Question

Consider a European call option on a non-dividend-paying stock where the stock price is $$\$ 40$$, the strike price is $$\$ 40$$, the risk-free rate is $4 \%$ per annum, the volatility is $30 \%$ per annum, and the time to maturity is 6 months. (a) Calculate $u, d$, and $p$ for a two-step tree. (b) Value the option using a two-step tree. (c) Verify that DerivaGem gives the same answer. (d) Use DerivaGem to value the option with $5,50,100$, and 500 time steps.

   Consider a European call option on a non-dividend-paying stock where the stock price is $$\$ 40$$, the strike price is $$\$ 40$$, the risk-free rate is $4 \%$ per annum, the volatility is $30 \%$ per annum, and the time to maturity is 6 months.
(a) Calculate $u, d$, and $p$ for a two-step tree.
(b) Value the option using a two-step tree.
(c) Verify that DerivaGem gives the same answer.
(d) Use DerivaGem to value the option with $5,50,100$, and 500 time steps.

Options, Futures, and Other Derivatives

John C. Hull 10th Edition

Chapter 13, Problem 25

Instant Answer

Step 1

In this case, the volatility is $30\%$ per annum, so $\sigma = 0.30$. The time to maturity is 6 months, so $\Delta t = \frac{1}{2}$ year. The risk-free rate is $4\%$ per annum, so $r = 0.04$. Plugging these values into the formulas, we get: $u = e^{0.30 Show more…

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Consider a European call option on a non-dividend-paying stock where the stock price is $$\$ 40$$, the strike price is $$\$ 40$$, the risk-free rate is $4 \%$ per annum, the volatility is $30 \%$ per annum, and the time to maturity is 6 months. (a) Calculate $u, d$, and $p$ for a two-step tree. (b) Value the option using a two-step tree. (c) Verify that DerivaGem gives the same answer. (d) Use DerivaGem to value the option with $5,50,100$, and 500 time steps.

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