OPTIONS AND FUTURES. Options Markets Options Valuation Futures and Hedging

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1 OPTIONS AND FUTURES Options Markets Options Valuation Futures and Hedging

2 OPTIONS BASICS 1 option contract = 100 shares of stock Long call the right (but not the obligation) to purchase 100 shares of stock at the exercise price (bullish, cash outflow) Short call the obligation to sell 100 shares of stock at the exercise price (bearish, cash inflow) Long put the right (but not the obligation) to sell 100 shares of stock at the strike price (bearish, cash outflow) Short put the obligation to buy 100 shares of stock at the exercise price (bullish, cash inflow) Expiration date, exercise (strike) price, premium, American vs. European, in (out, at) the money, covered, naked Can exercise, let expire, or reverse the position to close

3 OPTIONS QUOTES

4 USES OF OPTIONS Hedge positions against unwelcome changes in stock prices Change your risk and return profile For example, buying a call is analogous to buying stock on margin You can use options to reap greater rewards (or suffer large losses) because of the built-in leverage vs. a cash stock position Avoid short sale constraints Buy puts

5 WHY? - OPTIONS EXAMPLE Suppose a 6-month maturity call option with exercise price of $90 sells for $10 and the underlying equity is currently trading for $90. Consider the following three portfolio strategies for investing $9,000: A: Invest all in stock. B: Invest all in at-the-money call options. C: Purchase 100 call options and invest the remaining in T-Bills paying 2% What are the potential payoffs of these three strategies 6-months from now when the options expire?

6 WHY? OPTIONS EXAMPLE (CONT.) Stock Price Portfolio $80 $85 $90 $95 $100 $105 $110 A: 100 shares of stock $8,000 $8,500 $9,000 $9,500 $10,000 $10,500 $11,000 B: 900 call options $0 $0 $0 $4,500 $9,000 $13,500 $18,000 C: 100 calls plus $8,000 in T-bills $8,160 $8,160 $8,160 $8,660 $9,160 $9,660 $10, % 100.0% 50.0% 0.0% $80 $85 $90 $95 $100 $105 $ % % Stock Only Options Only Options and T-Bills

7 OPTION MARKETS & THE OCC Highly competitive markets Options Clearing Corporation (OCC) is owned by options exchanges OCC backs the performance of counterparties To limit risk to the OCC writers must post margin Margin requirements differ with option prices and whether the position is naked or covered (net positions considered) When an option contract is exercised the OCC selects a counterparty at random to make good on the contract A call writer must deliver (sell) 100 shares if exercised against A put writer must buy 100 shares if exercised against

8 CALL PROFIT AT EXPIRATION Profit $0 -$735 -C 0 $92.65 Bullish or bearish? Ex = $100 High or low volatility strategy? $100 $ Stock Price T IBM Jul 100 call option Stock Price = $96.14 Exercise = $100 Call premium = $735 Contract Size 100 shares

9 WRITING A NAKED CALL Profit $0 X Stock Price T Bullish or bearish? High or low volatility strategy?

10 BUYING A PUT OPTION Profit $8,834 Short position in IBM IBM Dec 100 put option Stock price = $96.14 Exercise = $100 Put premium = $1,166 Contract Size 100 shares $0 $88.34 $100 $ Stock Price t -$1,166 Ex = $100 Put Bullish or bearish? Alternative Stock Strategy? High or low volatility strategy?

11 WRITING A PUT OPTION Profit $1,166 $0 - $8,834 $88.34 Long Position in IBM Bullish or bearish? Stock Price t IBM Jul 100 put option Stock price = $96.14 Exercise = $100 Put premium = $1,166 Contract Size 100 shares Alternative Stock Strategy? $100 $ Xx = $100 High or low volatility strategy?

12 PROTECTIVE PUT LONG STOCK, LONG PUT Profit Long position in IBM Hedged Position $0 X Stock Price t Put Hedged profit equals sum of profits of put and stock at each stock price.

13 COVERED CALLS LONG STOCK, SHORT CALL Profit Long position in IBM Written call Covered Call $0 S 0 Stock Price t Bullish or bearish? High or low volatility strategy?

14 COMBO EXAMPLE: BULL STRADDLE BULL STRADDLE Profit Profit Table S T < X S T > X C 0 C 0 C 0 P 0 P 0 P 0 +C T 0 S T X +P T X S T 0 = Profit Breakeven X S T C 0 P 0 S T = X C 0 P 0 S T X C 0 P 0 S T = X + C 0 + P 0 $0 X C 0 P 0 X + C 0 + P 0 X Stock Price t Bullish or bearish? Neutral Max Loss: C 0 + P 0 High or low volatility strategy?

15 COMBO EXAMPLE: SHORT STRANGLE SELL OUT OF THE MONEY PUT AND CALL Short Strangle Profit Table S T < X L X L < S T < X H S T > X H + P 0L + P 0L + P 0L + P 0L +C 0H +C 0H +C 0H P TL 0 (X L S T ) 0 +C 0H C TH 0 0 (S T X H ) = Profit S T X L + P 0L + C 0H P 0L + C 0H X H S T + P 0L + C 0H Breakeven S T = X L P 0L C 0H + S T = X H + P 0L + C 0H Profit X L X H Stock Price t S T = X L P 0L C 0H S T = X H + P 0L + C 0H

16 OPTION(LIKE) Convertible bonds Instead of principle payoff investors have the right to be paid in shares (conversation ratio, strike price) Callable bonds Collateralized debt Investors have the right to seize assets if the debt contract (indenture) breached Warrants Shares as a sweetener to a bond Real options Corporate finance

17 OPTION VALUATION Thus far we have only considered intrinsic value Options also have speculative value based upon Time left in the contract Volatility of the underlying Interest rate assumptions Dividend yield

18 BLACK-SCHOLES OPTION VALUATION T rt C0 S0e N(d 1) X(e )N(d2 ) where d 1 S0 Ln X (r σ T σ 2 2 )T and d d1 2 σ T C 0 = Current call option value. X (or E) = Exercise Price S 0 = Current stock price = Annual dividend yield on the stock e = , the base of the natural log r = Risk-free interest rate (annualize with continuous compounding the return on a T-bill with the same maturity as the option) T = Time until expiration (not a point in time) in years, = Annual std. deviation of continuously compounded stock returns N(d) = probability that a random draw from a normal distribution will be less than d. To convert a regular return to a continuously compounded return take Ln (1 + return)

19 BLACK-SCHOLES NOTES d 1 comes from our assumptions about how stock prices move in continuous trading: E(r) = (r + 2 /2)T when returns are lognormally distributed Ln (S 0 / X) measures the continuous return needed for the stock to finish in the money Roughly speaking the d 1 numerator is a measure of the return needed to finish in the money, the denominator measures this relative to the standard deviation of the returns. N(d) terms measure the probability of how far in the money the stock price is likely to be at expiration While empirical evidence suggests that the B-S model is a good approximation on the price of an option it is more important to be hedged the price of a single option is less important than net exposure to stock movements It is very difficult to use the B-S formula to arbitrage mispriced options in the markets, even taking trading costs out of consideration

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21 FORWARD AND FUTURES CONTRACTS A forward contract is a contract directly negotiated between two parties calling for delivery of a commodity at a price agreed upon in advance i.e. if you ever pre-ordered a book or, say, an iphone, you were long a forward contract A futures contract is similar but has standardized terms and is traded upon an exchange Key differences: Futures have secondary trading = liquidity Clearinghouse marks to market, guarantees performance Standardized contract terms, i.e. delivery dates, quality, price units, contract size

22 OPTIONS VS. FUTURES Options have a strike price, futures don t Both options and futures are leveraged positions controlling a much larger asset Futures may be easier to understand: Long futures : agree to buy an asset at a price agreed upon in advance Short futures : agree to deliver (sell) an asset at the agreed upon price Profit from long position = futures price at maturity original futures price Profit from short position = original futures price maturity futures price

23 PAYOFFS

24 FUTURES CONTRACTS

25 TRADING FUTURES Opening a position long to open, short to open Closing positions Reverse the trade before maturity (short/long to close) Roll-over : reverse initial trade, take previous position in next month Take or make delivery Almost never with physical futures (>90% reversed) Cash settlement in case of interest rates, indices, etc. Initial margin, maintenance margin, and marking to market Breach of maintenance margin means a margin call Open interest number of open contracts and a sign of liquidity

26 SPECULATING VS. HEDGING Most contracts are speculative contracts Speculators provide liquidity to the markets Commodity trading advisors (CTAs), hedge funds Hedging involves locking in prices today so that the firm can better plan going forward Long hedge a paper mill buys lumber futures to protect against future prices rises (spot price increases) Short hedge a farmer sells grain futures to protect against drops in the price of grain (that he will harvest and sell in 6 months) Financial institutions want to protect bond portfolios against rising rates (dropping bond prices) could use interest rate futures

27 HEDGING PAYOFFS - OIL EXAMPLE Oil futures are at $ An oil producer would hedge by going short. Here, we look at revenues of a producer in a short position:

28 WRAP UP How are options and futures similar? Different? What purpose do the clearinghouses serve? Consider the different (broad) reasons to use derivative securities hedging vs. speculating