Identifying a Put Option: Financial Claim Analysis

This example investigates a financial claim with a payoff dependent on the price of a risky asset. The asset has an initial value of 10 (S_0 = 10 at time t=0). At time t=1, the asset price can take on two values, S_1 = {3, 14}. The financial claim at time t=1 is defined as:

F = 0 if S_1 = 3

F = 5 if S_1 = 14.

The question is: Is F a call or a put? What is the strike price?

Answer: Put, k=14

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 specified date. In this scenario, the claim pays off only when the asset price is low (S_1 = 3). This aligns with the characteristics of a put option, where the holder benefits from a decrease in the underlying asset's price.

• Strike Price: The strike price is the price at which the holder can sell the asset. The claim pays off when the asset price falls below 14 (S_1 = 3), indicating that the strike price is 14 (k=14).