credit risk measurement questions from GARP book

[southeuro]

Hi all,

Here's the question from GARP credit risk book:

Paul sells a put option on HRTB stock with time to expiration of 6 months, a strike price of $125, underlying asset price of $98, implied volatility of 20%, and a risk-free rate of 4%. What's Paul's CP expo in this transaction?

a. 0
b. 0.38
c. 1.75
d. 24.9

Answer is a since Paul is selling the option hence has no exposure (collects the premium and has no gain to expect). So far so good.

However, the explanation part also states that value of put option is 24.9, value of call option is 0.38, and one year call option is 1.75.

I've been using the BSM formula to find these value but can't.

i.e. for call: St * N(d1) - Xe^rt * N(d2)
where d1= [ln(98/125) + {(.04 + (.2^2)/2) .50}] / [sq .5 * .2]
and d2=d1 - .2 * sq .5

Can anyone pls help? Thank you.

 

[David Harper CFA FRM]

Hi @southeuro

I do get the answer's c[T=0.5] = $0.38, p[T=0.5] = $24.9 and p[T=1.0] = $1.75.

d1 = [ ln(98/125) + (0.04 + 0.20^2/2)*0.5] / [0.2*sqrt(0.5)] =[ -0.2433 + 0.03] / [0.2*sqrt(0.5)] = -1.5086
d2 = d1 - sigma*sqrt(T) = -1.5086 - 0.20*sqrt(0.5) = -1.650
N(d1) = 0.0657 and N(d2) = 0.0495
c = 98*0.0657 - 125*exp(-.04*0.5)*0.0495 = 0.377

 

[southeuro]

Thanks David - apparently I was getting the wrong N(d1) -- looked up the wrong # on the table