Question

Use DerivaGem to calculate the value of: (a) A regular European call option on a non-dividend-paying stock where the stock price is $$\$ 50$$, the strike price is $$\$ 50$$, the risk-free rate is $5 \%$ per annum, the volatility is $30 \%$, and the time to maturity is one year (b) A down-and-out European call which is as in (a) with the barrier at $$\$ 45$$ (c) A down-and-in European call which is as in (a) with the barrier at $$\$ 45$$. Show that the option in (a) is worth the sum of the values of the options in (b) and (c).

   Use DerivaGem to calculate the value of:
(a) A regular European call option on a non-dividend-paying stock where the stock price is $$\$ 50$$, the strike price is $$\$ 50$$, the risk-free rate is $5 \%$ per annum, the volatility is $30 \%$, and the time to maturity is one year
(b) A down-and-out European call which is as in (a) with the barrier at $$\$ 45$$
(c) A down-and-in European call which is as in (a) with the barrier at $$\$ 45$$.
Show that the option in (a) is worth the sum of the values of the options in (b) and (c).

Options, Futures, and Other Derivatives

John C. Hull 10th Edition

Chapter 26, Problem 22

Instant Answer

Step 1

The formula is given by: $$C = S_0 \cdot N(d_1) - X \cdot e^{-rT} \cdot N(d_2)$$ where: - $C$ is the value of the call option - $S_0$ is the current stock price - $N$ is the cumulative standard normal distribution function - $d_1 = Show more…

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Use DerivaGem to calculate the value of: (a) A regular European call option on a non-dividend-paying stock where the stock price is $$\$ 50$$, the strike price is $$\$ 50$$, the risk-free rate is $5 \%$ per annum, the volatility is $30 \%$, and the time to maturity is one year (b) A down-and-out European call which is as in (a) with the barrier at $$\$ 45$$ (c) A down-and-in European call which is as in (a) with the barrier at $$\$ 45$$. Show that the option in (a) is worth the sum of the values of the options in (b) and (c).

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