Question

You own a lot in Key West, Florida, that is currently unused. Similar lots have recently sold for $1,320,000. Over the past five years, the price of land in the area has increased 6 percent per year, with an annual standard deviation of 32 percent. You have approached a buyer and would like the option to sell the land in 12 months for $1,470,000. The risk-free rate of interest is 4 percent per year, compounded continuously.

  

What is the price of the put option necessary to guarantee your sales price? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

  

Price of put option

$

Answer 1

We can use the Black-Scholes option pricing model in following manner to calculate the price of the put option necessary to guarantee your sales price.

INPUTS		Outputs	Value
Standard deviation or Volatility (Annual) (σ)	32.00%	d1	-0.05135
Time until Expiration (in Years) (t)	1.00	d2	-0.37135
Risk free rates (Annual) (r)	4.00%	N(d1)	0.47952
Current Market Price (S0)	$1,320,000	N(d2)	0.35519
Expected Future Price or Strike price (X)	$1,470,000	B/S call value (C )	131316.67
Dividend yield	0.00%	B/S Put Value (P)	223677.15

The price of the put option is $223,677.15

Formulas used in excel calculation: