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 (pu=pd= 0.5). 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

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Answer:

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