Question

Queenstake Resources stock is currently selling for $30.00 a share but is expected to either decrease to $27 or increase to $33 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 $30?

		$1.63
		$1.71
		$1.94
		$2.02
		$1.85

Answer 1

Solution :

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

Sl.No.	Particulars	Notation	Value
1	Spot Price	SP0	$ 30.00
2	Exercise Price	EP	$ 30.00
3	Expected future Spot price – Lower Limit - FP1	FP1	$ 27.00
4	Expected future Spot price – Upper Limit FP2	FP2	$ 33.00
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 = ( $ 33.00 - $ 30.00 = $ 3.00 ) ]	Cu	$ 3.00
7	Weight for the lower scenario [FP1 / SP0 ] = ( 27 / 30 ) =	d	0.9
8	Weight for the upper scenario [FP2 / SP0 ] = ( 33 / 30 ) =	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:

= [ ( 3*[ (1.0408 - 0.9) / (1.1 – 0.9) ] ) + ( 0 *[ (1.1 – 1.0408) / ( 1.1 – 0.9) ] ) ] / 1.0408

= [ ( 3* [ (0.1408) / ( 0.2 ) ] ] / 1.0408

= [ 3 * 0.704 ] / 1.0408

= 2.1 / 1.0408

= 2.0176

= 2.02 ( when rounded off to two decimal places )

Therefore value of a call as per the Binomial Option pricing formula is $ 2.02

Thus the solution is Option 4 = $ 2.02