The value of an Asian call option is computed using the geometric average strike.What is the expected payoff if the observed prices to date are 69,70,72,71,75,and 73,respectively?

Question

Quizplus · Accepted Answer

The expected payoff of an Asian call option using the geometric average strike can be calculated by first finding the geometric average of the observed prices and then comparing it to the strike price. The geometric average of the observed prices $69, 70, 72, 71, 75, \text{ and } 73$ is calculated as $\sqrt[6]{69 \times 70 \times 72 \times 71 \times 75 \times 73}$, which equals approximately 71.79. Assuming the strike price is also the geometric average (as the question implies but does not specify a separate strike price), the option is at-the-money or slightly in-the-money depending on the exact calculation and rounding. However, without the specific formula or additional details on how the expected payoff is calculated (e.g., discounting, volatility, risk-free rate), it's not possible to directly calculate the expected payoff from the information given. The correct answer choice B, 1.36, suggests a specific calculation method was used, likely involving financial models or assumptions not detailed in the question. This answer is chosen based on the options provided and the understanding that the calculation of an option's expected payoff involves complex financial models that take into account not just the average price but also factors like volatility, time to expiration, and the risk-free rate.

The Value of an Asian Call Option Is Computed Using