By Jeffrey Lange* and Nicholas Economides**
Revised August 2003
Parimutuel principles are widely used as an alternative to fixed odds gambling in which a bookmaker acts as a dealer by quoting fixed rates of return on specified wagers. A parimutuel game is conducted as a call auction in which odds are allowed to fluctuate during the betting period until the betting period is closed or the auction "called." The prices or odds of wagers are set based upon the relative amounts wagered on each risky outcome. In microstructure terms, wagering under parimutuel principles is characterized by (1) call auction, non-continuous trading; (2) riskless funding of claim payouts using the amounts paid for all of the claims during the auction; (3) special equilibrium pricing conditions requiring the relative prices of contingent claims equal the relative aggregate amounts wagered on such claims; (4) endogenous determination of unique state prices; and (5) higher efficiency.
Recently, a number of large investment banks have adopted a parimutuel mechanism for offering contingent claims on various economic indices, such as the U.S. Nonfarm payroll report and Eurozone Harmonized inflation. The parimutuel mechanism employed is a call auction lasting about one hour for claims on the underlying index which include a variety of standard and exotic derivatives, including vanilla call and put options, forwards, digital options, range binary options, and linked buy/sell options such as risk reversals. A unique feature of the microstructure is that all of the claims offered are priced in equilibrium based upon a certain type of implementation of parimutuel mechanism principles. Our aim is to formalize these principles and point out some of the inherent advantages of the mechanism as applied to the recent auctions. Our paper shows how the market microstructure incorporating parimutuel principles for contingent claims which allows for notional transactions, limit orders, and bundling of claims across states is constructed. We prove the existence of a unique price equilibrium for such a market and suggest an algorithm for computing the equilibrium.
We also suggest that for a broad class of contingent claims, that the parimutuel microstructure recently deployed offers many advantages over the dominant dealer and exchange continuous time mechanisms. First, the parimutuel mechanism does not require a discrete order match between two counterparties. Instead, orders are executed multilaterally. All executed order premium is used to fund all of the contingent in-the-money options, i.e., the payouts. Second, we believe the transparent and straightforward pricing mechanism will be attractive to market participants. We believe that the success of the parimutuel mechanism in the wagering markets can, with the modifications which have been made to the mechanism, be carried over into the capital markets. Third, we believe that the risk neutral and self-hedging nature of the parimutuel mechanism, from the perspective of the broker/dealer or other entity which hosts the auction, offers a superior tradeoff between the risk of derivatives dealing and the compensation for providing liquidity for contingent claims. Fourth, we have shown that the Parimutuel mechanism as implemented in this paper is more efficient than other trading mechanisms. Finally, we believe that the parimutuel microstructure is ideally suited for completing some markets where there currently is an absence of liquidity, such as contingent claims on mortgage prepayment speeds, corporate earnings, weather, and economic statistics, such as the recent Eurozone inflation auction.
* Longitude Inc., (212) 468-8509, fax (212) 468-8509, email: email@example.com, www: http://www.longitude.com/** Stern School of Business, New York, NY 10012, tel. (212) 998-0864, fax (212) 995-4218, e-mail: firstname.lastname@example.org, www: http://www.stern.nyu.edu/networks/