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Answer: Bank A
The correct answer is A, Bank A will estimate a higher value for the 1-day 99% Value at Risk (VaR). The explanation for this lies in the different methodologies used by the two banks to calculate VaR. Bank A uses the delta-normal model, which is a linear approximation method. This model does not fully capture the non-linear characteristics of the option's price function, particularly the positive curvature effect on the portfolio value. As a result, the delta-normal model tends to overstate the probability of low option values, leading to a higher VaR estimate. On the other hand, Bank B employs a Monte Carlo simulation method for full revaluation. Monte Carlo simulation is a more sophisticated and accurate approach for valuing complex financial instruments like options. It takes into account the non-linearities and the entire distribution of possible outcomes, providing a more precise estimation of risk. Therefore, the VaR calculated using the Monte Carlo simulation is expected to be lower than that estimated by the delta-normal model. In summary, due to the limitations of the delta-normal model in capturing the non-linearities of the option's price function, Bank A's VaR estimate will be higher compared to Bank B's estimate, which uses a more comprehensive Monte Carlo simulation method.
Author: LeetQuiz Editorial Team
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Consider two investment banks, A and B, that are estimating the 1-day 99% Value at Risk (VaR) for a long position in an at-the-money call option on a non-dividend-paying stock. Bank A uses the delta-normal model for their VaR calculation, whereas Bank B employs a Monte Carlo simulation method for full revaluation. Given the following details:
Which bank will have a higher 1-day 99% VaR estimate for this call option, Bank A or Bank B?
A
Bank A
B
Bank B
C
Both banks will have the same VaR estimate
D
Insufficient information to determine
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