The Department of Finance and Risk Engineering welcomes Sanjay K. Nawalkha, Professor of Finance, University of Massachusetts, to the BQE Lecture Series.
A Theory of Equivalent Expectations Measures for Expected Prices of Contingent Claims
This paper introduces a theory of equivalent expectation measures, such as the R measure and the R1T measure, generalizing the martingale pricing theory of Harrison and Kreps (1979) for deriving analytical solutions of expected prices (both the expected current price and the expected future price) of contingent claims. We also present new R-transforms which extend the Q-transforms of Bakshi and Madan (2000) and Duffie et al. (2000), for computing the expected prices of a variety of standard and exotic claims under a broad range of stochastic processes. Finally, as a generalization of Breeden and Litzenberger (1978), we propose a new concept of the expected future state price density which allows the estimation of the expected future prices of complex European contingent claims as well as the physical density of the underlying asset's future price, using the current prices and only the first return moment of standard European OTM call and put options.
Sanjay Nawalkha is a Professor of Finance at the Isenberg School of Management. His areas of research are fixed income valuation, derivative pricing, and asset pricing. Professor Nawalkha chaired the Finance Department at the Isenberg School of Management from Sept. 2011 until August 2018. He has co-authored four books, Dynamic Term Structure Modeling: The Fixed Income Valuation Course (Wiley & Sons, 2007), Interest Rate Risk Modeling: The Fixed Income Valuation Course (Wiley & Sons, 2005), Interest Rate Risk Measurement and Management (Institutional Investors, 1999) and Closed-Form Duration Measures and Strategy Applications (The Research Foundation of the Institute of Chartered Financial Analysts, 1990). He has published over 35 scholarly articles in the areas of term structure modeling, risk management, and arbitrage pricing theory.