The price of a European call option is $5 at an implied volatility of 0.25.The vega of the call is 20.If the implied volatility increases to 0.26,what is the new value of a European put option with the same strike and maturity as the call that is currently priced at $6?

Question

Quizplus · Accepted Answer

The new value of the European call option can be calculated using the vega of the option. Vega measures the sensitivity of the option's price to changes in the volatility of the underlying asset. Given that the vega is 20 and the implied volatility increases by 0.01 (from 0.25 to 0.26), the price of the call option increases by 20 * 0.01 = $0.20. Therefore, the new price of the call option is $5 + $0.20 = $5.20.To find the new value of the European put option, we can use the put-call parity, which states that the price of a call option minus the price of a put option equals the current stock price minus the present value of the strike price, all else being equal. However, without information on the stock price or the strike price, we cannot directly apply the put-call parity to find the new price of the put option.Given that the question asks for the new value of the put option after the change in implied volatility and provides the current price of the put option, we can infer that the change in implied volatility affects the prices of both the call and put options similarly due to their relationship through the Greeks, particularly vega in this context.However, the direct impact of the change in implied volatility on the put option's price is not provided, and without additional information (such as the stock price, strike price, or interest rates), we cannot accurately calculate the new price of the put option using the information given. The question seems to focus on the change in the call option's price due to implied volatility, and the provided options do not directly relate to how the put option's price would be adjusted based on the given information.Therefore, the correct response based on the information provided and the typical relationship between call and put options through the Greeks would be to acknowledge the increase in the call option's price due to the change in implied volatility but also recognize that the direct impact on the put option's price cannot be accurately determined from the given details.

The Price of a European Call Option Is $5 at an Implied