# Options Question -

There doesn’t seem to be a whole lot of activity on the level 1 forum, so I’m posting this here. Can somebody please 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 implied volatility seems to be around 31. The way i calculate it, I get a volatility of 12.8.

I have to run out for a bit - will do a quick and dirty for you here. (e^0.12-1)/2= 0.06374843 R = log(1.06374843)=1.06179892 U = 60/50-1 =20% = 1.20 D = 42/50-1 = -16% = 0.84 piu = (1.06179892 - 0.84)/(1.20-0.84) =0.616108111111111 pid=0.383891888888889 S = 50 S+ =60 S- = 42 C+=12 C-=0 C = 12*0.616108111111111/1.06179892 = 6.962991950804

Thanks a lot mate. I was totally on the wrong track. You saved me at least a couple of hours of head scratching.

Swaption i dont get this bit: (e^0.12-1)/2= 0.06374843 R = log(1.06374843)=1.06179892 I thought it would just be e^(0.12*0.5) = 1.061836547…?

chedges - you are technically more correct - I just did a quick workaround to get to the 6 month, continuously compounded risk free rate. Usually this causes some rounding, but not a worry for the CFAI exams, as they make sure that the options are wide apart to adjust for the inherent rounding problems.

If this is for Level One, you might want to read the LOS’s this year. Doing this calc on the exam might not be required (for lev1). Depends how they asked the question. I recall lev one Q’s for equity options being only conceptual in December. - But that was last year. Can’t remember what the LOS’s say for level two but they’ll probably some calcs of some kind.