Chapter 11 Options and Other Derivative Securities

Chapter 11 Options and Other Derivative Securities

Call Option • Gives owner privilege (or choice) to buy specified number of shares of specified asset at specified price prior to an expiration date. • Example: – $60 December call option on Xerox common stock gives holder of option right to purchase from writer 100 shares of Xerox at $60 anytime up until option’s expiration date in December

Put Option • Permits owner to sell specified number of shares of specified asset at specified price prior to expiration date. • For example: – Holder of $60 December put option on Xerox stock has right to sell 100 shares of Xerox stock to writer of put at $60 anytime up until option’s expiration date in December

Long & Short • Long: owns option • Short (writer): sale of option not previous owned, thus creating new contract

Prices Associated with Options • Premium: price of option itself • Exercise (strike) price: price at which option can be exercised • Price of underlying security

Relationship between Stock Price and Strike Price • In-the-money • At-the-money • Out-of-the-money

In-the-Money • Option’s strike price more favorable to option holders than current market price of underlying security – For calls: current stock price > strike price – For puts: current stock price < strike price • Option has speculative or time value only

Out-of-the-Money • When option’s strike price is less attractive than current market price of its underlying stock – for calls: current stock price < strike price – for puts: current stock price > strike price • Option has no intrinsic value, but has speculative or time value based on potential stock price movements prior to option’s expiration.

At-the-Money • When the current stock price is same as strike price • No intrinsic value to option per se

Option Markets • • • American Stock Exchange Chicago Board Options Exchange International Securities Exchange Pacific Exchange Philadelphia Stock Exchange

Options Clearing Corporation • OCC acts as an intermediary between the two principals in every option trade – Each put and call buyer and seller is actually contracting with the OCC, rather than directly with the opposite party to the transaction • Writer places an order to buy an option with identical terms as one sold and OCC cancels the writer from that contract

Expiration Date & Exercise • Date on which an option expires – Saturday following third Friday of stated month in standard stock option contracts • American: exercisable up till expiration • European: exercisable only on expiration • Bermuda: exercisable on multiple dates

Why Options Have Value • Option may end up being in the money on or before expiration date • Value based on variability of price of underlying security, NOT its expected return

Intrinsic Value • The payoff obtained by exercising an option immediately – On the expiration date: premium = intrinsic value – Prior to expiration date: premium > or = intrinsic value

Speculative Value • Equals difference between market price of the option and intrinsic value • Also called time value of the option • Speculative value approaches zero as the option approaches the expiration date – Market price of premium approaches the intrinsic value

Example of Speculative Value (1 of 2) • Stock trades at $50 – In 6 mos. , 50% probability stock price will equal $60 & 50% probability it equals $40 – Expected value of stock price in 6 months: – > 50 x $60 +. 50 x $40 = $50 – Expected rate of return: 0%

Example of Speculative Value (2 of 2) • Intrinsic value of call option in 6 mos. : – If SP = $60, Call option = $10 – If SP = $40, Call option = $0 • Expected intrinsic value: – > 50 x $10 +. 50 x $0 = $5 • What is value today of something expected to be worth $5 in six month? Ans. : > zero!

Why Trade Options • Three roles in investment planning – Speculation – Hedging – Arbitraging

Profit and Payoff Functions • Profit function – Profit equals function of price of underlying asset on expiration date – Incorporates effect of premium • Payoff function – Payoff equals function of price of underlying asset on expiration date – Ignores effect of premium

Profit Function for Long a Call • Assume strike price = $50 • Premium = $8 • Long a call: pay $8 per share for the call option • If SP closes above $50, option has value • If SP closes below $50, option worthless

Call Option

Types of Call Options • Covered call: a call option written against stock that one owns • Naked call: call option written by investor who does not own underlying asset – Risky • Call writer is obligated to purchase the asset if the call is exercised • No limit to how high the asset’s market price might rise

Profit Function for Long a Put • Assume strike price = $50 • Premium = $3 • Long a put: pay $3 per share for the put option • If SP closes below $50, option has value • If SP closes above $50, option worthless

Put Option

Types of Put Options • Naked put: put option owned without any other position in asset • Married put: put option held by investor who also owns underlying security

Combinations of Puts & Calls • Straddle: combination put and call option on same stock at same strike price • Spread: one option is purchased and other is sold, with each option having different exercise price or expiration date (continued)

Figure 11 -9 Profit 10 8 6 Price at Exp Profit 4 110 5 105 0 100 95 90 2 -5 Price 0 5 90 95 -2 -4 -5 - 6 -8 -10 Loss 100 105 110 at Exp

Combinations of Puts & Calls (continued) • Bullish spread: buy call with lower strike price, sell call with higher strike price • Bearish spread: buy call with higher strike price, sell call with lower strike price

Bullish Spread

Bearish Spread

Models for Valuing Options • Black-Scholes option pricing model • Binomial option pricing model • Put-call parity

Black-Scholes Model • Assumes that a riskless hedge between an option and its underlying stock should yield the riskless return. • Option’s value function of – – – stock price strike price stock return volatility riskless interest rate length of time to expiration

Five Variables in Black-Scholes Model • Time to maturity: longer time to maturity, more valuable call • Interest rate: higher the interest rate, more valuable the call. • Price of underlying stock: higher the stock price, more valuable the call. • Volatility: more volatile price of underlying stock, more valuable the call. • Strike price: higher the strike price, less valuable the call.

Hedge Ratio • In Black-Scholes model, ratio of number of calls written that would exactly offset stock price movement of number of shares of underlying stock held • Small move in stock’s price would be precisely offset by change in value of option position with ratio of number of calls to number of shares of stock • Investor theoretically holding equivalent of riskfree asset.

Binomial Option Pricing Model • Full model mathematically complex • Simple model assumes – price at end of period will be one of two values – alternative to call option is to borrow enough so to buy one share of stock and just breakeven if stock closes at lower price – Price of call option will be based on how many calls are necessary to duplicate loan strategy, and equity to set up loan

Put-Call Parity C 0 = P 0 + S 0 – X erf x t C 0 P 0 rf e S 0 X t = = = = call value put value risk-free rate 2. 718 (the natural logarithmic constant) initial stock price strike price time to expiration as a fraction of the year

Simple Positions and Their Synthetic Equivalents Simple Position • Long Stock • Short Stock • Long a Call • Short a Call • Long a Put • Short a Put Synthetic Equivalent Long a Call & Short a Put Short a Call & Long a Put Long Stock & Long a Put Short Stock & Short a Put Short Stock & Long a Call Long Stock & Short a Call

Synthetic (Manufactured) Call • Call-like position generated by combination position in underlying stock and put • Position whose profit function is exact same shape as that of a call • C 0 = P 0 + S 0 – X/erfxt

Synthetic (Manufactured) Put • Put-like position generated by combination positions in underlying stock & call option • Position with payoff matrix similar to Put • P 0 = C 0 – S 0 + X/erfxt

Other Types of Options • Stock index options – option on value of a stock index – cash settlement • Interest rate options – option to buy or sell government securities • LEAPS® – options with initial maturities of up to three years

Convertible Securities • Convertible Bonds • Convertible Preferred Stocks • Concepts the same

Conversion Ratio • Conversion ratio = Par / Conversion Price • Conversion Price defined in indenture • Conversion ratio (or exchange ratio) = # of shares of common stock received upon conversion

Conversion Value & Premium • Conversion Value = Conversion Ratio x Price of Common Stock • Conversion Premium = Market Price of Bond – Conversion Value • % Conversion Premium = Conversion Premium / Conversion Value

44

Convertibles Always Callable • Allows company to force conversion • Investor must convert or sale • After call date, no longer accrues interest or is convertible

Rates of Return on Convertibles • Historically: – Better than non-convertibles – Worse direct ownership of equity • Less risky than equity, riskier than straight debt