Nadima El-Hassan

Chiarella, C., El-Hassan, N. & Kucera, A. 2008, 'The evaluation of discrete barrier options in a path integral framework' in Kontoghiorghes, E; Rustem, B; Winker, P (eds), Computational Methods in Financial Engineering: Essays in Honour of Manfred Gilli, Springer, Germany, pp. 117-144.
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The pricing of discretely monitored barrier options is a difficult problem. In general, there is no known closed form solution for pricing such options. A path integral approach to the evaluation of barrier options is developed. This leads to a backward recursion functional equation linking the pricing functions at successive barrier points. This functional equation is solved by expanding the pricing functions in Fourier-Hermite series. The backward recursion functional equation then becomes the backward recurrence relation for the coefficients in the Fourier-Hermite expansion of the pricing functions. A very efficient and accurate method for generating the pricing function at any barrier point is thus obtained. A number of numerical experiments with the method are performed in order to gain some understanding of the nature of convergence. Results for various volatility values and different numbers of basis functions in the Fourier-Hermite expansion are presented. Comparisons are given between pricing of discrete barrier option in the path integral framework and by use of finite difference methods.

Colwell, D., El-Hassan, N. & Kwon, O. 2007, 'Hedging Diffusion Processes by Local Risk Minimization with Applications to Index Tracking', Journal of Economic Dynamics and Control, vol. 31, no. 7, pp. 2135-2151.
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This paper extends the local risk-minimization criterion for hedging contingent claims, as introduced in F?er and Sondermann [Hedging of non-redundant contingent claims. In: Hildenbrand, W., Mas-Colell, A. (Eds.), Contributions to Mathematical Economics. Elsevier Science, North-Holland, Amsterdam, pp. 205?223], F?er and Schweizer [Hedging of contigent claims under incomplete information. In: Davis, M., Elliot, R. (Eds.), Applied Stochastic Analysis, Stochastic Monographs, vol. 5, Gordon and Breach, London/New York, pp. 389?414] and Schweizer [Option hedging for semimartingales. Stochastic Processes and their Applications 37, 339?363], to the hedging of entire stochastic processes, and determines the necessary and sufficient conditions under which this is possible. The results are then applied to the problem of stock index tracking to obtain simple criteria for selecting the optimal set of assets with which to form tracker portfolios, and to derive a value-at-risk type measure for the set of assets used.

Chiarella, C., Craddock, M.J. & El-Hassan, N. 2003, 'An implementation of Bouchouev's method for a short time calibration of option pricing models', Computational Economics, vol. 22, no. 2-3, pp. 113-138.
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El-Hassan, N. & Kofman, P. 2003, 'Tracking error and active profolio management', Australian Journal of Management, vol. 28, no. 2, pp. 183-207.

Bhar, R., Chiarella, C., El-Hassan, N., Zheng, X. 2000, 'Reduction of forward rate dependent HJM models to Markovian form: pricing European bond options', Journal of Computational Finance, vol. 3, no. 3, pp. 47-72.