The Parimutuel Equilibrium

Abstract

The Parimutuel Equilibrium Problem (PEP) represents a flexible approach for trading derivatives using parimutuel methods. Chapter 5 introduced the first two mathematical principles of the PEP, and this chapter presents the three remaining mathematical principles of the PEP. We proceed as follows. Section 6.1 describes the opening orders, which have several uses in a parimutuel derivatives auction. Section 6.2 presents the third, fourth, and fifth mathematical principles of the PEP. The third principle is that the PEP prices are arbitrage-free. The fourth principle is that the prices and fills are “self-hedging,” which means that the net premiums collected fund the net payouts, regardless of the value of the underlying at expiration.¹ The fifth principle is that the PEP maximizes a measure of auction volume called “market exposure.” Based on the five PEP principles, we can present the complete mathematical specification of the PEP, which is done in Table 6.7 and in shorthand form in Equation (6.28). Section 6.3 describes in more detail the features of the PEP. Throughout this chapter, we once again illustrate the material using an example based on the US Consumer Price Index (CPI) as an underlying.²