Question

Options Pricing Problem. Answer the following question Calculate the call option value at the end of one period for a European call option with the following terms: 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.

What is the fundamental or intrinsic value?

What is the time premium?

Answer 1

Answer-

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