A financial derivative is a contract that derives its value from an underlying asset, such as a stock, bond, commodity, or currency. One example of a financial derivative is a put option.
A put option is a contract that gives the buyer the right, but not the obligation, to sell an underlying asset at a predetermined price (known as the strike price) within a specified period of time. The seller of the put option is obligated to buy the underlying asset at the strike price if the buyer exercises their right to sell.
To illustrate the payoff of a put option, let's consider an example. Suppose that an investor purchases a put option on 100 shares of a company's stock. The strike price is $50 per share, and the option expires in 3 months.
If the price of the stock falls below the strike price before the option expires, the investor can exercise their right to sell the stock at the higher strike price. For example, if the stock price falls to $40 per share, the investor can sell 100 shares at the strike price of $50 per share and make a profit of $10 per share, or $1,000 in total.
On the other hand, if the price of the stock remains above the strike price, the investor can simply let the option expire and not exercise their right to sell. In this case, the investor loses the premium paid for the option but does not incur any further losses.
We can represent the payoff of the put option using a payoff matrix. The matrix shows the profit or loss of the investor based on the stock price and the decision to exercise the option.
| Stock Price | Exercise Option | Don't Exercise Option |
|---|---|---|
| $30 | $2,000 | -$500 |
| $40 | $1,000 | -$500 |
| $50 | $0 | -$500 |
| $60 | -$500 | -$500 |
| $70 | -$1,500 | -$500 |
In this matrix, the positive numbers represent profits, and the negative numbers represent losses. The diagonal line represents the strike price of $50 per share. If the stock price falls below this level, exercising the option becomes profitable. If the stock price stays above this level, the option expires worthless.
In conclusion, a put option is a financial derivative that gives the buyer the right to sell an underlying asset at a predetermined price within a specified period of time. The payoff of a put option can be represented using a payoff matrix, which shows the profit or loss of the investor based on the stock price and the decision to exercise the option.
0 Comments