Question

Franklin Resources stock is currently selling for $55.00 a share but is expected to either decrease to $49.50 or increase to $60.50 a share over the next year. The risk-free rate is 3 percent. What is the current value of a 1-year call option with an exercise price of $55?

		$2.95
		$3.21
		$3.47
		$3.73
		$3.96

Answer 1

Stock Price (S) = $55

Stock Price at Upmove (Su) = $60.5

Stock Price at Downmove (Sd) = $49.5

Risk Free Rate (r) = 3%

Strike Price (K) = $55

Using Risk - Neutral Arguement of Option Pricing, we can calculate value of 1 Year call option as follows:

UpMove (u) =

u = 60.5 / 55 = 1.1

DownMove (d) =

u = 49.5 / 55 = 0.9

Probability of Upmove =

Probability of Upmove =

Probability of Upmove = 0.65

Probability of Downmove = 1 - Probability of UpMove

Probability of Downmove = 1 - 0.65

Probability of Downmove = 0.35

Payoff at Upmove = Max($60.5 - $55, 0)

Payoff at Upmove = 5.5

Payoff at Downmove = Max($49.5 - $55, 0)

Payoff at Downmove = 0

Expected Payoff at Maturity = Probability of Upmove * Payoff at Upmove + Probability of Downmove * Payoff at Downmove

Expected Payoff at Maturity = 0.65 * 5.5 + 0.35 * 0 = $3.59

Present Value of Expected Payoff = $3.59 *

Present Value of Expected Payoff = $3.59 *

Present Value of Expected Payoff = $3.48

So, the Value of call option should be around $3.48 for Strike Price of $55. So, Option (c) i.e. $3.47 is correct.