Understanding Call Options: Example with Initial Value, Payoff, and Strike Price

This example demonstrates how to identify a call option based on its payoff structure. Consider a risky asset with an initial value of 10 (i.e. S_0 = 10 at time t=0), and at time t=1, S_1 = {3,14}. There is also a financial claim at time t=1 defined as follows:

F = 0 if S_1 = 3

F = 5 if S_1 = 14.

The claim F is a call option, and the strike price is 3. This is because the payoff is positive only when the asset price (S_1) is greater than the strike price (3). In this case, the option holder receives a payout of 5 when the asset price reaches 14.