Question

Question #1: Use the Black-Scholes formula to find the value of a call option on the following stock: 6 months Time to expiration Standard Deviation Exercise Price Stock Price Interest Rate 50% per year S50 $50 10% Question #2: Find the value of put option on the stock in the previous problem with the same information above (Hint: there are two ways of calculating such value).

please show all work. show all formulas. thank you

Answer 1

ValueofCall = SN(d1) - Ke-itN(D2)

Where(d1) = (Ln(S/K) + (r + 2)/2)/ovt

d2 = d1 - Vt

t= 6 month = 0.5 years

Standard deviation= 0.5

K = $50

S = $50

r = 0.10

By putting the values in the formula we get the value of call option.

Stock price	Annual Dividend yield (D/P)	Exercise Price (K)	Risk free Rate (r )	Time to expiration (yrs)	Volatility (Annualized)	Adjusted Stock Price (S)	d1	N'(d1)	d2	Option premium
50	0	50	0.1	0.5	0.5	50	0.318198	0.379249	-0.03536	8.131599

Value of Call = $ 8.13

ValueofPut = -SNC-d1) + Ke-N(-d2)

Stock price	Annual Dividend yield (D/P)	Exercise Price(K)	Risk free Rate (r )	Time to expiration (yrs)	Volatility (Annualized)	Adjusted Stock Price (S)	d1	N'(d1)	d2	Put Option premium	Option premium
50	0	50	0.1	0.5	0.220775	50	0.398339	0.368514	0.242228	4.40822	1.969691

Value of Put = 1.97