Options Question -

[najcfa]

Can somebody help me answer this:
A stock price is currently $50. It is known that at the end of six months it will be either $60 or $42. The risk-free rate of interest with continuous compounding is 12% per annum, compounded continuously. What is the value of a six-month European call option on the stock with an exercise price of $48?
The answer is 6.96. Can anyone see how that could be.
I am having trouble getting the volatility right. The way i calculate it, I get a volatility of 12.8.

 

[Factor hedge]

Hi
isn’t it [S-X/(RFR)]
50 - 48/1.1274 (12% is compounded continuously) . I am getting 7.42

 

[DTM86]

Where did this problem come from? Qbank? It seems like some information is missing, I’m not seeing how you could solve for volatility given that information.

 

[DTM86]

Nevermind, I figured it out. But where did you find this problem? It doesn’t seem like something out of the curriculum.
This page might help (slides 9 & 10): http://www.ulb.ac.be/cours/solvay/farber/Escp/Valuing%20financial%20opti...
Look at those slides. The inputs are:
uS=60
dS=48
Cu=12
Cd=0
S=50
r=~6.2% (12% compounded continuously, but only for 6 months)
Solve for Delta = ~.667
Solve for B =26.37
Solve for C=6.96

 

[wyantjs]

najcfa Wrote:
——————————————————-
> Can somebody help me answer this:
>
> A stock price is currently $50. It is known that
> at the end of six months it will be either $60 or
> $42. The risk-free rate of interest with
> continuous compounding is 12% per annum,
> compounded continuously. What is the value of a
> six-month European call option on the stock with
> an exercise price of $48?
>
> The answer is 6.96. Can anyone see how that could
> be.
>
> I am having trouble getting the volatility right.
> The way i calculate it, I get a volatility of
> 12.8.
What do you need volatility for? Answer goes as follows:
u=60/50=1.2
d=42/50=.84
p=(exp(.06)-.84)/(1.2-.84)=.6162
option only pays off in up state, and payoff is 12. So,
value = exp(-.06)*(.6162*12)=6.9640