Calculate the price of a European call option using the Black Scholes model and the following data: stock price = $56.80, exercise price = $55, time to expiration = 15 days, risk-free rate = 2.5%, standard deviation = 22%, dividend yield = 8%.
A) $1.49
B) $1.79
C) $2.19
D) $2.29

Question

Quizplus · Accepted Answer

d₁ = [ ln (56.80/55) + (0.025+ 0.222/2) × (15/365)] / [0.22 × sq rt 15/365] = 0.0342/0.0446 = 0.7682 d₂ = 0.7673 − [0.22 × sq rt 15/365] = 0.7236 N(d₁) = 0.7788 N(d₂) = 0.7650 Call value = S₀e^{- δT}N(d₁) - Xe-rTN(d₂) = (56.8)e-^{(0.08)(0.041)(0.7788)} - (55)×e^{-(0.025)(0.041)(0.7654)} = $2.19

Calculate the Price of a European Call Option Using the Black