Financial Risk Manager Part 1
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In a competitive setting, two investment banks, Bank A and Bank B, are assigned the task of calculating the 1-day 99% Value at Risk (VaR) for a long-standing at-the-money call option on a dividend-free stock. The necessary information for this calculation includes:
- Current stock price: USD 120
- Annual return volatility of the stock: 18%
- Present value of the Black-Scholes-Merton call option: USD 5.20
- Delta of the call option: 0.6
Bank A chooses to utilize the delta-normal model for their VaR calculation, while Bank B decides to apply a Monte Carlo simulation for a complete revaluation. The question to be answered is: which of the two banks is more likely to estimate a higher 1-day 99% VaR?
In a competitive setting, two investment banks, Bank A and Bank B, are assigned the task of calculating the 1-day 99% Value at Risk (VaR) for a long-standing at-the-money call option on a dividend-free stock. The necessary information for this calculation includes:
- Current stock price: USD 120
- Annual return volatility of the stock: 18%
- Present value of the Black-Scholes-Merton call option: USD 5.20
- Delta of the call option: 0.6 Bank A chooses to utilize the delta-normal model for their VaR calculation, while Bank B decides to apply a Monte Carlo simulation for a complete revaluation. The question to be answered is: which of the two banks is more likely to estimate a higher 1-day 99% VaR?
Explanation:
The explanation provided in the file content indicates that the delta-normal model used by Bank A provides a linear approximation of the portfolio value, which does not account for the positive curvature effect of the option's price function. This leads to an overstatement of the probability of low option values, resulting in a higher VaR estimate compared to a full revaluation conducted by Monte Carlo simulation analysis, which is used by Bank B. Therefore, Bank A will estimate a higher value for the 1-day 99% VaR than Bank B.