Parimutuel Applications In Finance: New Markets for New Risks (Finance and Capital Markets Series)

Financial intermediaries supply derivatives to their customers when they can hedge the exposures from these transactions. A static hedge is typically employed by arranging an offsetting transaction with a different customer or a dynamic hedge by trading in the underlying derivatives. There is however a broad range of uncertain exposures where intermediaries tend not to offer derivatives or risk management products, as they are unable to hedge the resulting exposures. Baron and Lange suggest a parimutuel auction system adapted from the betting industry as a solution to this problem. They introduce the parimutuel mechanism and the modifications required to apply the mechanism to the capital markets. The PDCA auction and its mechanics are analyzed and finally the mathematics behind the system are described and illustrated. Includes a forward by Robert J. Shiller, the Stanley B. Resor Professor of Economics, Yale University Contents......Page 8 List of Figures......Page 11 List of Tables......Page 12 List of Symbols......Page 15 List of Acronyms......Page 19 Foreword......Page 20 Acknowledgments......Page 23 Introduction......Page 26 PART I: Introduction to Parimutuel Markets......Page 30 1.1 Review of derivatives contracts......Page 32 1.2 Review of derivatives trading......Page 34 1.3 Recent growth in derivatives markets......Page 36 1.4 Innovations associated with the recent growth in derivatives markets......Page 37 2.1 The basic mathematics of parimutuel matching......Page 40 2.2 Comparing parimutuel matching and bilateral matching......Page 48 2.3 Academic research on parimutuel wagering......Page 53 3.1 Parimutuel wagering applications......Page 62 3.2 Longitude's parimutuel innovations......Page 63 3.3 Parimutuel derivatives applications......Page 65 3.4 Related financial markets......Page 68 3.5 Related matching engines......Page 69 3.6 Reasons for the recent introduction of parimutuel matching to the derivatives markets......Page 75 4.1 Background and data on NFP......Page 78 4.2 Demand for derivatives on NFP......Page 79 4.3 Comparative advantages of parimutuel trading of NFP derivatives......Page 86 4.4 Design, mathematics, and dynamics of parimutuel derivatives auctions on NFP......Page 90 PART II: The Mathematics of Parimutuel Derivatives Auctions......Page 104 5 Derivative Strategies and Customer Orders......Page 106 5.1 Digital options, vanilla options, and forwards......Page 107 5.2 Customer orders in a parimutuel derivatives auction......Page 116 5.3 The state claims......Page 119 5.A Proof of Theorem 5.1......Page 127 6.1 Opening orders in a parimutuel derivatives auction......Page 129 6.2 The mathematical principles of the parimutuel equilibrium......Page 130 6.3 Properties of the parimutuel equilibrium......Page 148 6.A The parimutuel equilibrium with a discount factor......Page 156 6.B The price of a range forward and put-call parity......Page 157 6.C Equivalent formulas for the net auction premium......Page 160 6.D Self-hedging and relative-demand pricing are equivalent......Page 162 7 The Solution Algorithm for the Parimutuel Equilibrium Problem......Page 164 7.1 Part one of the solution algorithm......Page 165 7.2 Part two of the solution algorithm......Page 179 7.3 Complementary orders and part two of the solution algorithm......Page 183 7.A Computing net auction premium based on net customer payouts......Page 189 7.B Proofs of Theorems 7.1 and 7.2......Page 194 7.C Limit-price restrictions for complementary orders......Page 198 8 Mathematical Properties of Parimutuel Equilibrium Prices......Page 200 8.1 Unique prices with market orders......Page 201 8.2 Unique prices with market orders and limit orders......Page 209 8.A Proofs of Theorems from Section 8.1......Page 217 8.B Proof that GPEP prices are unique......Page 220 8.C Jacobian properties......Page 224 9.1 Example with Multiple Vectors of Customer Fills......Page 233 9.2 Theorems related to multiple vectors of customer fills......Page 239 9.3 Competing orders......Page 242 9.4 Competing orders and additional theorems......Page 247 9.5 Rank conditions, competing orders, and multiple vectors of customer fills......Page 249 9.A Proofs of the Theorems......Page 252 Notes......Page 261 References......Page 287 E......Page 300 M......Page 301 Z......Page 302 C......Page 303 G......Page 304 P......Page 305 R......Page 306 Z......Page 307 Financial intermediaries typically offer derivatives to their customers only when they can hedge the exposures from these transactions. Baron and Lange show that parimutuel auctions can be used by financial intermediaries to offer derivatives without exposing themselves to risk.