A stock price is $40. A 6-month European call option on the stock with a strike price of

Chapter 20, Problem 20.16

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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 putcall 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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