Question

Current value of S&P500 is 2500, interest rate is 2% per year, annualized volatility of S&P500 is 30%, a call option has strike price 2250 and expires in 0.25 years.

1. Using Black-Scholes option pricing formula, find option premium

2. Find option delta

Answer 1

BC 2500 22501 0.25 2.00% 30.00% 1 Input Data 2 Stock Price now (P) 3 Exercise Price of Option (EX) 4 Number of periods to Exercise in years (t) 5 Compounded Risk-Free Interest Rate (if) 6 Standard Deviation (annualized o) 7 8 9 Output Data 10 Present Value of Exercise Price (PV(EX)) 11 ot15 12 d1 13 d2 14 Delta Nd1) Normal Cumulative Density Function 15 Bank Loan N(D2)*PV(EX) 16 17 Value of Call 18 Value of Put 19 2238.7781 0.1500 0.8107 0.6607 0.7912 1669.2540 308.85 47.63

A B с 1 Input Data 2 Stock Price now (P) 3 Exercise Price of Option (EX) 4 Number of periods to Exercise in years (t) 5 Compounded Risk-Free Interest Rate (if) 6 Standard Deviation (annualized o) 2500 2250 0.25 0.02 0.3 9 Output Data 10 Present Value of Exercise Price (PV(EX)) | 11 3*45 12 d1 13 d2 14 Delta N(D1) Normal Cumulative Density Function 15 Bank Loan N(D2)*PV(EX) 16 17 Value of Call 18 Value of Put 19 20 =++C3*EXP(-C5*C4) =+C6*C4^0.5 =++(LN(C2/C3)+(C5+C6*C6/2)*C4)(C6*C4^0.5) =+C12-C11 =NORMDIST(C12,0,1,TRUE) =NORMDIST(C13,0,1,TRUE)*C10 =+C14*C2-C15 =+C17+C10-C2

a. Call Option premium = $308.85

b. Option delta = 0.7912

(Both answers are in image)

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