Question

In a one-period binomial model, assume that the current stock price is $100, and that it...

In a one-period binomial model, assume that the current stock price is $100, and that it will rise to $110 or fall to $90 after one month. If the risk-free rate is 0.1668% per month in simple terms, what is the price of a 97–strike one-month put option?

A. $3.16

B. $3.44

C. $3.59

D. $3.67

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Homework Answers

Answer #1

At the end of 1 month, the value of the put option will be either $7 (if the stock price is $90) or $0 (if the stock price is $110).

Let us consider a portfolio :
- Δ : shares
+1 : option

The Δ of a put option is negative

The value of the portfolio is either -90Δ + 7 or -110Δ

-90Δ + 7 = -110Δ

=> Δ = -0.35

The value of the portfolio is certain to be -90*(-0.35) + 7 = 38.5. For this value of Δ, the portfolio is hence riskless

The current value of the portfolio is -100Δ + f

where f is the value of the option. Since the portfolio must earn the risk-free rate of interest,

=> (100*0.35 + f)(1+0.001668) = 38.5

=> f = 3.44

Hence, the value of the put option is $3.44

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