Nonparametric Finance

Chapter 17Option Strategies

Optionscan be used to create almost any type of a profit function. Trading with stocks allows the possibility of short selling and leveraging, but options open up a huge number of possibilities for creating a payoff that suits the expectations and the risk profile of an investor. For example, a protective put can be used to protect a portfolio of stocks from negative returns, and a straddle can be used to profit simultaneously from large positive and large negative returns of the stock.

We describe option strategies in three ways: the profit function, the return function, and the return distribution. The profit function shows the profit of the option strategy at the expiration, as a function of the value of the underlying. For example, the profit function of a long call strategy is equal to

17.1

where is the stock price at the expiration, is the strike price, is the premium of the call, and is the interest rate.¹ The return function shows the gross return ...