Question

A stock price is $$\$ 40$$. A 6-month European call option on the stock with a strike price of $$\$ 30$$ has an implied volatility of $35 \%$. A 6-month European call option on the stock with a strike price of $$\$ 50$$ has an implied volatility of $28 \%$. The 6-month risk-free rate is $5 \%$ and no dividends are expected. Explain why the two implied volatilities are different. Use DerivaGem to calculate the prices of the two options. Use put-call parity to calculate the prices of 6-month European put options with strike prices of $$\$ 30$$ and $$\$ 50$$. Use DerivaGem to calculate the implied volatilities of these two put options.

   A stock price is $$\$ 40$$. A 6-month European call option on the stock with a strike price of $$\$ 30$$ has an implied volatility of $35 \%$. A 6-month European call option on the stock with a strike price of $$\$ 50$$ has an implied volatility of $28 \%$. The 6-month risk-free rate is $5 \%$ and no dividends are expected. Explain why the two implied volatilities are different. Use DerivaGem to calculate the prices of the two options. Use put-call parity to calculate the prices of 6-month European put options with strike prices of $$\$ 30$$ and $$\$ 50$$. Use DerivaGem to calculate the implied volatilities of these two put options.

Options, Futures, and Other Derivatives

John C. Hull 10th Edition

Chapter 20, Problem 16

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Step 1

Implied volatility is a measure of the market's expectation of future volatility of the underlying stock. It is derived from the prices of options on the stock. In this case, the implied volatility of the call option with a strike price of $30 is higher (35%) Show more…

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A stock price is $$\$ 40$$. A 6-month European call option on the stock with a strike price of $$\$ 30$$ has an implied volatility of $35 \%$. A 6-month European call option on the stock with a strike price of $$\$ 50$$ has an implied volatility of $28 \%$. The 6-month risk-free rate is $5 \%$ and no dividends are expected. Explain why the two implied volatilities are different. Use DerivaGem to calculate the prices of the two options. Use put-call parity to calculate the prices of 6-month European put options with strike prices of $$\$ 30$$ and $$\$ 50$$. Use DerivaGem to calculate the implied volatilities of these two put options.

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