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MetLife, Inc. stock is currently trading at $50 per share. The price of MetLife stock can...

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?

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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


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