Chapter 21: Option Valuation

Black-Scholes Option Pricing Model
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Black-Scholes Option Pricing Model
A model for valuing options based upon five inputs: the current price of the stock, the exercise price, the time until the option expires, the risk-free rate, the standard deviation of the stock's rate of return
- widely used by traders so actual option prices conform reasonably well to values derived from the model
What is needed for for the standard deviation of the stock's rate of return?
the variability expected to occur
N(d)
risk adjusted probabilities, that the option will expire in the money
- highest probability = 100%
If N(d) = 1, then we're sure the call will be
in the money
If N(d) = 0, then we're sure the call will be
out of the money
What do you expect to happen as the stock price increases?
the N(d) terms will increase
The value of a put option using the Black-Scholes Model
Put = exercise price - stock
Would you expect a $1 increase in a call option's exercise price to lead to a decrease in the option's value of more or less than $1?
Less than $1
- change in the call price would equal $1 if there is a 100% probability that call would be exercised and interest rate is 0%
Is a put option on a high-beta stock worth more than one on a low-beta stock? The stocks have identical firm-specific risk
higher beta implies higher total stock volatility, so the value of the put option increases as beta increases
All else equal, is a call option on a stock with a lot of firm-specific risk worth more than one on a stock with little firm-specific risk? The betas of the two stocks are equal.
the stock with a lot of firm-specific risk has higher total volatility
- option on the stock w/ higher firm specific risk is worth more
Should the rate of return of a call option on a long-term Treasury bond be more or less sensitive to changes interest rates than is the rate of return of the underlying bond?Rate of return of a call option on a long-term Treasury bond should be more sensitive - option is effectively a levered investmentIf the stock price falls and the call price rises, then what has happened to the call option's implied volatility?increased - if not the call price would have fallen as a result in the decrease in stock priceIf the time to expiration falls and the put price rises, then what has happened to the put option's implied volatility?increased -if not the put price would have fallen as a result of the decreased time to expiration