# Dynamic Hedging Managing Vanilla and Exotic Options - Nassim T.

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Other Nonmarket Forms of Arbitrage

Many types of arbitrages, including the following, do not fall within the scope of this book because of their nonmarket orientation:

• Credit Arbitrage. It denotes acquiring debt in one security at a cheaper price than the debt in another. This is generally done as a passive arbitrage activity, defined earlier. It is usually difficult to short a corporate bond because of the occasional difficulties in borrowing them. However, a bonds portfolio manager can improve his expected return and maintain the overall rating in his portfolio by optimizing the mix between issues and swapping the expensive ones for better value bonds. Credit rating is not a market function, and as a trader first and last, the author recommends listening to the market rather than to the credit agencies in the definition of ranking. Such skepticism would therefore invalidate many perceived "value trades" and arbitrages.

• Tax Arbitrage. Many equity swaps are due to the privileged tax treatment of one party in the market. That party can then arbitrage its condition by transferring the tax to the other party for a profit. For example, German tax laws impose a dividend withholding tax on foreign, but not domestic, investors. A foreigner can replicate the position by entering in a transaction with a domestic German entity that matches the payoff of the equity swap. The German party can arbitrage the situation by buying the equities and selling the forward to foreign counterparties.

Arbitrage and the Arbitrageurs 87

• Legal Arbitrage. Some parties are disallowed by their authorities or their bylaws to engage in some specific transactions. Domestic French residents, to give an example, were banned at some point in the 1980s from buying puts or shorting their currency. Another case of legal arbitrage is the structured note market where the payoff is tied to the performance of some market, hence includes an option, but is flowering with fund managers who are not allowed to buy options. The law is skirted through the veil of the note and the fund manager is then "trapped" since he cannot deconstruct the note himself and needs to go to the bank to secure a market for the option.

Arbitrage and the Variance of Returns

The definition of arbitrage is becoming controversial as many forms of trading defined as arbitrage often carry a higher variance of returns than outright directional trading. This is partly because the average arbitrageur carries larger amounts on his books than the average speculative trader. It is also due to the accumulation of positions by like-minded arbitrageurs, which puts the pressure on relationships. When a security becomes perceived as expensive, there will be a rush of traders shorting it and buying a similar instrument. If the security stays so for a longer time owing to a specific buyer, the accumulation will turn too large for the arbitrage community to handle and traders will reach their limits. As the arbitrage community reaches its saturation level, pressure on the relationship between what is deemed expensive and what is deemed cheap will cause severe marks-to-market losses. Liquidation of the less capitalized arbitrageurs will ensue.

"Inefficiencies in the market will last longer than traders can remain solvent," an option trader once said. *

More advanced notions of arbitrage and stochastic dominance are presented in Module F.

Chapter Î

Volatility and Correlation

What traders and historians share is an ingrained distrust of the notion of correlation.

An option veteran

This chapter introduces the notion of volatility using minimum mathematics. The reader should try to develop a sense of where the notion of volatility can be ambiguous.

¦ Volatility is best defined as the amount of variability in the returns of a particular asset. (As will be discussed, there are many variations in the methods of measurement):

• Actual volatility is the actual movement experienced by the market. It is often called historical, sometimes historical actual.

• Implied volatility is the volatility parameter derived from the option prices for a given maturity. Operators use the Black-Scholes-Merton formula (and its derivatives) as a benchmark. It is therefore customary to equate the option prices to their solution using the Black-Scholes-Merton method, even if one believes that it is inappropriate and faulty, rather than try to solve for a more advanced pricing formula.

¦ Correlation refers to the least-square measured association between two random variables. It identifies the degree of certainty with which a person can predict the move in one random variable as a result of a change in the other variable. The random variables concerned are the logarithmic returns of the assets [or Log (Price Period t) — Log (Price Period t — 1)].

• Actual correlation is the amount of actual association between the moves of two markets. It is often called historical, sometimes historical actual.

• Implied correlation is the correlation parameter derived from option prices of the components. There will be as many implied correlations as existing maturities. (Module D includes an explanation for calculating the implied correlation using the triangle.)

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