Question

You own a lot in Key West, Florida, that is currently unused. Similar lots have recently sold for $1,220,000. Over the past five years, the price of land in the area has increased 4 percent per year, with an annual standard deviation of 33 percent. A buyer has recently approached you and wants an option to buy the land in the next 12 months for $1,370,000. The risk-free rate of interest is 4 percent per year, compounded continuously. How much should you charge for the option?

Answer 1

Assuming European option and solving using Black Scholes model i.e. BSM

For European options:	#
S = Current price =	1220000
K = Expected price after a year =	1370000
r = rate =	4.00%
e = exponential value = exp(1) =	2.71828183
t = time =	1
s = standard deviation or volatility =	33%

* N(d1) is Normal distribution probability value

* N(d2) is Normal distribution probability value

Use normal distribution table

d1 = (Ln(S/(K*exp(-r*t))+0.5*s^2*t)/(s*t^0.5)                                                             

=(LN(1220000/((1370000*EXP(-4%*1))))+0.5*33%^2*1)/(33%*1^0.5)                                                              

d1 =-0.065181   Hence,

N(d1) = 0.474015           

---                                                                   

d2 = d1 - (s*t^0.5)                                                                   

d2 = -0.065181-(33%*1^0.5)                                                               

d2 =-0.395181   Hence, N(d2) = 0.346354657     

                                                                       

C = S*N(d1)-K*exp(-r*t)*N(d2)                                                           

=1220000*0.474015-1370000*exp(-4%*1)*0.346355                                                               

C =         122,398                                                       

Value of call option = 122,398