Question

The price of Ervin Corp. stock will either be $61 or $90 at the end of the year. Call options are available with one year until expiration. Continuously compounded T-bills currently yield 5.07 %. Suppose the current price of Ervin stock is $76.

What is the value of the call option, using the risk-free approach, if the strike price is $75 per share? (Round answer to 2 decimal places. Do not round intermediate calculations).

Answer 1

The current stock price = 76. The stock price is expected to either go up to 90 or go down to 61

So u = 90/76 = 1.1842

d = 61/76 = 0.8026

Risk free rate, RFR = 5.07%

The risk neutral probability with which stock price can go up is given by the formula,

So   

p = 0.65011 = 65.011%

The risk neutral probability with which stock price can go down is given by, 1-p = 1-0.65011 = 0.349890 = 34.989%

Value of option after 1 year = Spot price - Strike price

Spot price after 1 year = 90 or 61. Strike price = 75.

If the stock price goes up to 90, it is beneficial for the call option holder, as it can be bought at 75 itself (lower than stock price of 90), by exercising the option.

If the stock price goes down to 61, call option will not be exercised (Strike price = 75 & the option holder will not pay a price higher than the stock price). So the value will be 0.

We know the risk neutral probabilities of the 2 scenarios. So we can find out the weighted average of the call option value as,

= (0.65011*15) + (0.34989*0) = 9.7517

Discounting the above value to get present value, using risk free rate,

Value of the call option = 9.7517 / (1+5.07%) = 9.28