
Explanation:
This scenario demonstrates that the implied volatility of a European call option is always the same as the implied volatility of a European put option when the two have the same strike prices and maturity dates. This is because the Black-Scholes-Merton model, which is used to calculate the prices of these options, assumes that the volatility of the underlying asset is constant and does not depend on the type of option or its strike price or maturity date. Therefore, if the implied volatility of a put option is 25%, the implied volatility of a call option with the same strike price and maturity date should also be 25%. This is consistent with the principle of put-call parity, which states that the price of a call option implies a certain price for a put option, and vice versa, given the same strike price and expiration date.
Choice B is incorrect. The scenario does not show that the implied volatility of a European call option is always different from the implied volatility of a European put option when they have the same strike prices and maturity dates. In fact, it demonstrates the opposite – that under these conditions, their implied volatilities are equal.
Choice C is incorrect. The scenario does not provide any information about situations where the strike prices and maturity dates of a European call and put option are different. Therefore, we cannot infer from this scenario that their implied volatilities would be equal in such cases.
Choice D is incorrect. This statement incorrectly compares European call options with American put options. The given scenario only discusses European options (both call and put), so we cannot draw conclusions about American options based on this information.
Ultimate access to all questions.
No comments yet.
Q.1710 After reading the following scenario, pick the statement which CORRECTLY depicts it.
Suppose that the implied volatility of a put option = 25% meaning that when volatility of 25% is being applied in the Black-Scholes-Merton model. From the following equation, , then when this volatility is used. The implied volatility of the call is also 25%.
A
This scenario shows that the implied volatility of a European call option is always the same as the implied volatility of a European put option when the two have the same strike prices and maturity dates.
B
This scenario shows that the implied volatility of a European call option is always the different as the implied volatility of a European put option when the two have the same strike prices and maturity dates.
C
This scenario shows that the implied volatility of a European call option is always the same as the implied volatility of a European put option when the two have different strike prices and maturity dates.
D
This scenario shows that the implied volatility of a European call option is always the same as the implied volatility of an American put option when the two have the same strike prices and maturity dates.