Dilip Madan

Madan's valuation model research has contributed to the improvement and development of valuation models in various fields including business and finance.[6] In his analysis of the impact of model risk on the valuation of barrier options, he highlighted the divergent pricing outcomes of up-and-out call options resulting from the use of different stochastic processes to calibrate the underlying vanilla options surface.[7] He conducted pricing comparisons between Sato processes and conventional models, revealing that Sato processes exhibit relatively higher pricing for cliquets, while effectively preserving the value of long-dated out-of-the-money realized variance options.[8] Focusing his research efforts on credit value adjustments, his study proposed a theory of capital requirements to address the problem of cross-default exposures.[9] Furthermore, he presented a Markov chain-based method for valuing structured financial products, offering financial institutions a tool to assess locally capped and floored cliquets, as well as unhedged and hedged variance swap contracts.[10] He also introduced a conic finance-based nonlinear equity valuation model, which integrated risk charges contingent upon measure distortions.[11] More recently in 2016 and 2022, he co-authored with Wim Schoutens two books titled Applied Conic Finance and Nonlinear valuation and non-Gaussian risks in finance, which provided an overview of the newly established conic finance theory, including its theoretical framework and various applications.[3]

Madan's options pricing research has focused on conducting empirical studies to test the performance of various option pricing models using real-world data.[12][13] While exploring the valuation of European call options employing the Vasicek-Gaussian stochastic process, his research proposed an approach to approximate and determine the equilibrium change of measure in incomplete markets, using log return mean, variance, and kurtosis.[14] In a collaborative study with Robert A. Jarrow, he demonstrated the application of term-structure-associated financial instruments in formulating dynamic portfolio management tactics, specifically aimed at mitigating distinct systematic jump hazards inherent in asset returns.[15] In his early works, he introduced the variance gamma process, a stochastic model for log stock price dynamics, highlighting its symmetric statistical density with some kurtosis and negatively skewed risk-neutral density with higher kurtosis.[16] His study further proposed using Markov Chains and homogeneous Levy processes, specifically the variance gamma process, as a robust modeling approach for financial asset prices, thereby facilitating the computation of option and series prices.[17] His research work on pricing European options involved exploring self-similar risk-neutral processes and proposing two parameter stability-based models, highlighting their usefulness in studying the time variation of option prices.[18] Concentrating his research on risk premia in options markets, he used the variance gamma model for density synthesis, revealing mean reversion and predictability in premia, with particular emphasis on short-term market crashes and long-term market rallies.[19] His recent work in 2021 has contributed to the understanding of risk-neutral densities and jump arrival tails by introducing theoretical examples and practical models based on quasi-infinitely divisible distributions.[20]

Madan's contributions to asset pricing research have resulted in the development of asset pricing models.[21] His early research examined the minimum variance estimator with the objective of achieving a singular optimal power and provided approximations for estimating the scalar diffusion coefficient through the application of Ito calculus and Milstein methods.[22] He also addressed the paradox posed by Artzner and Heath, offering a solution determining that completeness pertains to the topology of the cash flow space and is associated with the singular nature of the price functional in the topological dual space.[23] In 2001, he proposed a modeling approach for asset price processes[24] and illustrated that asset price dynamics are more suitably represented by pure jump processes, devoid of any continuous martingale component.[25] In his analysis of equilibrium asset pricing, his work established that factor prices are influenced by exponentially tilted prices due to non-Gaussian factor risk exposures, which can be determined from the univariate probability distribution of the factor exposure.[26] Moreover, with Wim Schoutens, he co-developed a technique that uses historical data to establish upper and lower valuations, leading to enhanced risk evaluation in the stock market through the integration of risk attributes into required returns.[27]

• Mathematical Finance – Bachelier Congress 2000 (2002) ISBN 9783540677819
• Structured Products (2008) ISBN 9781904339618
• Stochastic Processes, Finance and Control: A Festschrift in Honor of Robert J Elliott (2012) ISBN 9789814383301
• Applied Conic Finance (2016) ISBN 9781107151697
• Nonlinear Valuation and Non-Gaussian Risks in Finance (2022) ISBN 9781316518090

• Madan, D. B., & Seneta, E. (1990). The variance gamma (VG) model for share market returns. Journal of business, 511–524.
• Madan, D. B., Carr, P. P., & Chang, E. C. (1998). The variance gamma process and option pricing. Review of Finance, 2(1), 79–105.
• Carr, P., & Madan, D. (1999). Option valuation using the fast Fourier transform. Journal of computational finance, 2(4), 61–73.
• Carr, P., Geman, H., Madan, D. B., & Yor, M. (2002). The fine structure of asset returns: An empirical investigation. The Journal of Business, 75(2), 305–332.
• Bakshi, G., Kapadia, N., & Madan, D. (2003). Stock return characteristics, skew laws, and the differential pricing of individual equity options. The Review of Financial Studies, 16(1), 101–143.
• Carr, P., Geman, H., Madan D. B., and Yor, M. (2007). Self-Decomposability and Option Pricing. Mathematical Finance 17, 31-57.
• Cherny, A., and Madan, D. B. (2009). New Measures of Performance Evaluation. Review of Financial Studies. 12, 213-230.
• Eberlein, E., Madan, D. B., Pistorius, M., and Yor, M. (2014). Bid and Ask Prices as Non-Linear Continuous Time G-Expectations Based on Distortions. Mathematics and Financial Economics 8, 265-289.
• Elliott, R. J., Madan, D. B., and Wang K. (2022). High Dimensional Markovian Trading of a Single Stock. Forntiers of Mathematical Finance 1, 375-396.