IV. Black-Scholes Compute the Black-Scholes option pricing formula where to dete

Question

IV. Black-Scholes Compute the Black-Scholes option pricing formula where to determine the value of a European call on a non-dividend paying stock 4 months from expiration with spot price 75, strike price 70, volatility of 15%, a risk free rate of 3%. 31. What is the value of d: (a) 0.122; (b) 0.273; (c) 0.955; (d) 1.202; 32. What is the value of d2: (a) 0.869; (b) 0.562; (c) 0.433; (d) 0.128; 33. What is N(d): (a) 0.830; (b) 0.23; (c) 0.78; (d) 0.95; 34. What is N(d2): (a) 0.012; (b) 0.453; (c) 0.349; (d) 0.808; 35. What is the value of the entire first term SN(di): (a) 62.278; (b) 45.672; (c) 89.902; (d) 55.546; 36. What is the value of the entire second term Ke-TTN(d2): (a) 23.784; (b) 33.459; (c) 52.792; (d) 55.968; 37. What is the value of the call: (a) 6.309; (b) 0.000; (c) 4.353; (d) 8.992; 38. Calculate the delta of this option: (a) 0.830; (b) 0.566; (c) 0.784; (d) 0.953; 39. If the call price is 7.50, the implied volatility is: (a) 12.32; (b) 16.97; (c) 24.27; (d) 36.33;

Explanation / Answer

31.- S0 = 75

SX = 70

r = 3%

s = 15%

T = 4/12 = 0.33

d1 = (ln(S0/SX) + (2/2 + r)T)/

d1 = (ln(75/70) + (0.152/2 + 0.03)*4/12)/0.15 *        

d1 = (0.06899 + 0.01375)/0.08660

d1 = 0.955 - Option (c) is the correct answer

32. -

d2 = d1 –

d2 0.955 – 0.086 = 0.869 - Option (a) is the correct answer.

33. - N(d1) = N(0.955) = 0.830 - Option (a) is the correct answer.

34. - N(d2) = N(0.869) = 0.808 - Option (d) is the correct answer.

35. - S(Nd1) = 75 * 0.830 = 62.274 - Option (a) is the correct answer.

36. - Ke-rTN(d2) = (70 * 0.869 * e-0.03 * 4/12) = 55.968 - Option (d) is the correct answer.

37. - VAlue of Call = S(Nd1) - Ke-rTN(d2) = 62.274 - 55.968 = 6.309 - Option (a) is the correct answer

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