Put Option Valuation

Our examples thus far have focused only on call options. Only a little extra work is needed to value put options. Basically, we just pretend that a put option is a call option and use the Black-Scholes formula to value it. We then use the put-call parity (PCP) condition to solve for the put value. To see how this works, suppose we have the following:

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Edition, Alternate Edition

CHAPTER 24 Option Valuation 817

R = 4% per year, continuously compounded ct = 80% per year t = 4 months

What's the value of a put option on the stock?

For practice, calculate the Black-Scholes call option price and see if you agree that a call option would be worth about $7.52. Now, recall the PCP condition:

which we can rearrange to solve for the put price:

Plugging in the relevant numbers, we get:

Thus, the value of a put option is $6.99. So, once we know how to value call options, we also know how to value put options.

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