Question

Stock price	=	$85
Exercise price	=	$80
Risk-free rate	=	3.80% per year, compounded continuously
Maturity	=	5 months
Standard deviation	=	55% per year

Find the call price of the option. Round your Z scores to 2 decimal spaces and provide an answer accurate to the nearest cent without the $ sign.

Answer 1

Call price of the option is calculated using black-Scholes. Formula to calculate call price of the option is as follows: C=S N(d,)-Ke"N (d,) Here, current stock price is S Exercise price of the call is K, risk-free interest rate is r time to maturity is t, Normal distribution is N, (d,) and (d,) is calculated using the below mention formula In (d) And (d2)d,-ov Here, standard deviation is o It is quoted that the stock price S is $85, Exercise price of the call (K) is $80, risk-free 5 and standard deviation o rate (r) is 3.80%, time to maturity is 5 months therefore, t 12 is 0.55 Calculate (d, and (d,) as follows: In rt (d) (0.55) 0.038+ $85 In $80 5 12 0.55 0.0606 0.0789 0.3550 -0.3929 Thus, value of (d,) is 0.3929 or 0.39 (d2) d-ov 5 -0.3929-0.55, V12 0.3929-0.3550 =0.0379 Thus, value of (d,) is 0.0379or 0.04 Calculate call price of the option as follows: C-S N(d,)-Ke "N( d,) -S85x N(0.39)-$80 xe -S85x0.6517-S80x 0.9843 x 0.5160 xN(0.04) $55.39-$40.63 - S14.76 Note, value of N (0.39) and N (0.04) is taken from Normal distribution table Therefore, call price of the option is S14.76