Question

You own a lot in Key West, Florida, that is currently unused. Similar lots have recently sold for $1,270,000 million. Over the past five years, the price of land in the area has increased 7 percent per year, with an annual standard deviation of 36 percent. You would like an option to sell the land in the next 12 months for $1,420,000. The risk-free rate of interest is 5 percent per year, compounded continuously. What is the price of the put option necessary to guarantee your sales price?

Answer 1

As per Black Scholes model,

Put option price = E*(e)^-rt * (N(-d2)) - (S*N (-d1))

Where,

S = Asset price = 1,270,000

E = Strike Price = 1,420,000

e = exp constant = 2.7183

r = continuously compounded rate = 5%

t = time remaining until expiration = 12 months = 1 yr

N (d) = value of standard normal distribution function.

= Annual Standard deviation = 36% = 0.36

d1 = (ln(S/E) + (r + ^2/2)t)/t

d1 = (-0.112 + 0.1148)/0.36 = 0.009

and d2 = d1 - t

So, d2 = 0.009 - 0.36 = -0.351

So, Put price = {1420,000*0.95 * N (0.351)} - {1270,000 * N (-0.009)}

Here N (0.351) can be calculated in excel using 'NORMSDIST' function

So, N (0.351) = NORMSDIST (0.351) = 0.637

Simillarly, N (-0.009) = NORMSDIST (-0.009) = 0.496

So, Put option Price = {1420,000*0.95 * 0.637} - {1270,000 * 0.496}

Put option Price = 859313 - 629920 = 229,393