Question

You own a lot in Key West, Florida, that is currently unused. Similar lots have recently sold for $1,210,000. Over the past five years, the price of land in the area has increased 5 percent per year, with an annual standard deviation of 32 percent. A buyer has recently approached you and wants an option to buy the land in the next 12 months for $1,360,000. The risk-free rate of interest is 3 percent per year, compounded continuously. How much should you charge for the option? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Call price= _________

Answer 1

d1 = [{ln(S0/X)} + {t(r - q + ²/2)}] / [(t)^1/2]

= [{ln($1,210,000/$1,360,000)} + {1.00(0.03 + 0.32²/2)}] / [0.32(1)^1/2]

     = -0.0357 / 0.32 = -0.1115

d2 = d1 - [(t)^1/2]

= -0.1115 - [0.32(1)^1/2]

= -0.1115 - 0.32 = -0.4315

C = [S0 x e^-qt x N(d1)] - [X x e^-rt x N(d2)]

         = [$1,210,000 x e^-0*1 x N(-0.1115)] - [$1,360,000 x e^-0.03*1 x N(-0.4315)]

         = [$1,210,000 x 1 x 0.4556] - [$1,360,000 x 0.9704 x 0.3331]

= $551,288.02 - $439,564.57 = $111,723.44