## FRM-VAR

anbu.edu
Finance Junkie
Posts: 205
Joined: Mon Feb 04, 2013 3:35 pm

### FRM-VAR

Annual volatility: σ = 20.0%

Annual risk-free rate = 6.0%

Exercise price (X) = 24

Time to maturity = 3 months

Stock price, S

\$21.00

\$22.00

\$23.00

\$24.00

\$24.75

\$25.00

Value of call, C

\$0.13

\$0.32

\$0.64

\$1.14

\$1.62

\$1.80

% Decrease in S

−16.00%

−12.00%

−8.00%

−4.00%

−1.00%

% Decrease in C

−92.83%

−82.48%

−64.15%

−36.56%

−9.91%

Delta (ΔC% / ΔS%)

5.80

6.87

8.02

9.14

9.91

Suppose that the stock price is currently at \$25.00 and the 3-month call option with an exercise price of \$24.00 is \$1.60. Using the linear derivative VAR method and the information in the above table, what is a 5% VAR for the call option’s weekly return?

A) 50.7%.
B) 45.3%.
C) 43.4%.
D) 21.6%.
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.

The question is from Schweser
My doubt is why they have taken Delta value as 9.91 instead of 9.14.

content.pristine
Finance Junkie
Posts: 356
Joined: Wed Apr 11, 2012 11:26 am

### FRM-VAR

Dear Anbu,
The way the question is displayed, I really can't understand the data given.
Please provide the whether it is from the schweser question bank or schweser book and which page.
Otherwise, please try to format this in a different way.