You own a lot in Key West, Florida, that is currently unused. Similar lots have

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. A buyer has recently approached you and wants an option to buy the land in the next 12 months for $1,420,000 million. The risk-free rate of interest is 5 percent per year, compounded continuously How much should you charge for the option? (Enter your answer in dollars, not millions of dollars, i.e. 1,234,567. Do not round intermediate calculations and round your answer to the nearest whole dollar amount. (e.g., 32) Call price

Explanation / Answer

Using Black Scholes Merton Model to calculate the call price:

For European options:

#

S = Stock price =

1270000

K = Strike price =

1420000

r = rate =

5.00%

e = exponential value = exp(1) =

2.71828183

t = time =

1

s = standard deviation or volatility =

36%

* 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(1270000/((1420000*EXP(-5%*1))))+0.5*36%^2*1)/(36%*1^0.5)                                                              

d1 =       0.008778            Hence, N(d1) = 0.503502           

              ------------------------------                                             

d2 = d1 - (s*t^0.5)                                                                   

=0.008778-(36%*1^0.5)                                                         

d2 =       -0.351222           Hence, N(d2) = 0.362710903     

              ---------------------------------                                                       

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

=1270000*0.503502-1420000*exp(-5%*1)*0.362711                                                               

C =         149,517                                                       

                                          

Call price = $149,517                                  

For European options:

#

S = Stock price =

1270000

K = Strike price =

1420000

r = rate =

5.00%

e = exponential value = exp(1) =

2.71828183

t = time =

1

s = standard deviation or volatility =

36%

* N(d1) is Normal distribution probability value

* N(d2) is Normal distribution probability value

Use normal distribution table

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