Question

Use the Black-Scholes formula to calculate the value of a European call option on silver futures. The option matures in six months. The current nine-month futures price is $10 per oz, the strike price of the option is $8, the risk free interest rate is 12% per annum and the volatility of the futures price is 18% per annum. Use the NORM.S.DIST(x) function in Excel. Round to two decimals.

What is the delta of the call option on the futures contract from Problem #1?

Answer 1

the above is formula of Black Scholes model for call valuation , value of Spot price (S) is not given ,

for Future price , F = S* e^{r t}

=> S = 10 / e ^0.12*0.75 = $ 9.14.

Input Data
Stock Price now (S)		9.14
Exercise Price of Option (K)		8
Number of periods to Exercise in years (t)		0.50
Compounded Risk-Free Interest Rate (rf)		12.00%
Standard Deviation (annualized s)		18.00%
Output Data
Present Value of Exercise Price (PV(K))		7.5341
s*t^.5		0.1273
d1		1.5817
d2		1.4544
Delta N(d1) Normal Cumulative Density Function		0.9431
N(d2)*PV(K)		6.9848
Value of Call		1.6355