Question

The current price of LAD stock is $100. The annual variance of LAD stock return is 0.225 and the continuously compounded interest rate is 5% per annum. A six-month call option on LAD stock has a strike price of $95. Use the Black-Scholes model to value the six-month put option on LAD stock with the same exercise price.

Answer 1

So current stock price = 100

K strike price = 95

r risk free rate = 5% = 0.05

variance = 0.225

s: standard deviation = (0.225)^0.5 = 0.474

t: time to maturity = 6month = 0.5 year

d1 = (0.05129 + 0.08125)/0.33516 = 0.3954

d2 = 0.3954 - 0.474*(0.5)^0.5 = 0.0602

N(d1) = normsdist(d1) = 0.654

N(d2) = normsdist(d2) = 0.524

C: value of call option

e: natural exponent

c = 65.4 - 48.55 = 16.849