Training course for PhD/Master students.
March 6th, 2021 at 4 p.m. (GMT+1).
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Prof. Nabil Tahani
School of Administrative Studies, York University, Canada.
Short Bio: Nabil Tahani is an Associate Professor of Finance at York University since 2004. He received his Ph.D. in Finance from HEC Montréal. His research interests include derivatives pricing, credit risk and more generally financial engineering, as well as personal finance and retirement planning. He has published in the Journal of Futures Markets, the Journal of Derivatives, the Multinational Finance Journal, Managerial Finance, Applied Mathematical Finance and the Financial Services Review. He has presented his work at several conferences and seminars around the world. He has taught different courses both at the undergraduate and graduate levels such as derivative securities, fixed income, risk management, corporate finance, probability and statistics. He was a visiting professor at Amsterdam Business School, University of Amsterdam, in February-March 2012, where he taught a graduate course in fixed income.
Title: On Some Numerical Techniques and the Pricing of Interest-Rate Derivatives
Abstract: This short seminar will introduce some numerical techniques applied to mathematical finance problems, such as the pricing of interest rate derivatives in continuous-time models. Particularly, it will focus on how some ODEs can be solved using Frobenius series expansion, and how the Gaussian quadrature rules can be used to compute the cumulative probabilities by inverting the corresponding characteristic function.
References:
Cox J., J. Ingersoll, and S. Ross, 1985, “A Theory of the Term Structure of Interest Rates”, Econometrica, Vol 53, 385-407.
Fong, G. H. and Vasicek, O.A., 1991, “Fixed-Income Volatility Management”, Journal of Portfolio Management, Summer, 41-46.
Geman, H., El Karoui, N. and Rochet, J.C., 1995, “Changes of Numeraire, Changes of Probability Measure and Option Pricing”, Journal of Applied Probability, Vol. 32 No. 2, 443-458.
Heston S.L., 1993, “A Closed-form Solution for Options with Stochastic Volatility, with Applications to Bond and Currency Options”, The Review of Financial Studies, Vol. 6, 327-343.
Jamshidian F., 1989, “An Exact Bond Option Formula”, Journal of Finance, Vol. 44, 205-209.
Kendall M., and A. Stuart, 1977. “The Advanced Theory of Statistics (Vol. 1)”, Macmillan Publishing Co., Inc., New York.
Munk C., 1999, “Stochastic duration and fast coupon bond option pricing in multi-factor models”, Review of Derivatives Research, Vol. 3 No. 2, pp. 157-81.
Selby M.J.P., and C. Strickland, 1995, “Computing the Fong and Vasicek Pure Discount Bond Price Formula”, Journal of Fixed Income, Vol. 5, 78-84.
Tahani N., 2004, “Valuing Credit Derivatives Using Gaussian Quadrature: A Stochastic Volatility Framework”, The Journal of Futures Markets, Vol. 24, 3-35.
Tahani N., and X. Li, 2011,“Pricing Interest Rate Derivatives under Stochastic Volatility”, Managerial Finance, Vol. 37, 72-91.
Vasicek, O.A., 1977, “An Equilibrium Characterization of the Term Structure”, Journal of Financial Economics, Vol. 5 No. 2, 177-188.
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