Lecture Presentation Software to accompany Investment Analysis and Portfolio Management Seventh Edition by Frank K. Reilly & Keith C. Brown Chapter 23

Derivatives Forwards –fix the price or rate of an underlying asset Options –allow holders to decide at a later date whether such fixing is in their best interest

Option Market Conventions Option contracts have been traded for centuries Customized options traded on OTC market In April 1973, standardized options began trading on the Chicago Board Option Exchange Options Clearing Corporation (OCC) acts as guarantor of each CBOE -traded options

Price Quotations for Exchange-Traded Options Equity options –CBOE, AMEX, PHLX, PSE –typical contract for 100 shares –require secondary transaction if exercised –time premium affects pricing

Price Quotations for Exchange-Traded Options Stock index options –only settle in cash Foreign currency options –allow sale or purchase of a set amount of non-USD currency at a fixed exchange rate –quotes in USD Options on futures contracts (futures options) –Give the right, but not the obligation, to enter into a futures contract at a later date at a predetermined price

The Fundamentals of Option Valuation Risk reduction tools when used as a hedge Forecasting the volatility of future asset prices –direction and magnitude hedge ratio is based on the range of possible option outcomes related to the range of possible stock outcomes risk-free hedge buys one share of stock and sells call options to neutralize risk hedge portfolio should grow at the risk-free rate

The Binomial Option Pricing Model Two-state option pricing model –up movement or down movement –forecast stock price changes from one subperiod to the next up change down change number of subperiods

The Binomial Option Pricing Model

The Black-Scholes Valuation Model continuous changes rather than discrete geometric Brownian motion –volatility factor, 

The Black-Scholes Valuation Model Value is a function of five variables: 1. Current security price 2. Exercise price 3. Time to expiration 4. Risk-free rate 5. Security price volatility C = f(S, X, T, RFR,  )

Estimating Volatility Mean and standard deviation of a series of price relatives

Problems With Black-Scholes Valuation Stock prices do not change continuously Arbitrageable differences between option values and prices (due to brokerage fees, bid-ask spreads, and inflexible position sizes) Risk-free rate and volatility levels do not remain constant until the expiration date

Problems With Black-Scholes Valuation Empirical studies showed that the Black- Scholes model overvalued out-of-the- money call options and undervalued in-the- money contracts Any violation of the assumptions upon which the Black-Scholes model is based could lead to a misevaluation of the option contract

Option Valuation: Extensions and Advanced Topics Valuing European-style put options Valuing options on dividend bearing securities Valuing American-style options Stock index options Foreign currency options Futures options

Exotic Options Asian options –terminal payoff determined by the average price of the underlying security during the life of the contract –path dependent payoff Lookback options –distribution based on the maximum price the underlying security achieves during the life of the contract –preserves volatility –always European-style Digital options - fixed payoff amount regardless of how deep in the money the contract is at expiration

Option Trading Strategies Options are a leveraged alternative to making a direct investment in the asset on which the contract is based Put options could be used in conjunction with an existing portfolio to limit the portfolio’s loss potential

Option Trading Strategies Protective put options Covered call options Straddles, strips, and straps Strangle Chooser options Spreads Range forwards