by Valery A. Kholodnyi and John F. Price Foundations of Foreign Exchange Option Symmetry introduces a fundamental symmetry in a foreign exchange market that associates financially equivalent options on opposite sides of the market. This symmetry holds in a general foreign exchange market environment, and requires no assumptions to be made on the nature of a probability distribution for exchange rates. In fact, this symmetry does not even require the existence of a probability distribution. Furthermore, the symmetry is applicable in two-currency or multiple-currency foreign exchange markets. The symmetry presented in Foundations of Foreign Exchange Option Symmetry has significant and far-reaching applications. The symmetry provides practical criteria for detecting a new type of true arbitrage in foreign exchange markets. The symmetry also offers a screen for testing consistency of option pricing models and a reduction in the cost of developing software for valuing and analyzing portfolios of foreign exchange options. In addition, the symmetry is not limited to foreign exchange markets, but remains valid for any financial markets. Foundations of Foreign Exchange Option Symmetry and a related book by the same authors, Foreign Exchange Option Symmetry (World Scientific Publishing Co., 1998) are both conceptually based on a book published by IES Press in August 1998: Beliefs-Preferences Gauge Symmetry Group and Replication of Contingent Claims in a General Market Environment by Dr. Valery A. Kholodnyi. Beliefs-Preferences Gauge Symmetry Group and Replication of Contingent Claims in a General Market Environment, which is based on Dr. Kholodnyi's original 1995 article of the same name, introduces to finance for the first time such fundamental notions from modern physics as observables, invariant or coordinate-free descriptions of phenomena, symmetries and related group-theoretical methods. Readership: Financial practitioners, researchers, mathematicians, physicists, engineers. Contents: Foreign Exchange Option Symmetry in a General Market Environment: Introduction; Notations and Results; Applications; Validity of the Symmetry Relationships for European Options; Validity of the Symmetry Relationships for Bermudan and American Options; Validity of the Symmetry Relationships for Barrier Options; Continuous Strike Range Call and Put Options; Conclusion. Foreign Exchange Option Symmetry in a Multiple Currency General Market Environment: Introduction; Graph Theoretic Formalism for a Map of the World Foreign Exchange Market; Vector Bundle Formalism for Foreign Exchange Contingent Payoffs; Particular Bases for the Vector Lattice of all Abstract Payoffs; Foreign Exchange Abstract Options. Valery A. Kholodnyi received his Ph.D. in Applied Mathematics from the Moscow Institute of Electronics and Mathematics in 1990. He has held university positions in various departments, such as the Department of Microwave and Quantum Electronics, the Department of Mathematical Modeling of Physical Processes, and the Department of Physics, in both Russia and the United States. He has authored or co-authored two other monographs and over 60 research papers in finance, mathematics, theoretical physics and engineering and has published in journals such as the Journal of Mathematical Physics, the Journal of Integral Equations and Applications, and Nonlinear Analysis, Theory, Methods and Applications. He was an Invited Speaker at the Second World Congress of Nonlinear Analysts and at numerous international and national conferences, as well as at research seminars in university departments and industry. Currently, he is the Vice-President of Research and Development for Integrated Energy Services, L.C., an independent research institute for financial capital markets.
John F. Price received his Ph.D. in Mathematics from the Australian National University in 1970 and has since held university positions in many countries, including Australia, Cambodia, Canada, England, Italy, Switzerland and the United States. He has published over 60 papers in mathematics, physics and finance in journals such as Advances in Mathematics, the Journal of Functional Analysis and Notices of the American Mathematical Society. He has also written articles for financial practitioners in Risk, Export Today and Derivatives Strategy, and has designed and implemented risk management software for major corporations.
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