Financial Engineering Workshop - Zhenyu Cui (Stevens Institute of Technology)

Zhenyu Cui is an Assistant Professor in Financial Engineering, Stevens School of Business. He will be giving an online seminar titled "Applications of the Dirac Delta Family Method in Implied Volatility, Risk-neutral Density, and High-dimensional Stochastic Control" on Wednesday 9th February 2022 from 18:10 - 19:15.

Abstract
In this talk, the Dirac Delta family method is introduced, which is based on orthogonal polynomial representations of the Dirac Delta function. We show how this method can lead to new valuation results in three financial applications. First, when combined with the change of variable technique, we obtain an explicit model-free formula for the Black-Scholes implied volatility. The formula is expressed through either a limit or as an infinite series of elementary functions, and we establish that the proposed formula converges to the true implied volatility value. Numerical and empirical examples illustrate the accurateness of the formula. Second, when combined with the celebrated Carr-Madan spanning formula, we derive a novel model-free representation of the risk-neutral density in terms of market-observed options prices. Compared to the widely used method for obtaining the risk-neutral densities via the Breeden–Litzenberger device, our method yields estimates of risk-neutral densities that are model-free, automatically smooth, and in closed-form. Third, when applied to calculating the conditional expectations arising from dynamical programming, we show that it leads to a novel numerical time-stepping approach for solving corresponding HJB system. We demonstrate the accuracy and efficiency of the method through solving some one-dimensional and two-dimensional control problems.

Bio
Zhenyu Cui is currently an Assistant Professor of Financial Engineering in the School of Business at Stevens Institute of Technology. His research interests lie in derivatives valuation, Monte Carlo simulation, and optimal control. His research has been published in Mathematical Finance, Econometric Theory, Journal of Economic Theory, European Journal of Operational Research, and INFORMs Journal on Computing.

The Financial Engineering Workshop will take place online via Zoom.

To access the link to the online seminar, please register before 2pm on the day of the seminar otherwise you will not be given access.

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