Assume a call option on Greshak COrp currently sells for $6.00 in the market and

Question

Assume a call option on Greshak COrp currently sells for $6.00 in the market and the current rate on S-T Federal securities is 5.00%. The call option on Greshak's stock has 4 months to expiration and a strike price of $35.00. If the underlying shares of Creshak Corp sell for $46.00, what is the price of a put option with a $52.00 strick price and 4 months to expiration (assume the options are European style options)? Please show all work and use at least 4 decimal place for calculations and answer.

Explanation / Answer

Soln : Step 1 : As per Black scholes call option formula:

C = S*N(d1) - K*e-rt*N(d2)

Putting all corresponding values will give us

6 = 46*N(d1) - 35*e-0.05/3 *N(d2)

d1 = (ln(S/K) + (r+s2/2)*t)/s*t0.5 , here s = volatility of price

Also, d2 = d1 - s*t0.5 and N(d) can be calculated using the normal distribution z table.

On considering the value of s = 34%, in excel and hit and trial method we will get call option price = $6 approx.

We consider the same for put option

Again for Put option the black scholes formula is:

P =  K*e-rt*N(-d2) - S*N(-d1) =  K*e-rt*(1-N(d2)) - S*(1-N(d1)) = 52*e-0.05/3 (1-N(d2) ) - 46*(1-N(d1))

We need to calculate the values of N(d1) and N(d2) here

d1 = (ln(S/K) + (r+s2/2)*t)/s*t0.5 , on solving this with S = 46, K = 52 s = 34% , r = 5%

we will get d1 = -0.4232 and d2 = -0.6258

Putting these values and calculate N(d1) = 0.3372 and N(d2) = 0.2345 and using in binomial put option value, P = $8.65

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