Option Trading: Pricing and Volatility Strategies and Techniques

CHAPTER 3

Arbitrage Bounds for Option Prices

Before we even consider any models for pricing options, we can make some statements about option values. These are based on the principle of no arbitrage.

This is probably the closest thing finance has to a fundamental law. Sometimes known as the “law of one price,” this states that if two securities are the same, then they will have the same price. If they do not, then traders called arbitrageurs will trade the securities and make a risk-free profit. Making money with no risk is very difficult, so these opportunities tend to arise infrequently. Moreover, once these divergences from value do occur, the trading action of arbitrageurs tends to eliminate the discrepancy. Thus the law of no arbitrage is somewhat self-fulfilling. This concept is crucially important so we will look at some simple examples.

First, imagine we can buy a share of Microsoft on one exchange for $32.00 and sell it immediately on another for $32.02. These shares are exactly the same, so by doing this we would make 2 cents with no risk. Note that to do this our trading costs would need to be less than one cent per share (as we have traded two shares in total). Sometimes what appears to be an arbitrage opportunity is merely a situation with larger than anticipated transaction costs. Second, there will be an instant when we own a share and have not yet sold one (or vice versa). If the price changes in this time we can lose money. This is an example of execution risk. ...