Question

1. The current stock price of International Paper is $69, and the stock does not pay dividends. The instantaneous risk-free rate of return is 10%. The instantaneous standard deviation of International Paper's stock is 25%. You want to purchase a call option on this stock with an exercise price of $70 and an expiration date 73 days from now.
   
   Using the Black-Scholes OPM, the put option should be worth __________ today.
   

   		$1.50
   		$2.88
   		$2.55
   		$3.00

Answer 1

In this case, S0 = 69; K = 70; r = 0.10; $\sigma$ = 0.25 and T = 73/365

d1 = [{ln(S0/X)} + {t(r - q + $\sigma$ ²/2)}] / [$\sigma$(t)^1/2]

= [{ln(69/70)} + {(73/365)(0.10 + 0.25²/2)}] / [0.25(73/365)^1/2]

= 0.0119 / 0.1118 = 0.1061

d2 = d1 - [$\sigma$(t)^1/2]

= 0.1061 - [0.25(73/365)^1/2]

= 0.1061 - 0.1118 = -0.0057

P = [X * e^-rt * N(-d2)] - [S0 * e^-qt * N(-d1)]

= [70 * e^{-0.10*(73/365)} * N(0.0057)] - [69 * e^-0*(73/365) * N(-0.1061)]

= [70 * 0.9802 * 0.5023] - [69 * 0.4578]

= 34.46 - 31.59 = 2.88, or $2.88

So, 2nd option is correct.