Use the following data for an eight-period binomial model to answer the questions that follow.
- The stock's price S is $100.The stock price evolves according to an eight-period binomial model.
- Options mature after T = 1 year and have a strike price of K = $70.
- The continuously compounded risk-free interest rate r is 5 percent per year.
- The annualized volatility of stock price returns $\sigma$ = 0.25 or 25 percent per year.
-Today's price of a European put in this eight-period binomial model is:

Question

Quizplus · Accepted Answer

To price the European put option, we need to use the risk-neutral binomial pricing model. We first calculate the up and down factors:
u = e^(σ√(T/n)) = e^(0.25√(1/8)) ≈ 1.0805
d = 1/u ≈ 0.9250
where T is the time to maturity (1 year), n is the number of periods (8), and σ is the annualized volatility (0.25).
We also calculate the risk-neutral probability of an up movement:
p = (e^(rT/n) - d) / (u - d) = (e^(0.05/8) - 0.9250) / (1.0805 - 0.9250) ≈ 0.5165
Using the put-call parity, we can calculate the price of a European put option as:
p = Ke^(-rT) - S_0(1 - p)^n
= 70e^(-0.05) - 100(1 - 0.5165)^8
≈ 0.3719
Therefore, the best choice is B.

Use the Following Data for an Eight-Period Binomial Model to Answer