Question

Calculate the call option value at the end of one period for a European call option with the following terms:

1. • The current price of the underlying asset = $80.
   • The strike price = $75
   • The one period, risk-free rate = 10%
   • The price of the asset can go up or down 10% at the end of one period.
2. What is the fundamental or intrinsic value?
3. What is the time premium?

Answer 1

A European option can be exercised only at expiration, and not at anytime before.

A European call option has value at expiration if the price of the underlying asset (S) > strike price of the option (X)

The value of a European call option in this case is given by S minus X (S - X)

However, at expiration, if the price of the underlying asset (S) < strike price of the option (X), the call option is worthless, and its value is zero.

Question b. :

• Fundamental/Intrinsic Value if asset price at the end of period goes up by 10% : (S - X)
  • S = 80*1.10 = 88
  • S - X = 13

• Fundamental/Intrinsic Value if asset price at the end of period goes down by 10% :
  • S = 80*0.90 = 72
  • The value of the call option here is zero as S < X

Question c. :

The time premium is calculated by Call Option Price (C) minus Intrinsic Value (V), or C - V

In this example, the current price of the underlying asset is $80. Hence the current Intrinsic Value (V) is $80 minus $75, or $5.

If the European Call Option is traded today at a price of, say $7. The time value or time premium in this case would be calculated by C ($7) - V ($5) = $2