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Statement of Research Interests
Overview My research interests are in financial engineering, mathematical and computational finance. My dissertation focuses on stochastic modeling of credit and equity risk. The celebrated Black-Scholes-Merton option pricing model (Black & Scholes 1973, Merton 1973) set the mathematical foundation for pricing options and other financial securities. However, the accumulated empirical evidence, including the current and on-going problems in the credit markets, have made it clear that some of the fundamental assumptions in the original Black–Scholes–Merton framework do not hold. On one hand, assumptions such as continuity of the stock price process and the constant volatility of the stock returns contradict market evidence that shows that unexpected news can abruptly shift stock prices and that assets become more volatile as their prices drop. On the other hand, credit risk, or the risk of an obligor failing to repay the principal and interests on his/her issued debt in a timely manner is also absent in the Black–Scholeframework, since it assumes that the stock price is a stochastic process with infinite lifetime. My dissertation research consolidates the credit and equity risk into a unified class of models called hybrid credit-equity models.
Using time-changed Markov process and the spectral theory, I develop a rich class of analytical tractable models that include jumps, stochastic volatility, and default. As part of this research, I have developed an analytical methodology to price an insurance-type financial instrument that provides protection if the underlying firm defaults or if its stock price drops significantly (the so-called equity default swap (EDS)). My current research is devoted to developing models of correlated defaults in a multi-firm setting where I study the so-called “clustering effect” in which adverse market conditions could potentially trigger defaults of multiple firms at the same time. 我要提问
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