Using the linear derivative VAR method and the information in the table, and assuming 255 trading days in a year, what is a 1-percent VAR for the call option’s daily return? A. 11.9%. B. 26.1%. C. 15.8%. D. 43.4%.
The daily volatility is approximately equal to 0.94 percent a day (). The 1 percent VAR for the stock price is equivalent to a two standard deviation move, or 2.33 for the normal curve. The 1 percent VAR of the underlying stock is 0 – 0.94%(2.33) = 2.19%. A one percent change in the stock price results in a 11.92 percent change in the call option value, therefore, the delta = 0.1192/0.01 = 11.92. 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 = 11.92(2.19%) = 0.261 or 26.1%. In words, the 1 percent VAR implies there is a 1 percent probability that the call option value will decline by 26.1% or more.
). The 1 percent VAR for the stock price is equivalent to a two standard deviation move, or 2.33 for the normal curve. The 1 percent VAR of the underlying stock is 0 – 0.94%(2.33) = 2.19%. A one percent change in the stock price results in a 11.92 percent change in the call option value, therefore, the delta = 0.1192/0.01 = 11.92. 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 = 11.92(2.19%) = 0.261 or 26.1%. In words, the 1 percent VAR implies there is a 1 percent probability that the call option value will decline by 26.1% or more.
