Question

GoodLife stock is currently selling for $25.00 a share but is expected to either decrease to $22.50 or increase to $27.50 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 $25?

		$1.35
		$1.58
		$1.77
		$1.94
		$2.03

Answer 1

Solution :

Calculations as per the Binomial Options pricing model for obtaining the value of a call:

Sl.No.	Particulars	Notation	Value
1	Spot Price	SP0	$ 25.00
2	Exercise Price	EP	$ 25.00
3	Expected future Spot price – Lower Limit - FP1	FP1	$ 22.50
4	Expected future Spot price – Upper Limit FP2	FP2	$ 27.50
5	Value of call at lower limit [ Action = Lapse, Since FP1 < EP. Therefore value = Nil ]	Cd	NIL
6	Value of call at upper limit [ Action = Exercise, Since FP2 > EP. Therefore value = ( $ 27.50 - $ 25.00 = $ 2.50 ) ]	Cu	$ 2.50
7	Weight for the lower scenario [FP1 / SP0 ] = ( 22.50 / 25 ) =	d	0.9
8	Weight for the upper scenario [FP2 / SP0 ] = ( 27.50 / 25 ) =	u	1.1
9	Risk free rate	r	0.03
10	Duration of the call	t	1 Year
11	Future value factor (Continuous Compounding factor) = er * t = e0.03 * 1 = e0.03 = 1.0305 ( Value taken from e tables)	f	1.0305

As per the Binomial Option Pricing formula the value of a call is given by the following formula:

Value of a Call = [ ( C_u * [(f-d)/(u-d) ] ) + ( C_d * [ (u-f)/(u-d) ] ) ] / f

Therefore applying the values from the table above to the formula we now have:

= [ ( 2.50*[ (1.0305 - 0.9)/(1.1 – 0.9) ] ) + ( 0 *[ (1.1 – 1.0305 )/( 1.1 – 0.9) ] ) ] / 1.0305

= [ ( 2.50* [ (0.1305)/( 0.2 ) ] ] / 1.0305

= [ 2.50 * 0.6525 ] / 1.0305

= 1.631250 / 1.0305

= 1.582969

= 1.58 ( when rounded off to two decimal places )

Therefore value of a call as per the Binomial Option pricing formula is $ 1.58

Thus the solution is Option 2 = $ 1.58