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Unformatted text preview: WEB CHAPTER I Options ...and Hedging web-options.tex: ©Ivo Welch, 2004. Confidential: Access by Permission Only! last file change: Feb 23, 2006 (15:35h). compile date: Thursday 30 th March, 2006 (14:02h). This chapter provides a brief introduction to the most important aspects of the area of options. It covers options basics, arbitrage relationships, put-call parity, the Black-Scholes formula (and binomial option pricing), and less traditional applications of option pricing methods—but all in a very condensed form. You may prefer to resort to a full book on options and derivatives if this chapter is too telegraphic for you. Anecdote : A Brief History of Options Options have been known since Aristotle’s time. The earliest known option contract is a real option. It was recorded by Aristotle in the story of Thales the Milesian, an ancient Greek philosopher. Believing that the upcoming olive harvest would be especially bountiful, Thales entered into agreements with the owners of all the olive oil presses in the region. In exchange for a small deposit months ahead of the harvest, Thales obtained the right to lease the presses at market prices during the harvest. As it turned out, Thales was correct about the harvest, demand for oil presses boomed, and he made a great deal of money. A few thousand years later, in 1688, Joseph de la Vega describes in Confusion de Confusiones how options were widely traded on the Amsterdam Stock Exchange. It is likely that he actively exploited put-call-parity, an arbitrage relation between options discussed in this chapter. In the United States, options were traded over-the- counter since the 19th centry. A dedicated option market, however, was organized only in 1973. Source: Wisegeek’s “What Are Futures?” 1 2 file=web-options.tex: LP Web Chapter I. Options. 1 · 1. Two Basic Derivatives: Call Options and Put Options A derivative (also known as a contingent claim ) is an investment whose value is itself deter- Base assets and Contingent Claims. mined by the value of some other underlying base asset. For example, a bet that a Van Gogh painting—the base asset—will sell for more than $1 million is an example of a contingent claim, because the bet’s payoffs are derived from the value of the Van Gogh painting (the underlying base asset). Similarly, a contract that states that you will make a cash payment to me that is equal to the square of the price per barrel of oil in 2010 is a contingent claim, because it depends on the price of the underlying base asset, oil. As with other financial contracts, we be- lieve that both parties engage in derivatives contracts because it makes them better off ex-ante. For example, your car insurance is a contingent claim that depends on the value of your car (the base asset). Having the insurance is valuable only if the underlying base asset has been in- volved in an unfortunate accident. Ex-ante, both the insurance company and you are better off contracting to this contingent claim than you would be without the insurance contract. Ex-post,contracting to this contingent claim than you would be without the insurance contract....
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