Question

Concord stock is currently selling for $20.00 a share but is expected to either decrease to $18 or increase to $22 a share over the next year. The risk-free rate is 4 percent. What is the current value of a 1-year call option with an exercise price of $20? $1.35 $1.59 $1.78 $1.99 $2.14

Answer 1

Solution:

Sl.No.	Particulars	Notation	Value
1	Spot Price	SP0	$ 20.00
2	Exercise Price	EP	$ 20.00
3	Expected future Spot price – Lower Limit - FP1	FP1	$ 18.00
4	Expected future Spot price – Upper Limit - FP2	FP2	$ 22.00
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 = ( $ 22.00 - $ 20.00 = $ 2.00 ) ]	Cu	$ 2.00
7	Weight for the lower scenario [FP1 / SP0 ] = ( 18 / 20 ) =	d	0.9
8	Weight for the upper scenario [FP2 / SP0 ] = ( 22 / 20 ) =	u	1.1
9	Risk free rate of Return	r	0.04
10	Duration of the call	t	1 Year
11	Future value factor (Continuous Compounding factor) = er * t = e0.04 * 1 = e0.04 = 1.0408 ( Value taken from e tables)	f	1.0408

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*[ (1.0408 - 0.9)/(1.1 – 0.9) ] ) + ( 0 *[ (1.1 – 1.0408)/( 1.1 – 0.9) ] ) ] / 1.0408

= [ ( 2* [ (0.1408)/( 0.2 ) ] ] / 1.0408

= [ 2 * 0.704 ] / 1.0408

= 1.408 / 1.0408

= 1.352806

= 1.35 ( when rounded off to two decimal places )

Therefore value of a call as per the Binomial Option pricing formula is $ 1.35

Thus the solution is Option 1 = $ 1.35