EOO Arbitrage Summary

The Concept:

The Trade is based on a disparity between the conventional wisdom in current option modeling and statistical reality. In essence it is a function of current option models being incorrect in their assessment of the differences between American style options and their European counterparts as they relate to Early Exercise premium.

It exists for several reasons:

1. Commonly used option models do not account for the correlation factor and term structure in underlying commodity movement. They do not have a coefficient for other futures as related to the spot month.
2. Their valuation of Early Exercise premium does not properly handicap liquidity gaps, leptokurtosis, jump diffusion and skew for options.
3. The correlation between interest rates and Early Exercise probability should not be the most important determinant of premium in Commodity Options.

Early Exercise Defined

Early Exercise is a function of Variation Margin in the Commodity markets. Variation Margin is a lending process that results from a trader’s inability to cross margin option profits with future’s losses as long as the option position exists.

Except for infrastructure and systemic risk, there is no material risk to the trader or his Prime Broker, but that Prime Broker may charge a fee for lending a trader’s own profits back to him for margining purposes. This phenomenon is tied to regulations in the industry.

Early Exercise Conditions

An option is considered eligible for early exercise when all of the following criteria are met:

1. The in-the-money (ITM) option trades at parity with the future (100 delta)
2. The value of the equivalent out-of-the-money (OTM) option is less than the cost of borrowing on the ITM option
3. The theta of the OTM option is less than the cost of carry per day on the ITM option.
4. There is liquidity in the corresponding OTM option

If any of these 4 conditions are not met, then it will not save money to exercise the ITM option. Consequently, assuming the other side of the trade borrows money at the same or better rate, any option exercised early not meeting the requirements above will be a profit for him.

The Trade:

A sale of the American style option and a buy of the European equivalent. It is a neutral trade from a volatility and directional perspective.

The Risks
Risks are minimal at the option level but potentially large at the systemic level.

The main risk is Early Exercise.

Early Exercise is a function of interest rates, direction, volatility and liquidity.

1. Interest rates- as these rise, money is lost in opportunity cost.
• Early Exercise probability change is little to none
2. As the market moves away from strikes, their chance of Early Exercise increases.
3. Volatility- As volatility decreases, the chance of Early Exercise increases.
4. Liquidity- as liquidity in options with a 3 less delta increases, the chances of Early Exercise increases.
5. Strike Selection- little understood but very important, it is a function of leptokurtosis, Skew and mean regression as they relate to option liquidity.
6. Diversification of Open Interest- the less counterparties there are on the trade, the more likely an “All or None” scenario for Early Exercise. Therefore, volatility of Early Exercise increases as number of counterparties decreases.

Profitable Exit

Exiting profitably is dependent on several factors:

1. Familiarity with the marketplace and its universe of counterparties
2. Familiarity with the nuances of the underlying commodity and its term structure
3. Option Risk management
4. A thorough statistical understanding of Early Exercise risk.

For more information, contact Vincent Lanci at (212) 223-1000.