Question

MetLife, Inc. stock is currently trading at $50 per share. The price of MetLife stock can either increase by 20% or decrease by 20% each year. The probability of an increase is equal to the probability of a decrease (). The risk-free rate of return is 10% per year. What is the current equilibrium price (premium) of a 1-year European call option on MetLife with a strike price of $50?

Answer 1

Solution:

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

Sl.No.	Particulars	Notation	Value
1	Spot Price	SP0	$ 50.00
2	Strike Price	EP	$ 50.00
3	Expected future Spot price – Lower Limit - FP1 = ( $ 50 * ( 1 - 0.20 ) ) = ( $ 50 * 0.80 ) = $ 40	FP1	$ 40.00
4	Expected future Spot price – Lower Limit - FP1 = ( $ 50 * ( 1 + 0.20 ) ) = ( $ 50 * 1.20 ) = $ 60	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 - $ 50.00 = $ 10.00 ) ]	Cu	$ 10.00
7	Weight for the lower scenario [FP1 / SP0 ] = ( 40 / 50 ) =	D	0.80
8	Weight for the upper scenario [FP2 / SP0 ] = ( 60 / 50 ) =	U	1.20
9	Risk free rate of Return	R	0.10
10	Duration of the call	T	1 Year
11	Future value factor (Continuous Compounding factor) = er * t = e0.10 * 1 = e0.10 = 1.1052 ( Value taken from e tables)	F	1.1052

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:

= [ ( 10 * [ ( 1.1052 - 0.8 ) / ( 1.2 – 0.8) ] ) + ( 0 * [ (1.2 – 1.1052) / ( 1.2 – 0.8) ] ) ] / 1.1052

= [ ( 10 * [ (0.3052 )/( 0.4 ) ] ] / 1.1052

= [ 10 * 0.7630 ] / 1.1052

= 7.630 / 1.1052

= 6.903728

= 6.90 ( when rounded off to two decimal places )

= $ 7 ( when rounded off to the nearest dollar )

Therefore value of a call as per the Binomial Option pricing formula is $ 6.90