Question

You are attempting to value a call option with an exercise price of $140 and one year to expiration. The underlying stock pays no dividends, its current price is $140, and you believe it has a 50% chance of increasing to $160 and a 50% chance of decreasing to $120. The risk-free rate of interest is 10%. Based upon your assumptions, calculate your estimate of the the call option's value using the two-state stock price model. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Value of the call $

Answer 1

Current trading price=$140

It can go up =U=$160

It can go down=D=$120

Probability of going up=p=0.5

Probability of going down=1-p=0.5

Call strike price=$140(at the money)

Payoff if price goes up=(160-140)=$20

Pay off if it comes down=$0

Net expected payoff after one year=20*0.5+0= $ 10

Risk free Interest rate=10%=0.1

Present value of payoff=10/(e^0.1)= 9.048374

Call Option price= $ 9.05

Value of the Call

$9.05

			$160
		p=0.5
	$140
		1-p=0.5
			$120