Question

Q29) The common stock of WIN is currently priced at $52.50 a share. One year from now, the stock price is expected to be either $54 or $60 a share. The risk-free rate of return is 4 percent. What is the per share value of one call option on WIN stock with an exercise price of $55?

$.51

$.45

$.48

$.39

$.41

Answer 1

Solution :

Sl.No.	Particulars	Notation	Value
1	Spot Price	SP0	$ 52.50
2	Exercise Price	EP	$ 55.00
3	Expected future Spot price – Lower Limit - FP1	FP1	$ 54.00
4	Expected future Spot price – Upper Limit FP2	FP2	$ 60.00
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 = ( $ 60.00 - $ 55.00 = $ 5.00 ) ]	Cu	$ 5.00
7	Weight for the lower scenario [FP1 / SP0 ] = ( 54 / 52.50 ) = 1.0286	d	1.0286
8	Weight for the upper scenario [FP2 / SP0 ] = ( 60 / 52.50 ) = 1.1429	u	1.1429
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:

= [ ( 5*[ (1.0408 – 1.0286 )/(1.1429 – 1.0286) ] ) + ( 0 *[ (1.1429 – 1.0408)/( 1.1429 – 1.0286) ] ) ] / 1.0408

= [ ( 5* [ (0.0122) / ( 0.1143 ) ] ] / 1.0408

= [ 5 * 0.106737 ] / 1.0408

= 0.533683 / 1.0408

= 0.512763

= 0.51 ( when rounded off to two decimal places )

Therefore the value of one call option on WIN stock as per the Binomial Option pricing formula is $ 0.51

Thus the solution is Option 1 = $ 0.51