Question

QUESTION 7

1. Agritech's stock is currently selling for $45.00 a share but is expected to decrease to either $40.50 or increase to $49.50 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 $45?

   		$2.84
   		$2.62
   		$2.48
   		$2.26
   		$3.04

Answer 1

Step 1 : Fist Find out the Pay off in all States
Upstate Payoff : Cu		= max { 0 , $49.5 - $45 }
		= max { 0 , $49.5 - $45 }
		= $4.5
Downstate Payoff : Cd		= max { 0 , Sd - X }
		= max { 0 , $40.5 - $45 }
		= loss , so option will not be exercise
Step 2 : Calculate Hedge Ratio
	H =	Cu - Cd
		Su - Sd
	Where,
	Cu =	Upstate Payoff
	Cd =	Downstate Payoff
	Su =	Upper Price
	Sd =	Lower Price
	=	$4.50 - 0
		$49.50 - $40.50
	=	$4.50 / $9
		0.50

Step 3 : Hedge Portfolio
Upstate =	Hedge Ratio * Su - Cu
=	0.50 * 49.5 - 4.5
=	20.25
Downstate=	Hedge Ratio * Sd - Cd
=	0.50 * 40.5 - 0
=	20.25
Step 4 : Find The Present Value
	Payoff is risk free
	means rate of return on the portfolio is risk free rate
	payoff is today is be worth the present value of that payoff
PV (20.25)	Payoff
	1 + Risk-free rate
	$20.25
	1.03
	= $19.660194
Step 5 : Current Value
PV ($20.25) =	Hedge Ratio * So - Co
$19.660194 =	0.50 * $45 - Co
Co =	$22.50 - $19.660194
Current Value	$2.84
Option	I