The weekly volatility is approximately equal to 2.77% a week (0.20 / √52). The 5% VAR for the stock price is equivalent to a 1.65 standard deviation move for a normal curve. The 5% VAR of the underlying stock is 0 − 2.77%(1.65) = −4.57%. A −1% change in the stock price results in a 9.91% change in the call option value, therefore, the delta = −0.0991 / −0.01 = 9.91. For small moves, delta can be used to estimate the change in the derivative given the VAR for the underlying asset as follows: VARCall = ΔVARStock = 9.91(4.57%) = 0.4529, or 45.29%. In words, the 5% VAR implies there is a 5% probability that the call option value will decline by 45.29% or more over one week. |
