Pricing Options on Bonds Using the Black-Scholes Model

Pricing Options on Bonds Using the Black-Scholes Model 

The theoretical price of a call option written on a zero-coupon bond is calculated using equation (8.28). 

EXAMPLES OptioHS Pricing IJsinP the Black-Scholes Model  

1 Calculate the price of a call option written with strike price 21 and a maturity of three months written on a non-dividend-paying stock whose current share price is 25 and whose implied volatility is 23 percent, given a short-term risk-free interest rate of 5 percent. 

Using the approximation of the cumulative Normal distribution at the points 1.68 and 1.56, the price of the call option is 

P = the price of the underlying bond All other parameters remain the same. 

Note that although a key assumption of the model is that interest rates are constant, in the case of bond options, it is applied to an asset price that is essentially an interest rate assumed to follow a stochastic process. 

For an underlying coupon-paying bond, the equation must be modified by reducing P by the present value of all coupons paid during the life of the option. This reflects the fact that prices of call options on couponpaying bonds are often lower than those of similar options on zero-coupon bonds because the coupon payments make holding the bonds themselves more attractive than holding options on them. 

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