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.
El-Hassan, N. & Kofman, P. 2003, 'Tracking error and active profolio management', Australian Journal of Management, vol. 28, no. 2, pp. 183-207.
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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.
Chiarella, C., El-Hassan, N. & Kucera, A. 1999, 'Evaluation Of American option prices in a path integral framework using Fourier-Hermite series expansions', Journal Of Economic Dynamics & Control, vol. 23, no. 9-10, pp. 1387-1424.
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In this paper we review the path integral technique which has wide applications in statistical physics and relate it to the backward recursion technique which is widely used for the evaluation of derivative securities. We formulate the pricing of equity
Chiarella, C. & El-Hassan, N. 1997, 'Evaluation of derivative security prices in the Heath-Jarrow-Morton framework as path integrals using fast fourier transform techniques', Journal of Financial Engineering, vol. 6, no. 2, pp. 121-147.
Chiarella, C. & El-Hassan, N. 1996, 'A preference free partial differential equation for the term structure of interest rates', Financial Engineering and the Japanese Markets, vol. 3, no. 4, pp. 217-238.
Colwell, D.B., El-Hassan, N. & Kwon, O.K. 2016, 'Variance Minimizing Strategies for Stochastic Processes with Applications to Tracking Stock Indices'.
Chiarella, C., El-Hassan, N. & Kucera, A. 2004, 'Evaluation of point barrier options in a path integral framework using fourier-hermic expansion (QFRC paper #126)'.
Colwell, D., El-Hassan, N. & Kwon, O. 2004, 'Hedging processes by local risk-minimisation with applications to index tracking.'.
El-Hassan, N. & Kofman, P. 2003, 'Tracking error and active portfolio management (QFRC paper #98)', Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney.
Chiarella, C., Craddock, M.J. & El-Hassan, N. 2000, 'The calibration of stock option pricing models using inverse problem methodology', Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney.
Research Paper Number: 39 Abstract: We analyse the procedure for determining volatility presented by Lagnado and Osher, and explain in some detail where the scheme comes from. We present an alternative scheme which avoids some of the technical complications arising in Lagnado and Osher's approach. An algorithm for solving the resulting equations is given, along with a selection of numerical examples.
Bhar, R., Chiarella, C., El-Hassan, N. & Zheng, X. 2000, 'The reduction of forward rate dependent volatility HJM models to Markovian form: Pricing European bond option', Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney.
Research Paper Number: 36 Abstract: We consider a single factor Heath-Jarrow-Morton model with a forward rate volatility function depending upon a function of time to maturity, the instantaneous spot rate of interest and a forward rate to a fixed maturity. With this specification the stochastic dynamics determining the prices of interest rate derivatives may be reduced to Markovian form. Furthermore, the evolution of the forward rate curve is completely determined by the two rates specified in the volatility function and it is thus possible to obtain a closed form expression for bond prices. The prices of bond options are determined by a partial differential equation involving two spatial variables. We discuss the evaluation of European bond options in this framework by use of the ADI method.
Chiarella, C. & El-Hassan, N. 1999, 'Pricing American Interest Rate Options in a Heath-Jarrow-Morton Framework Using Method of Lines'.
We consider the pricing of American bond options in a Heath-Jarrow-Morton framework in which the forward rate volatility is a function of time to maturity and the instantaneous spot rate of
interest. We have shown in Chiarella and El-Hassan (1996) that the resulting pricing partial differential operators are two dimensional in the spatial variables. In this paper we investigate an
efficientnumerical method to solve there partial differential equations for American option prices and the corresponding free exercise surface. We consider in particular the method of lines which other
investigators (eg Carr and Faguet (1994) and Van der Hoek and Meyer (1997)) have found to be efficient for American option pricing when there is one spatial variable. In extending this method for the two
dimensional case, we solve the pricing equation by discretising the time variable and one state varialbe and using the spot rate of interest as a continuous variable. We compare our method with the lattice
method of Li, Ritchken and Sankarasubramanian (1995).
Chiarella, C. & El-Hassan, N. 1997, 'A Survey of Models for the Pricing of Interest Rate Derivatives'.