Question

You own a one-year European call option to buy one acre of Los Angeles real estate. The exercise price is $2.11 million. Suppose the land is occupied by a warehouse generating rents of $205,000 after real estate taxes and all other out-of-pocket costs. The present value of the land plus the warehouse is $1.81 million. The annual standard deviation is 13% and the interest rate is 13%.

How much is your call worth?

Call value

Answer 1

The call option is similar to the call option on a dividend paying stock.paying $205000 dividend after one year, current price of $1.81 million and strike price of $2.11 million

Let the interest rate be continuously compounded

Adjusted Value of Real Estate today (S)  = $1810000 - 205000*exp(-0.13) = $1629990.44

Strike price (K) = $2110000

s= 13%

r= 13%

t=1

The price of the call option is given by

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

where d1= ( ln(S/K) + (r + s^2/2) *t ) / (s*t^0.5)

and d2 = ( ln(S/K) + (rd- s^2/2) *t ) / (s*t^0.5)

and N(d1) and N(d2) are the cumulative probability under Normal Distribution curve

Putting in the values

d1 =-0.92 and N(d1) = 0.1786582

d2 = -1.0504908 and N(d2) = 0.1467463

and

C= $19322.37

So, the value of the call option should be $19322.37