Part III: Derivative Securities

Transcription

1 Investments Analysis Last Lecture and This: Bond portfolio Risk: measurement Bond portfolio Risk: immunization vs. swaps Next 2 lectures (#8 & 9): Part III Derivatives Part III: Derivative Securities Options (Forwards &) Futures Outline Options Futures market microstructure some principles of option pricing futures vs. forwards market microstructure Definition The Nature of Derivatives A derivative security or derivative is a financial instrument whose value depends on the values of other more basic underlying variables Examples Options Forward & Futures Swaps right The Nature of Derivatives 2 obligation forward Customized Standardized OTC option exchangetraded option futures Ways Derivatives are Used To invest or speculate To hedge risks To infer views about the future direction of the market To lock in arbitrage profits To change the nature of a liability of an investment

2 Ways Derivatives are Used 2 Types of Traders Hedgers» want to reduce risk of existing assets or liabilities Speculators» willing to take risk based on their forecasts» try to exploit price movements Arbitrageurs» use risk-free trading strategies» to exploit asset mis-pricings Terminology Number of parties 2 (buyer & seller) + intermediaries (sometimes) The party that has agreed to: BUY has what is termed a LONG position SELL has what is termed a SHORT position Options Definitions Definitions basic idea, call vs. put, European vs. American, etc. Payoffs at maturity naked European positions trading strategies Market microstructure OTC vs. exchange-traded options A call is an option to BUY a certain asset by a certain date for a certain price that is fixed today A put is an option to SELL a certain asset by a certain date for a certain price that is fixed today Option Terminology Option Terminology & Notation 2 Call vs. Put right to buy vs. right to sell (bullish view vs. bearish view) Buying vs. Writing (= selling) American vs. European strike by a given date vs. strike at a given date Option premium vs. Exercise price price of the option vs. price at which buyer strikes : Strike price = exercise price c : European call option price p : European put option price C : American call option price P : American put option price t : Current time T : Maturity = time when option expires S t : Stock price at time t σ: Volatility of the underlying s price D : PV of Dividends r : Risk-free rate

3 Option Terminology 3 Moneyness (Investor s possible situations) in-the money» calls: S t >»put: S t < at-the money» S t = out-of-the-money» calls: S t <»put: S t > Option Payoffs at Maturity Naked European positions (BKM 4, Figs to 20.8) buyer» calls: Max[0, -]-c» put: Max[0, - ] - p writer» calls: Min[0, - ] + c» put: Min[0, -] + p Time value of money? Option Payoffs at Maturity 2 Profit from Long naked Call on IBM (buy an IBM European call option; price = $5, strike = $100) Option Payoffs at Maturity 3 Profit from Short naked Call on IBM (write an IBM European call option; price = $5, strike = $100) Profit ($) Terminal stock price ($) Profit ($) Terminal stock price ($) Option Payoffs at Maturity 4 Profit from Long naked Put on Enron (buy an Enron European put option; price = $7, strike = $70) Option Payoffs at Maturity 5 Profit from Short naked Put on Enron (write an Enron European put option; price = $7, strike = $70) Profit ($) Terminal stock price ($) Profit ($) Terminal stock price ($)

4 Summary: Option Payoffs at Maturity 6 Payoff Payoff = Strike price = Price of asset at maturity Payoff Payoff Option Payoffs at Maturity 7 Covered positions protective put (BKM 4 Fig & Table 20.1) what?» buy stock + buy put why?» portfolio insurance» comparative payoffs (BKM 4 Fig ) protective put vs. stop-loss order» right to sell vs. obligation to sell» execution price guarantee vs. who knows? Option Payoffs at Maturity 8 Covered positions covered call (BKM 4 Fig & Table 20.2) what?» buy stock + write call» cover + naked sale why? central banks (gold reserves) mutual funds & other investors» enforces discipline» while boosting cash Option Payoffs at Maturity 9 Option+Underlying Profit Profit (a: covered call) (c: protect. put) Profit Profit (b) (d) Option Market Microstructure Exchange trading vs. OTC standardized vs. customized tailoring vs. market liquidity and depth risk control» my word is my bond vs. clearing house Our focus exchange-traded options (why?) major exchanges US: Philly, Chicago, American, Pacific (what about Nasdaq?) other countries (ex.: Canada: Toronto, Montreal, Vancouver) Market Microstructure 2 Maturity dates 3 rd Friday of the month» exception: EOM 3-month cycles (Jan., Feb. or March) & 2 near-months» exception: LEAPS (LT equity appreciation securities) Reading stock option quotes (Fig & Fig. 20.1) quotes are for American options» exceptions (F, stock index) option price (per share) vs. option contract (round lot) strike price intervals»$10 vs. $5 (30<S<100) vs. $2.50 (S<$30)

5 Market Microstructure 3 Types of options (traded on exchanges) stock options index options (Fig 20.2) most traded: S&P 100» what about dividends? cash settlement» $100 x (value of index - strike value of index) currency (F) options futures options interest rate options» Treasuries, CD s, agency issues, etc. Risk Control through Clearing House What? Why? US: Options Clearing Corporation (OCC)» owned jointly by all US options exchanges Canada: TransCanada Options Inc. (TCO)» owned by Montreal, Toronto & Vancouver exchanges market liquidity vs. knowing counterparts margin posts and calls vs. word is bond Risk Control through Clearing Houses 2 How? effective buyer and seller of all options» counter-party to all trades» guarantees execution» open interest in practice» reversing trades» how do option strikes get carried out? risk for the clearing house» writers default Risk Control through Clearing Houses 3 How? (continued) risk control» margins and margin calls» for writers (why not for buyers?) margin determinants» volatility of underlying asset» extent of in-the-moneyness» naked or covered position American Options: Early Exercise? Calls Puts often not optimal» never optimal for non-dividend paying stocks» ditto for options on income-generating assets importance of capturing dividends can be optimal to exercise early impact of dividend payments»dividends probability of early exercise Option Pricing Principles Fundamentals time value vs. intrinsic value key determinants of option values American vs. European options Put-call parity non-dividend paying stocks dividend adjustment Option pricing Black-Scholes formula

6 Option Pricing: Fundamentals intrinsic value vs. time value intrinsic value» calls: Max[0, S t -]» put: Max[0, -S t ] time value = option premium - intrinsic value» at worst, equal to 0 (intuition: rights; Fig. 21.1)» strictly positive for out-of the money options» usually positive for in-the-money options Option Pricing: The Big Picture Key determinants of option prices American options vs. European options» at least as valuable» equal values at maturity time to maturity» American options: T P and C» European options? strike price» p&p but c&c Option Pricing: The Big Picture 2 Key determinants of option prices (continued) price of underlying asset» S t p but c volatility of underlying asset» σ p and c» intuition hard floors vs. soft floors Bounds on Option Prices: Calls Calls never worth more than underlying asset» upper bound: S t c hard floor (American calls: can be exercised early)»c Max[0, S t -]» if not satisfied, arbitrage exists soft floor (NOT exam material)»s t c Max[0, S t -/(1+r) T ]» consequence: early exercise not optimal Bounds on Option Prices: Calls 2 Bounds on Option Prices: Calls 3 Soft & Hard Floors: example Question: Suppose an American call option is written on Nortel stock. The exercise price is $105 ( ) and the present value of the exercise price is $100. (a) What is the hard floor price of the option if Nortel stock sells for $160? Sketch a graph of the hard floor option prices against (i.e., in terms of) the Nortel stock s price. (b) At a stock price of $125, you notice the option selling for $18. Would this option price be an equilibrium price? Explain. Soft & Hard Floors: example (continued) Answer: (a) Hard floor price = VS = $160 - $105 = $55. (b)an option price of $18 is below the hard floor price of $20. In this case, everyone would want the call option. You could then acquire a share of Nortel stock for less than the current market price. Simply buy the option (for $18), exercise it (paying $105), and you would then own a share of Nortel for a total price of $123.

7 Bounds on Option Prices: Puts Puts hard floor (American puts)»max[0, -S t ]» if not satisfied, arbitrage exists soft floor? (NOT exam material) Option Pricing in Practice Black-Scholes gives price of European call r( T t) r( T t) c = e [ S N( d )e N( d )] ln( S / ) + ( r+ σ /2)( T t) where d = 1 σ T t 2 ln( S / ) + ( r σ /2)( T t) d = = d σ T t 2 σ T t 1 interpretation? Option Pricing in Practice 2 Option Pricing in Practice 3 r( T t) r( T t) c = e [ S N( d1)e N( d2)] N(z) = Prob(Z<z)» Z is standard normal N(d 2 )» = probability of exercise. N(d 2 )» = expected pay-out at exercise SN(d 1 )exp(r(t-t))» = expected value of the stock price, if exercised. Black-Scholes (continued) gives price of European call price of European put?» use put-call parity Profit» intuition: American options?» optimality of early exercise Option Pricing in Practice 4 Binomial option pricing (NOT exam material) problem» assumptions needed for B&S are not always realistic» example: deterministic interest rates solution: numerical approximations» grid» risk-neutral probabilities accuracy» as accurate as needed/desired Option-like Securities Callable bonds Fig time value of option» smooth curve Convertible securities Fig default likelihood» curvature

8 Warrants Option-like Securities 2 main difference» issuer settles up with holder when warrant is exercised» change in number of underlying shares trading» traded in the same way as stocks call warrants» issued by a corporation on its own stock» exercise leads to issue of new treasury stock monopolistic exercise strategies» supplementary packet: Spatt and Sterbenz (JF 89) Forwards and Futures Forward contracts definition participants, major contracts, risks Futures contracts participants, major contracts, exchanges differences with forwards (contracts & prices) links between spot and futures prices forward as predictor of future spot prices spot-futures parity theorem Forwards Definition contract calling for delivery of a given asset at a given future date, at a price agreed-upon today no money changes hands today (caveat) Market microstructure OTC market Market participants hedgers-traders-arbitrageurs speculators Forwards 2 Market participants traders-arbitrageurs hedgers» try to avoid impact of price movements» short hedgers: have long position, go short» long hedgers: have short position, go long speculators» try to profit from price movements Futures Fundamentals participants, major contracts, exchanges Differences w/ forward contracts (main ones) exchange-traded (not OTC) standardized marking-to-market / risk control Differences b/ forward & futures prices in theory in practice / arbitrage NOTE The following pages are NOT exam material They are provided only for completeness I will be happy to discuss them during office hours with all students interested

9 Futures 2 Definition basic principle: similar to forward in practice: side bets (long position vs. short position) Differences w/ forward contracts (main ones) exchange-traded regulated by: US: CFTC Canada: markets vs. trading» provincial securities commissions vs. self» exception: WCE (federal regulation) Futures 3 Differences w/ forward contracts (main ones) exchange-traded (continued) terminology» open interest»ticks» spot month (when the contract expires)» reversing a trade participants in the pits» brokers (cust.) vs. traders (own) vs. broker-traders Futures 4 Futures 5 Differences w/ forward contracts (main ones) exchange-traded (continued) implications» clearing house» marking to market» margin requirements (T-bills)» standardized contracts (sizes, settlement dates, etc.) Differences w/ forward contracts (cont d) standard contracts maturity dates» currencies and indices: M-J-S-D» mostly 3 rd Friday of the month» exceptions exist (ex.: KC Value Line: EOM) reading futures quotes (Fig. 21.1) example: F futures consequences» difficulty to hedge, but easier for speculation Futures 6 Differences w/ forward contracts (cont d) margins & marking-to-market what?» daily settlement of gains and losses» resetting of all positions why?» risk control how?» numerical example consequence: futures price vs. forward price Futures 7 Forward price delivery price price at which the underlying asset will be delivered agreed upon at time forward is entered into forward price delivery price that would make the contract have 0 value changes during life of contract (but, who cares) forward price = delivery price when contract is created

10 Futures 8 Futures price delivery price price at which the underlying asset will be delivered agreed upon at time futures is bought futures price delivery price that would make the contract have 0 value changes during life of contract (and, it matters) futures price = delivery price when contract is bought Futures 9 Futures price (cont d) marking to market replacement of the futures contract at the end of trading every day by a new contract with new delivery price» delivery date unchanged» new delivery price = futures price at close Futures 10 time futures price (a) margin requirement cash-flow $/SF $2,150 (b) - $2,150 (c) (morning) $/SF (d) + $ 625 (d) (close) $/SF (e) - $ 375 (f) (close) $/SF - $ 1,500 (g) (close) + $ 2,150 (h) SF 125,000 (i) - $ 92,500 (i) +SF 125,000 (i) - $ 93,750 (i) Futures 11 Differences b/ forward & futures prices in theory deterministic interest rates stochastic interest rates interest rate vs. futures price (or price of underlying asset)» positive correlation: futures price > forward price» negative correlation: futures price < forward price in practice / arbitrage Futures 12 Some specific items Cash or actual delivery? example: S&P 500» short position: gives $500 x value of index at maturity» long position: gives $500 x delivery price Basis risk basis = futures price - spot price convergence property» futures price = spot price at maturity (why?) Links between Futures & Spot Prices Futures-Spot Parity idea» (1) borrow today» (2) buy an asset» (3) short a futures on the asset» the position should have zero risk and zero cost» hence the rate of return should be zero

11 Links between Futures & Spot Prices 2 t T (1) borrow S 0 -S 0 (1+r) (2) buy asset -S 0 D= S 0 d + asset + asset (3) short forward + F 0 -asset total 0 -S 0 (1+r) + S 0 d+ F 0 hence: 0 = - S 0 (1+r) + S 0 d+ F 0 and thus F 0 = S 0 (1 + r - d) Links between Futures & Spot Prices 3 Generalization multiperiod: F 0 = S 0 (1 + r - d) T commodities: F 0 = S 0 (1 + r + c) T» carrying costs vs. convenience yield» seasonal variations (e.g., harvests) Dividends problem» varies over time (May vs. other periods) solution» theory (no-arbitrage bands) vs. practice (triple witching) Links between Futures & Spot Prices 4 Cost-of-Carry relationship other name for Futures-Spot Parity idea» buy forward vs. buy spot and carry»f 0 vs. S 0 (1 + r - d) Interest rate parity theorem = Futures-Spot Parity for currencies Links between Futures & Spot Prices 5 Futures and expected future spot convergence property (maturity only) expectation hypothesis» no uncertainty» risk neutrality normal backwardation» futures price < expected future spot» idea: natural hedgers = producers contango» futures price > expected future spot Index Futures Idea cash-settled futures contract reduces transactions costs Types US: S&P 500, Kansas City Value Line, NYSE, Canada: TSE 35 Popularity allows construction of cheap synthetic stock positions Index Futures 2 Synthetic stock positions sentiment» bullish: hold long futures position, buy T-bills» bearish: opposite practical numerical example S&P 500 is 1500 for spot and 1515 for 3-month hence 3-month interest rate = 1% investor can» either buy shares of all S&P 500 shares» or go long futures and buy T-bills to cover settlement

12 Index Futures 3 Synthetic stock positions example (continued) S&P 500 is 1500 for spot and 1515 for 3-month hence 3-month interest rate = 1% investor wants to invest $150m in US market for 3 months» go long 200 contracts: 200 x 500$ (multiplier) * 1500 buy T-bills to cover payment of futures price» 200 x 500 x 1515 / (1+1%) = $150m at maturity: net = 200 x 500 x» 200 x 500 x ( -F 0 ) = 100,000 - $151.5m» $500m(1.01) = $ 151.5m Index Arbitrage Index Futures 4 idea: exploit deviations from parity triple witching hour 4 Fridays per year» S&P index futures + index option + some stock options»all expire volatility» supposedly increases (program trading)» fundamentals vs. market depth» price levels vs. arbitraging price differences