Question

You own a lot in Key West, Florida, that is currently unused. Similar lots have recently sold for $1,340,000. Over the past five years, the price of land in the area has increased 8 percent per year, with an annual standard deviation of 31 percent. A buyer has recently approached you and wants an option to buy the land in the next 12 months for $1,490,000. The risk-free rate of interest is 4 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

We need to use Black-Scholes formula for calculation of call price. below is the formula.

Call price = S*e^-T*N(d₁) - K*e^-rT * N(d₂)

Where S = Stock price or in our case lot price of $1,340,000

K = strike price of the option i.e. $1,490,000

= dividend yield which is zero here

T = time which is 12 months or 1 year

N (d₁) = [ln(S/K) + (r - + 1/2*²)T]/*T

N (d₂) = N (d₁) -

   = annual standard deviation which is 31%

r = risk-free rate of interest which is 4 percent per year, compounded continuously

Call price = $1,340,000*e^-0*1*N{ln($1,340,000/$1,490,000) + [(0.04 - 0 + 0.31²/2) *1]/0.31} - $1,490,000*e^-0.04*1*N{ln($1,340,000/$1,490,000) + [(0.04 - 0 - 0.31²/2) *1]/0.31}

Call price = $1,340,000*1*N[(-0.1061 + 0.0881)/0.31] - $1,490,000*0.9608*N[(-0.1061 - 0.0081)/0.31]

Call price = $1,340,000*1*N(-0.0180/0.31) - $1,490,000*0.9608*N(-0.1142/0.31)

Call price = $1,340,000*1*-0.0581 - $1,490,000*0.9608*-0.3684

Call price = -77,854 - (-527,398.49) = -77,854 + 527,398.49 = 449,544.49