R H + R H + R L = (R L R H ). Thus, her expected gross gain from deviating to selling is given by: [R L R H + x] κ M SNB. Thus, she will not deviate to selling if and only if κ κ M SNB. It is straightforward to verify that the condition R H R L > 4 x is suffi cient for κm SNB equilibrium conditions to be satisfied. to be negative and for the additional Trade Equilibrium T. Under the positively-informed speculator s equilibrium strategy of buying: 0

21 W.p., X =, and she is fully revealed. Her payoff is 0. W.p., X =. In the case of feedback, she pays λ (R H + x)+ λ λ (R L x) c per share, and so her payoff is R H +x c ( λ (R H + x)+ λ λ (R L x) c) = λ λ (R H R L + x). In the case of no feedback, she pays λ R H + λ λ R L per share, and so her payoff is R H ( λ R H + λ λ R L) = λ λ (R H R L ). W.p., X = 0, and she pays R H + R L per share. Her payoff is R H ( R H + R L) = (R H R L ). If she deviates to selling: W.p., X =, and her payoff is (R H x c) + R L + x c = R L R H + x. λ W.p., X =. In the case of feedback, she receives (R λ H x) + (R λ L + x) c per share, and so her payoff is (R H x c) + λ λ (R H x) + λ (R L + x) c κ = (R λ L R H + x). In the case of no feedback, she receives λr λ H + R λ L per share, and so her payoff is R H + λ λ R H + λ R L = λ (R L R H ). W.p., X = 0, and she receives R H + R L per share. Her payoff is R H + R H + R L = (R L R H ). Thus, she will not deviate if 4 λ x < (R H R L ) in the case of feedback and x < (R H R L ) in the case of no feedback. The condition R H R L > 4 x implies (R H R L ) > 4x λ and R H R L > x, and thus the additional equilibrium conditions. References Bikhchandani, Sushil (99): A Bargaining Model with Incomplete Iformation. Review of Economic Studies 59, Gul, Frank and Hugo F. Sonnenschein (988): On Delay in Bargaining with One-Sided Uncertainty. Econometrica 56, 60 6.

### 2. Information Economics

2. Information Economics In General Equilibrium Theory all agents had full information regarding any variable of interest (prices, commodities, state of nature, cost function, preferences, etc.) In many

### Financial Markets. Itay Goldstein. Wharton School, University of Pennsylvania

Financial Markets Itay Goldstein Wharton School, University of Pennsylvania 1 Trading and Price Formation This line of the literature analyzes the formation of prices in financial markets in a setting

### A Simple Model of Price Dispersion *

Federal Reserve Bank of Dallas Globalization and Monetary Policy Institute Working Paper No. 112 http://www.dallasfed.org/assets/documents/institute/wpapers/2012/0112.pdf A Simple Model of Price Dispersion

### Financial Market Microstructure Theory

The Microstructure of Financial Markets, de Jong and Rindi (2009) Financial Market Microstructure Theory Based on de Jong and Rindi, Chapters 2 5 Frank de Jong Tilburg University 1 Determinants of the

### Not Only What But also When: A Theory of Dynamic Voluntary Disclosure

Not Only What But also When: A Theory of Dynamic Voluntary Disclosure Ilan Guttman, Ilan Kremer, and Andrzej Skrzypacz Stanford Graduate School of Business September 2012 Abstract The extant theoretical

### Moral Hazard. Itay Goldstein. Wharton School, University of Pennsylvania

Moral Hazard Itay Goldstein Wharton School, University of Pennsylvania 1 Principal-Agent Problem Basic problem in corporate finance: separation of ownership and control: o The owners of the firm are typically

### Finance 400 A. Penati - G. Pennacchi Market Micro-Structure: Notes on the Kyle Model

Finance 400 A. Penati - G. Pennacchi Market Micro-Structure: Notes on the Kyle Model These notes consider the single-period model in Kyle (1985) Continuous Auctions and Insider Trading, Econometrica 15,

### Chapter 7. Sealed-bid Auctions

Chapter 7 Sealed-bid Auctions An auction is a procedure used for selling and buying items by offering them up for bid. Auctions are often used to sell objects that have a variable price (for example oil)

### Sharing Online Advertising Revenue with Consumers

Sharing Online Advertising Revenue with Consumers Yiling Chen 2,, Arpita Ghosh 1, Preston McAfee 1, and David Pennock 1 1 Yahoo! Research. Email: arpita, mcafee, pennockd@yahoo-inc.com 2 Harvard University.

### Non-Exclusive Competition in the Market for Lemons

Non-Exclusive Competition in the Market for Lemons Andrea Attar Thomas Mariotti François Salanié October 2007 Abstract In order to check the impact of the exclusivity regime on equilibrium allocations,

### Competition for Order Flow as a Coordination Game

Competition for Order Flow as a Coordination Game Jutta Dönges and Frank Heinemann Goethe Universität Frankfurt No. 64 January 25, 21 ISSN 1434-341 Authors addresses: Frank Heinemann Jutta Dönges Goethe

### Sharing Online Advertising Revenue with Consumers

Sharing Online Advertising Revenue with Consumers Yiling Chen 2,, Arpita Ghosh 1, Preston McAfee 1, and David Pennock 1 1 Yahoo! Research. Email: arpita, mcafee, pennockd@yahoo-inc.com 2 Harvard University.

### Economics of Insurance

Economics of Insurance In this last lecture, we cover most topics of Economics of Information within a single application. Through this, you will see how the differential informational assumptions allow

### Unraveling versus Unraveling: A Memo on Competitive Equilibriums and Trade in Insurance Markets

Unraveling versus Unraveling: A Memo on Competitive Equilibriums and Trade in Insurance Markets Nathaniel Hendren January, 2014 Abstract Both Akerlof (1970) and Rothschild and Stiglitz (1976) show that

### 1 Portfolio mean and variance

Copyright c 2005 by Karl Sigman Portfolio mean and variance Here we study the performance of a one-period investment X 0 > 0 (dollars) shared among several different assets. Our criterion for measuring

### Trading Frenzies and Their Impact on Real Investment

Trading Frenzies and Their Impact on Real Investment Itay Goldstein University of Pennsylvania Wharton School of Business Emre Ozdenoren London Business School and CEPR Kathy Yuan London School of Economics

### Credible Discovery, Settlement, and Negative Expected Value Suits

Credible iscovery, Settlement, and Negative Expected Value Suits Warren F. Schwartz Abraham L. Wickelgren Abstract: This paper introduces the option to conduct discovery into a model of settlement bargaining

### Persuasion by Cheap Talk - Online Appendix

Persuasion by Cheap Talk - Online Appendix By ARCHISHMAN CHAKRABORTY AND RICK HARBAUGH Online appendix to Persuasion by Cheap Talk, American Economic Review Our results in the main text concern the case

### National Responses to Transnational Terrorism: Intelligence and Counterterrorism Provision

National Responses to Transnational Terrorism: Intelligence and Counterterrorism Provision Thomas Jensen October 10, 2013 Abstract Intelligence about transnational terrorism is generally gathered by national

### Quality differentiation and entry choice between online and offline markets

Quality differentiation and entry choice between online and offline markets Yijuan Chen Australian National University Xiangting u Renmin University of China Sanxi Li Renmin University of China ANU Working

### Market Power and Efficiency in Card Payment Systems: A Comment on Rochet and Tirole

Market Power and Efficiency in Card Payment Systems: A Comment on Rochet and Tirole Luís M. B. Cabral New York University and CEPR November 2005 1 Introduction Beginning with their seminal 2002 paper,

### Options: Valuation and (No) Arbitrage

Prof. Alex Shapiro Lecture Notes 15 Options: Valuation and (No) Arbitrage I. Readings and Suggested Practice Problems II. Introduction: Objectives and Notation III. No Arbitrage Pricing Bound IV. The Binomial

### CHAPTER 11: ARBITRAGE PRICING THEORY

CHAPTER 11: ARBITRAGE PRICING THEORY 1. The revised estimate of the expected rate of return on the stock would be the old estimate plus the sum of the products of the unexpected change in each factor times

### ECON 459 Game Theory. Lecture Notes Auctions. Luca Anderlini Spring 2015

ECON 459 Game Theory Lecture Notes Auctions Luca Anderlini Spring 2015 These notes have been used before. If you can still spot any errors or have any suggestions for improvement, please let me know. 1

### Price Dispersion. Ed Hopkins Economics University of Edinburgh Edinburgh EH8 9JY, UK. November, 2006. Abstract

Price Dispersion Ed Hopkins Economics University of Edinburgh Edinburgh EH8 9JY, UK November, 2006 Abstract A brief survey of the economics of price dispersion, written for the New Palgrave Dictionary

### Online Appendix to Stochastic Imitative Game Dynamics with Committed Agents

Online Appendix to Stochastic Imitative Game Dynamics with Committed Agents William H. Sandholm January 6, 22 O.. Imitative protocols, mean dynamics, and equilibrium selection In this section, we consider

### Spot Market Power and Futures Market Trading

Spot Market Power and Futures Market Trading Alexander Muermann and Stephen H. Shore The Wharton School, University of Pennsylvania March 2005 Abstract When a spot market monopolist participates in the

### Labor Economics, 14.661. Lecture 3: Education, Selection, and Signaling

Labor Economics, 14.661. Lecture 3: Education, Selection, and Signaling Daron Acemoglu MIT November 3, 2011. Daron Acemoglu (MIT) Education, Selection, and Signaling November 3, 2011. 1 / 31 Introduction

### On the Efficiency of Competitive Stock Markets Where Traders Have Diverse Information

Finance 400 A. Penati - G. Pennacchi Notes on On the Efficiency of Competitive Stock Markets Where Traders Have Diverse Information by Sanford Grossman This model shows how the heterogeneous information

### Derivative Users Traders of derivatives can be categorized as hedgers, speculators, or arbitrageurs.

OPTIONS THEORY Introduction The Financial Manager must be knowledgeable about derivatives in order to manage the price risk inherent in financial transactions. Price risk refers to the possibility of loss

### Second degree price discrimination

Bergals School of Economics Fall 1997/8 Tel Aviv University Second degree price discrimination Yossi Spiegel 1. Introduction Second degree price discrimination refers to cases where a firm does not have

### Nonparametric adaptive age replacement with a one-cycle criterion

Nonparametric adaptive age replacement with a one-cycle criterion P. Coolen-Schrijner, F.P.A. Coolen Department of Mathematical Sciences University of Durham, Durham, DH1 3LE, UK e-mail: Pauline.Schrijner@durham.ac.uk

### 1 Introduction to Option Pricing

ESTM 60202: Financial Mathematics Alex Himonas 03 Lecture Notes 1 October 7, 2009 1 Introduction to Option Pricing We begin by defining the needed finance terms. Stock is a certificate of ownership of

### At t = 0, a generic intermediary j solves the optimization problem:

Internet Appendix for A Model of hadow Banking * At t = 0, a generic intermediary j solves the optimization problem: max ( D, I H, I L, H, L, TH, TL ) [R (I H + T H H ) + p H ( H T H )] + [E ω (π ω ) A

### Schooling, Political Participation, and the Economy. (Online Supplementary Appendix: Not for Publication)

Schooling, Political Participation, and the Economy Online Supplementary Appendix: Not for Publication) Filipe R. Campante Davin Chor July 200 Abstract In this online appendix, we present the proofs for

α α λ α = = λ λ α ψ = = α α α λ λ ψ α = + β = > θ θ β > β β θ θ θ β θ β γ θ β = γ θ > β > γ θ β γ = θ β = θ β = θ β = β θ = β β θ = = = β β θ = + α α α α α = = λ λ λ λ λ λ λ = λ λ α α α α λ ψ + α =

### 9 Basics of options, including trading strategies

ECG590I Asset Pricing. Lecture 9: Basics of options, including trading strategies 1 9 Basics of options, including trading strategies Option: The option of buying (call) or selling (put) an asset. European

### Problem Set 9 Solutions

Problem Set 9 s 1. A monopoly insurance company provides accident insurance to two types of customers: low risk customers, for whom the probability of an accident is 0.25, and high risk customers, for

### ON PRICE CAPS UNDER UNCERTAINTY

ON PRICE CAPS UNDER UNCERTAINTY ROBERT EARLE CHARLES RIVER ASSOCIATES KARL SCHMEDDERS KSM-MEDS, NORTHWESTERN UNIVERSITY TYMON TATUR DEPT. OF ECONOMICS, PRINCETON UNIVERSITY APRIL 2004 Abstract. This paper

### Perfect Bayesian Equilibrium

Perfect Bayesian Equilibrium When players move sequentially and have private information, some of the Bayesian Nash equilibria may involve strategies that are not sequentially rational. The problem is

### A Theory of Intraday Patterns: Volume and Price Variability

A Theory of Intraday Patterns: Volume and Price Variability Anat R. Admati Paul Pfleiderer Stanford University This article develops a theory in which concentrated-trading patterns arise endogenously as

Chapter 3 Adverse Selection Adverse selection, sometimes known as The Winner s Curse or Buyer s Remorse, is based on the observation that it can be bad news when an o er is accepted. Suppose that a buyer

### Decentralised bilateral trading, competition for bargaining partners and the law of one price

ECONOMICS WORKING PAPERS Decentralised bilateral trading, competition for bargaining partners and the law of one price Kalyan Chatterjee Kaustav Das Paper Number 105 October 2014 2014 by Kalyan Chatterjee

### Options. Moty Katzman. September 19, 2014

Options Moty Katzman September 19, 2014 What are options? Options are contracts conferring certain rights regarding the buying or selling of assets. A European call option gives the owner the right to

### Should Ad Networks Bother Fighting Click Fraud? (Yes, They Should.)

Should Ad Networks Bother Fighting Click Fraud? (Yes, They Should.) Bobji Mungamuru Stanford University bobji@i.stanford.edu Stephen Weis Google sweis@google.com Hector Garcia-Molina Stanford University

### Entry Cost, Tobin Tax, and Noise Trading in the Foreign Exchange Market

Entry Cost, Tobin Tax, and Noise Trading in the Foreign Exchange Market Kang Shi The Chinese University of Hong Kong Juanyi Xu Hong Kong University of Science and Technology Simon Fraser University November

### On Market-Making and Delta-Hedging

On Market-Making and Delta-Hedging 1 Market Makers 2 Market-Making and Bond-Pricing On Market-Making and Delta-Hedging 1 Market Makers 2 Market-Making and Bond-Pricing What to market makers do? Provide

### Strategic futures trading in oligopoly

Strategic futures trading in oligopoly Jhinyoung SHIN Department of Business Administration, Yonsei University, Seoul, Korea Kit Pong WONG School of Economics and Finance, University of Hong Kong Pokfulam

### ECON20310 LECTURE SYNOPSIS REAL BUSINESS CYCLE

ECON20310 LECTURE SYNOPSIS REAL BUSINESS CYCLE YUAN TIAN This synopsis is designed merely for keep a record of the materials covered in lectures. Please refer to your own lecture notes for all proofs.

### Regulation and Bankers Incentives

Regulation and Bankers Incentives Fabiana Gómez University of Bristol Jorge Ponce Banco Central del Uruguay May 7, 2015 Preliminary and incomplete Abstract We formally analyze and compare the effects of

### Work incentives and household insurance: Sequential contracting with altruistic individuals and moral hazard

Work incentives and household insurance: Sequential contracting with altruistic individuals and moral hazard Cécile Aubert Abstract Two agents sequentially contracts with different principals under moral

### Motivated by the mixed evidence concerning the adoption level and value of collaborative forecasting (CF)

Published online ahead of print October 14, 2011 Articles in Advance, pp. 1 17 issn 1523-4614 eissn 1526-5498 MANUFACTUING & SEVICE OPEATIONS MANAGEMENT http://dx.doi.org/10.1287/msom.1110.0351 2011 INFOMS

### Reputation in repeated settlement bargaining

Reputation in repeated settlement bargaining Jihong Lee Birkbeck College, London and Yonsei University Qingmin Liu Cowles Foundation and University of Pennsylvania PRELIMINARY and INCOMPLETE commets welcome!

### Online Appendix for. Poultry in Motion: A Study of International Trade Finance Practices

Online Appendix for Poultry in Motion: A Study of International Trade Finance Practices P A C. F F May 30, 2014 This Online Appendix documents some theoretical extensions discussed in Poultry in Motion:

### Capital Structure. Itay Goldstein. Wharton School, University of Pennsylvania

Capital Structure Itay Goldstein Wharton School, University of Pennsylvania 1 Debt and Equity There are two main types of financing: debt and equity. Consider a two-period world with dates 0 and 1. At

### TOPIC 6: CAPITAL STRUCTURE AND THE MARKET FOR CORPORATE CONTROL

TOPIC 6: CAPITAL STRUCTURE AND THE MARKET FOR CORPORATE CONTROL 1. Introduction 2. The free rider problem In a classical paper, Grossman and Hart (Bell J., 1980), show that there is a fundamental problem

### Early-Stage Financing and Firm Growth in New Industries

ROMAN INDERST HOLGER MÜLLER Early-Stage Financing and Firm Growth in New Industries Institute for Monetary and Financial Stability JOHANN WOLFGANG GOETHE-UNIVERSITÄT FRANKFURT AM MAIN WORKING PAPER SERIES

### February 2013. Abstract

Marking to Market and Ine cient Investments Clemens A. Otto and Paolo F. Volpin February 03 Abstract We examine how mark-to-market accounting a ects investment decisions in an agency model with reputation

### Analyst Forecasts : The Roles of Reputational Ranking and Trading Commissions

Analyst Forecasts : The Roles of Reputational Ranking and Trading Commissions Sanjay Banerjee January 31, 2011 Abstract This paper examines how reputational ranking and trading commission incentives influence

### Using clients rejection to build trust

Using clients rejection to build trust Yuk-fai Fong Department of Economics HKUST Ting Liu Department of Economics SUNY at Stony Brook University March, 2015 Preliminary draft. Please do not circulate.

### Session IX: Lecturer: Dr. Jose Olmo. Module: Economics of Financial Markets. MSc. Financial Economics

Session IX: Stock Options: Properties, Mechanics and Valuation Lecturer: Dr. Jose Olmo Module: Economics of Financial Markets MSc. Financial Economics Department of Economics, City University, London Stock

### How to Sell a (Bankrupt) Company

How to Sell a (Bankrupt) Company Francesca Cornelli (London Business School and CEPR) Leonardo Felli (London School of Economics) March 2000 Abstract. The restructuring of a bankrupt company often entails

### An information-based trade off between foreign direct investment and foreign portfolio investment

Journal of International Economics 70 (2006) 271 295 www.elsevier.com/locate/econbase An information-based trade off between foreign direct investment and foreign portfolio investment Itay Goldstein a,,

Brunel University Msc., EC5504, Financial Engineering Prof Menelaos Karanasos Lecture Notes: Volatility Trading Strategies 1 Volatility Trading Strategies As previously explained, volatility is essentially

### Imperfect information Up to now, consider only firms and consumers who are perfectly informed about market conditions: 1. prices, range of products

Imperfect information Up to now, consider only firms and consumers who are perfectly informed about market conditions: 1. prices, range of products available 2. characteristics or relative qualities of

### On Prevention and Control of an Uncertain Biological Invasion H

On Prevention and Control of an Uncertain Biological Invasion H by Lars J. Olson Dept. of Agricultural and Resource Economics University of Maryland, College Park, MD 20742, USA and Santanu Roy Department

### Do Institutional Investors Improve Capital Allocation?

Do Institutional Investors Improve Capital Allocation? Giorgia Piacentino Washington University in St Louis Abstract Whereas the existing literature shows that portfolio managers career concerns generate

### Do Institutional Investors Improve Capital Allocation?

Do Institutional Investors Improve Capital Allocation? Giorgia Piacentino LSE November 2012 Abstract I explore delegated portfolio managers influence on firms funding, economic welfare and shareholders

### Choice under Uncertainty

Choice under Uncertainty Part 1: Expected Utility Function, Attitudes towards Risk, Demand for Insurance Slide 1 Choice under Uncertainty We ll analyze the underlying assumptions of expected utility theory

### Institute for Empirical Research in Economics University of Zurich. Working Paper Series ISSN 1424-0459. Working Paper No. 229

Institute for Empirical Research in Economics University of Zurich Working Paper Series ISSN 1424-0459 Working Paper No. 229 On the Notion of the First Best in Standard Hidden Action Problems Christian

### Overlapping ETF: Pair trading between two gold stocks

MPRA Munich Personal RePEc Archive Overlapping ETF: Pair trading between two gold stocks Peter N Bell and Brian Lui and Alex Brekke University of Victoria 1. April 2012 Online at http://mpra.ub.uni-muenchen.de/39534/

### Platform Competition under Asymmetric Information

Platform Competition under Asymmetric Information Hanna Hałaburda Yaron Yehezkel Working Paper 11-080 Copyright 2011 by Hanna Hałaburda and Yaron Yehezkel Working papers are in draft form. This working

### Notes V General Equilibrium: Positive Theory. 1 Walrasian Equilibrium and Excess Demand

Notes V General Equilibrium: Positive Theory In this lecture we go on considering a general equilibrium model of a private ownership economy. In contrast to the Notes IV, we focus on positive issues such

### An Empirical Analysis of Insider Rates vs. Outsider Rates in Bank Lending

An Empirical Analysis of Insider Rates vs. Outsider Rates in Bank Lending Lamont Black* Indiana University Federal Reserve Board of Governors November 2006 ABSTRACT: This paper analyzes empirically the

### CHAPTER 22: FUTURES MARKETS

CHAPTER 22: FUTURES MARKETS PROBLEM SETS 1. There is little hedging or speculative demand for cement futures, since cement prices are fairly stable and predictable. The trading activity necessary to support

### CPC/CPA Hybrid Bidding in a Second Price Auction

CPC/CPA Hybrid Bidding in a Second Price Auction Benjamin Edelman Hoan Soo Lee Working Paper 09-074 Copyright 2008 by Benjamin Edelman and Hoan Soo Lee Working papers are in draft form. This working paper

### Buyer Search Costs and Endogenous Product Design

Buyer Search Costs and Endogenous Product Design Dmitri Kuksov kuksov@haas.berkeley.edu University of California, Berkeley August, 2002 Abstract In many cases, buyers must incur search costs to find the

### EXP 481 -- Capital Markets Option Pricing. Options: Definitions. Arbitrage Restrictions on Call Prices. Arbitrage Restrictions on Call Prices 1) C > 0

EXP 481 -- Capital Markets Option Pricing imple arbitrage relations Payoffs to call options Black-choles model Put-Call Parity Implied Volatility Options: Definitions A call option gives the buyer the

### Lecture 6: Arbitrage Pricing Theory

Lecture 6: Arbitrage Pricing Theory Investments FIN460-Papanikolaou APT 1/ 48 Overview 1. Introduction 2. Multi-Factor Models 3. The Arbitrage Pricing Theory FIN460-Papanikolaou APT 2/ 48 Introduction

### The Black-Scholes Formula

FIN-40008 FINANCIAL INSTRUMENTS SPRING 2008 The Black-Scholes Formula These notes examine the Black-Scholes formula for European options. The Black-Scholes formula are complex as they are based on the

### Customer Service Quality and Incomplete Information in Mobile Telecommunications: A Game Theoretical Approach to Consumer Protection.

Customer Service Quality and Incomplete Information in Mobile Telecommunications: A Game Theoretical Approach to Consumer Protection.* Rafael López Zorzano, Universidad Complutense, Spain. Teodosio Pérez-Amaral,

### The Effect of Third-Party Funding of Plaintiffs on Settlement. Andrew F. Daughety and Jennifer F. Reinganum. Online Appendix

1 The Effect of Third-Party Funding of Plaintiffs on Settlement Andrew F. Daughety and Jennifer F. Reinganum Online Appendix See the main paper for a description of the notation, payoffs, and game form

### On the Existence of Nash Equilibrium in General Imperfectly Competitive Insurance Markets with Asymmetric Information

analysing existence in general insurance environments that go beyond the canonical insurance paradigm. More recently, theoretical and empirical work has attempted to identify selection in insurance markets

### MARKET STRUCTURE AND INSIDER TRADING. Keywords: Insider Trading, Stock prices, Correlated signals, Kyle model

MARKET STRUCTURE AND INSIDER TRADING WASSIM DAHER AND LEONARD J. MIRMAN Abstract. In this paper we examine the real and financial effects of two insiders trading in a static Jain Mirman model (Henceforth

### THE FUNDAMENTAL THEOREM OF ARBITRAGE PRICING

THE FUNDAMENTAL THEOREM OF ARBITRAGE PRICING 1. Introduction The Black-Scholes theory, which is the main subject of this course and its sequel, is based on the Efficient Market Hypothesis, that arbitrages

### Figure S9.1 Profit from long position in Problem 9.9

Problem 9.9 Suppose that a European call option to buy a share for \$100.00 costs \$5.00 and is held until maturity. Under what circumstances will the holder of the option make a profit? Under what circumstances

### The Disposition of Failed Bank Assets: Put Guarantees or Loss-Sharing Arrangements?

The Disposition of Failed Bank Assets: Put Guarantees or Loss-Sharing Arrangements? Mark M. Spiegel September 24, 2001 Abstract To mitigate the regulatory losses associated with bank failures, efforts

### Working Paper Does retailer power lead to exclusion?

econstor www.econstor.eu Der Open-Access-Publikationsserver der ZBW Leibniz-Informationszentrum Wirtschaft The Open Access Publication Server of the ZBW Leibniz Information Centre for Economics Rey, Patrick;

### A Battle of Informed Traders and the Market Game Foundations for Rational Expectations Equilibrium

A Battle of Informed Traders and the Market Game Foundations for Rational Expectations Equilibrium James Peck The Ohio State University Abstract Potential manipulation of prices and convergence to rational

### 1.1 Some General Relations (for the no dividend case)

1 American Options Most traded stock options and futures options are of American-type while most index options are of European-type. The central issue is when to exercise? From the holder point of view,

### Bayesian Nash Equilibrium

. Bayesian Nash Equilibrium . In the final two weeks: Goals Understand what a game of incomplete information (Bayesian game) is Understand how to model static Bayesian games Be able to apply Bayes Nash

### Put-Call Parity and Synthetics

Courtesy of Market Taker Mentoring LLC TM Excerpt from Trading Option Greeks, by Dan Passarelli Chapter 6 Put-Call Parity and Synthetics In order to understand more-complex spread strategies involving

### A New Interpretation of Information Rate

A New Interpretation of Information Rate reproduced with permission of AT&T By J. L. Kelly, jr. (Manuscript received March 2, 956) If the input symbols to a communication channel represent the outcomes

### Lecture 3: Growth with Overlapping Generations (Acemoglu 2009, Chapter 9, adapted from Zilibotti)

Lecture 3: Growth with Overlapping Generations (Acemoglu 2009, Chapter 9, adapted from Zilibotti) Kjetil Storesletten September 10, 2013 Kjetil Storesletten () Lecture 3 September 10, 2013 1 / 44 Growth

### Explaining Insurance Policy Provisions via Adverse Selection

The Geneva Papers on Risk and Insurance Theory, 22: 121 134 (1997) c 1997 The Geneva Association Explaining Insurance Policy Provisions via Adverse Selection VIRGINIA R. YOUNG AND MARK J. BROWNE School

### Working Paper Series

RGEA Universidade de Vigo http://webs.uvigo.es/rgea Working Paper Series A Market Game Approach to Differential Information Economies Guadalupe Fugarolas, Carlos Hervés-Beloso, Emma Moreno- García and

### Example 1. Consider the following two portfolios: 2. Buy one c(s(t), 20, τ, r) and sell one c(s(t), 10, τ, r).

Chapter 4 Put-Call Parity 1 Bull and Bear Financial analysts use words such as bull and bear to describe the trend in stock markets. Generally speaking, a bull market is characterized by rising prices.