VAR

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

VAR

Postby anbu.edu » Tue Oct 01, 2013 1:15 am

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

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

VAR

Postby pradeeppdy » Tue Oct 01, 2013 11:26 am

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

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

VAR

Postby pradeeppdy » Tue Oct 01, 2013 11:38 am

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


Return to “FRM Part I”



cron

Disclaimer

Global Association of Risk Professionals, Inc. (GARP®) does not endorse, promote, review or warrant the accuracy of the products or services offered by EduPristine for FRM® related information, nor does it endorse any pass rates claimed by the provider. Further, GARP® is not responsible for any fees or costs paid by the user to EduPristine nor is GARP® responsible for any fees or costs of any person or entity providing any services to EduPristine Study Program. FRM®, GARP® and Global Association of Risk Professionals®, are trademarks owned by the Global Association of Risk Professionals, Inc

CFA Institute does not endorse, promote, or warrant the accuracy or quality of the products or services offered by EduPristine. CFA Institute, CFA®, Claritas® and Chartered Financial Analyst® are trademarks owned by CFA Institute.

Utmost care has been taken to ensure that there is no copyright violation or infringement in any of our content. Still, in case you feel that there is any copyright violation of any kind please send a mail to abuse@edupristine.com and we will rectify it.