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
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 = [ ( Cu * [(f-d)/(u-d) ] ) + ( Cd * [ (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
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