Question

5.What is the value of a call option if the underlying stock price is $78, the strike price is $80, the underlying stock volatility is 42 percent, and the risk-free rate is 5.5 percent? Assume the option has 110 days to expiration.

6. Suppose you buy one SPX call option contract with a strike of 1300. At maturity, the S&P 500 Index is at 1321. What is your net gain or loss if the premium you paid was $14?

Answer 1

1.

Α 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 0.301369863 5.50% 42.00% 8 9 Output Data 10 Present Value of Exercise Price (PV(EX)) 11 6*1.5 12 d1 13 d2 14 Delta N(d1) Normal Cumulative Density Function 15 Bank Loan N(D2)*PV(EX) 16 17 Intrinsic Value of Call 18 Intrinsic Value of Put 78.6849 0.2306 0.0774 -0.1532 0.5308 34.5521 0.0000 2.0000 20 Time Value of Call 21 Time Value of Put 6.8530 5.5379 22 23 Total Value of Call 24 Total Value of Put 6.8530 7.5379

C 78 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 (rf) 5 Standard Deviation (annualized o) 80 =110/365 0.055 0.42 3 Output Data O Present Value of Exercise Price (PV(EX)) 1 o*1.5 2 d1 =++C3*EXP(-C5*C4) =+C6*C4^0.5 =++(LN(C2/C3)+(C5+C6*C6/2)*C4)(C6*C440.5) =+C12-C11 =NORMDIST(C12,0,1,TRUE) =NORMDIST(C13,0,1,TRUE)*C10 3 d2 4 Delta N(d1) Normal Cumulative Density Function 5 Bank Loan N(02)*PV(EX) 7 Intrinsic Value of Call 8 Intrinsic Value of Put =MAX(C2-C3,0) =MAX(C3-C2,0) 0 Time Value of Call 1 Time Value of Put =C23-C17 =C24-C18 3 Total Value of Call 4 Total Value of Put =+C14*C2-C15 =+C23+C10-C2

2.

Profit=multiplier*(premium per option-MAX(spot-strike,0))

=100*(14-MAX(1321-1300,0))=-700

Net loss of 700