VAR

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

VAR

Hello every one ... I Dont know how to answer thew last two questiosns... Can any one help..

A stock price follows geometric Brownian motion with an expected return of 16% per
annum and a volatility of 35% per annum. The current price is \$38.

What is the probability that a European call option on the stock with an exercise
price of \$40 and a maturity date in 6 months will be exercised
What is the 95% absolute value at risk (VaR) at the end of six months?
What is the 95% relative value at risk (VaR) at the end of six months

Finance Junkie
Posts: 258
Joined: Thu Sep 20, 2012 3:42 pm

VAR

Hence, The required probability is the probability of the stock price being above \$40 in six months time.Let we take the stock price in six months is St.
Ln(St) ~ Ø{Ln(38) + (.16-.35^2/2)0.5,.35^2*.5}

Since Ln(40) = 3.689, the required probability is
1-N(3.689-3.687/(0.06125)^.5

= 1- N(0.008)
Then from normal distribution tables N(.008)= .5032

So, that the required probability is .4968. In general the required probability is N(d2).

But in this case the required probability is the probabilty of the stock price being less than \$40 in 6 months time. So, it is 1 - .4968= .5032

hope it is clear

Finance Junkie
Posts: 258
Joined: Thu Sep 20, 2012 3:42 pm

VAR

Confidence interval of the stock price in 6 months is (\$24.58,\$64.85).
And the 95% absolute value at risk(Var) at the end of six months= \$38 - \$26.57 = \$11.43
The 95% relative value at risk(Var) at the end of six months = \$39.92 - \$26.57 = \$13.35