Identifying Call or Put Options: A Financial Claim Example

This example illustrates the concept of a financial claim based on the price movement of a risky asset. Consider a risky asset with an initial value of 10 (i.e. S_0 = 10 at time t=0), and at time t=1, its value S_1 can be either 3 or 14, represented as S_1 = {3, 14}. We have a financial claim at time t=1 defined as follows:

F = 0 if S_1 = 3

F = 5 if S_1 = 14

The question is: Is F a call or a put option? And what is the strike price?

Answer:

The claim is a put option with a strike price of k=25.

Explanation:

• Put Option: A put option gives the holder the right, but not the obligation, to sell an asset at a predetermined price (the strike price) on or before a specific date. In this case, when the asset value (S_1) is 3, the claim (F) is 0, meaning the holder of the claim benefits from the lower price. This is characteristic of a put option.

• Strike Price: The strike price is the price at which the holder of the option can buy or sell the underlying asset. To find the strike price, we need to understand the payoff structure of the put option. We see that the claim has a payoff only when the asset price is low (S_1 = 3) and this payoff is 0. If the asset price is high (S_1 = 14), the claim has no value (F = 5). This suggests that the strike price must be higher than 3 and lower than 14. Therefore, the only possible strike price is k=25. Since the payoff is 0 when S_1 = 3, the strike price k = 25 results in a payoff of 0 when S_1 = 3, which aligns with the defined claim.