Portfolio Theory and Financial Engineering

1
Portfolio Theory and Financial Engineering

• FIN 428
• Lecture Eighteen Options
• Tuesday, March 27, 2007

2
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

3
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
• 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
• Give the right, but not the obligation, to enter
  into a futures contract on an underlying security
  or commodity at a later date at a predetermined
  price

4
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

5
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

6
The Black-Scholes Valuation Model

• Continuous changes rather than discrete
• Geometric Brownian motion
• volatility factor, s

7
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, s)

8
Estimating Volatility

• Mean and standard deviation of a series of price
  relatives

9
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
• 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

10
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

11
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 portfolios loss
  potential

12
Option Trading Strategies

• Protective put options
• Covered call options
• Straddles, strips, and straps
• Strangle
• Chooser options
• Spreads
• Range forwards

13
Project 2
14
Next Class

• Reading
• none
• Topics to be discussed in the next class
• Options continued