Option Contracts and Their Valuation

16 Pages Posted: 21 Oct 2008

See all articles by Robert S. Harris

Robert S. Harris

University of Virginia - Darden School of Business

Robert M. Conroy

University of Virginia - Darden School of Business

Abstract

This note introduces options (both calls and puts) and their valuation. After covering the history of options and the basic nature of their payoffs, the note provides an intuitive discussion of the determinants of an option's value. The note then introduces and applies the Black-Scholes option-pricing model to real data, using an Excel-based version of the model. Throughout, the emphasis is on the basics of options and their valuation.

Excerpt

UVA-F-1519

Option Contracts and Their Valuation

Every financial transaction involves a contract specifying when, to whom, and how money will be conveyed from one party to another. These contracts can be very simple, such as a car loan, or extremely complex, such as the financial arrangements for a leveraged buyout. All financial contracts ultimately specify when payments are due and how the payments are to be made. For example, when the U.S. government issues a bond, it receives cash today in return for a contract (the bond) that promises a series of future payments of interest and principal. Another example is when a firm issues new common stock and receives cash in return. The share of stock is just a contract that entitles the holder to certain voting rights and a pro rata share of the equity of the firm. For tradable assets, the original purchaser can then sell the contract to someone else. Financial-market prices reported in the newspaper or running across computer screens result from trading in these contracts. The variety of financial contracts is large and increasing all the time.

One contract of particular interest is the option. As its name implies, an option contract gives its owner the right (“option”), but not the obligation, to trade assets according to terms specified in the contract. Option contracts in one form or another play a major role in a wide array of settings. Option contracts on shares of stock are traded daily on exchanges around the world. Executives receive option contracts as part of their compensation. Corporate treasurers can buy options based on future interest rates or currency-exchange rates. Options and their valuation are the subjects of this note.

History of Option Contracts

Contracts involving options have been around for centuries. For instance, in medieval England, there was a prohibition against Christians paying or collecting interest on loans. This made making loans difficult, but people are always innovative. One particular innovation involved land. Often, a landowner wished to borrow money using land as security. As a mortgage that involved paying interest was prohibited, different contracts evolved. The landowner would transfer ownership of the land to the lender in return for an up-front cash payment. The lender, in turn, would hold the land and collect the revenues. At the end of an agreed-upon period, the original landowner would have the right to repurchase the land at an agreed-upon price. This is similar to a loan, but the form of the contract is different. Here, the land is sold to the lender, but the original landowner retains an option to repurchase the land. These types of case-specific options have long been used.

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Keywords: options, valuation, Black-Scholes option-pricing model

Suggested Citation

Harris, Robert S. and Conroy, Robert M., Option Contracts and Their Valuation. Darden Case No. UVA-F-1519, Available at SSRN: https://ssrn.com/abstract=1279955

Robert S. Harris (Contact Author)

University of Virginia - Darden School of Business ( email )

P.O. Box 6550
Charlottesville, VA 22906-6550
United States
434-924-4823 (Phone)
434-924-4859 (Fax)

HOME PAGE: http://www.darden.virginia.edu/faculty/harris.htm

Robert M. Conroy

University of Virginia - Darden School of Business ( email )

P.O. Box 6550
Charlottesville, VA 22906-6550
United States

HOME PAGE: http://www.darden.virginia.edu/faculty/conroy.htm

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