Question

Helios' stock is currently selling for $82.00 a share but is expected to decrease to either $77.90 or increase to $90.20 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 $82?

		$4.25
		$3.95
		$3.65
		$2.75
		$0.00

Answer 1

Let S⁺ be the expected upward stock price in one year, S^-, expected downward price and X be the exercise price.

Call value in 1 year, if price increases, c⁺ = Max(0,S⁺-X) = Max(0,90.2-82) = $8.20

Call value in 1 year, if price goes down, c^- = Max(0,S^--X) = Max(0,77.90-82) = 0

Hedge ratio (h) = (c⁺-c^-)/(S⁺-S^-)

= (8.20-0)/(90.2-77.9)

= 0.66667

According to no-arbitrage approach

c = hS + PV(-hS^-+c^-)

Where, c is current value of call option

PV is present value factor

S is current stock price

c = 0.66667*82 + [1/(1+0.03)]*(-0.66667*77.90+0)

= 54.67-50.42

= 4.25

Therefore, the current value of 1 year call option is $4.25