Question

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The current price of asset W is $30. No cash distributions are expected for this asset...

The current price of asset W is $30. No cash distributions are expected for this asset for the next year. The one-year interest rate is 8%. The asset's price will be either $45 or $15 one year from now. What is the price of a European call option on asset W with a strike price of $5 that expires in one year's time?

Expert Solution

Calculation of price of European call option:

Given,

Spot price of asset W = $30

One year Interest rate = 8%

Asset price may go up to $45

Or May go down to $15

Strike price of call option = $5

Required: Price of European call option:

Up move factor(u) = 45÷30 = 1.5

Down move factor(d) = 15÷30 = 0.5

Interest rate factor(R) = 1.08

Probability of price going up(p)

= (R - d)÷(u - d) = (1.08 - 0.5)÷(1.5 - 0.5) = 0.58÷1 = 0.58

Therefore probability of price going down (1-p) = 1 - 0.58 = 0.42

If asset price goes up to 45, will exercise the call option hence pay off will be (45 - 5) = 40

If asset price goes down to 15, will exercise the call option hence pay off will be (15 - 5) = 10

Value of call option = (40×0.58 + 10×0.42)÷1.08 = 25.37

jeff jeffy answered 2 years ago

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