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So, Bank ANZ owns a portfolio of options on the USD/GBP exchange rate. The delta equivalent position of the portfolio is GBP 56.00. The current exchange rate is 1.5, with a daily volatility of 0.7 percent. Using the given information and assuming that changes in portfolio value are normally distributed, the 99 percent /10-day VaR for this portfolio is:
I have noted that: Daily VaR = Daily Volatility * Delta Equivalent Position * Exchange Rate)
How do I use this to calculate the 10-day VaR?
In general, the P&L of options is non-linear with respect to the underlying. Unless the options are very far in or out of the money, the delta alone does not accurately tell you what the value of the option will be if the underlying exchange rate moves 2.33 standard deviations.
Even if you were told the gamma, estimating the change in value of the options using delta and gamma (Taylor expansion) for a 2.33 sd move would be very inaccurate.
Also, unless again the options are very far in or out of the money, they have material vega. Your VaR should include the possible change in option value because implied volatility changes.
Your delta-only approach would be OK if instead of options you just had foreign currency as cash.
I multiplied the delta equivalent by the daily volatility by the current exchange rate: 56 x 1.5 x 0.7 = 58.8
I then multiplied this by the square root of 10 to get the 10-day VaR = 185.942.
I then multiplied this answer by 2.33 (99 percent confidence interval) to get 433.245.
I assume we then divide this by 100 to get the final answer of 4.33?
