Nadima joined the School of Finance and Economics as a full-time staff member in July 1997. Her research interests include the pricing and hedging of complex derivatives, term structure modeling, risk management and portfolio attribution analysis. She has publications in a number of the leading international journals in finance including The Journal of Financial Engineering, Asian Capital Markets, Journal of Economic Dynamics and Control and Journal of Computational Finance.
Nadima also has considerable practical experience in derivative security pricing, hedging and risk management issues gained through her work experience in product development and risk management areas of the financial markets. As an academic, she has maintained links with industry through various collaborative projects.
Pricing and hedging of complex derivatives, term structure modeling, risk management and portfolio attribution analysis
Dewynne, J & El-Hassan, N 2017, 'The Valuation of Self-funding Instalment Warrants', International Journal of Theoretical and Applied Finance, vol. 20, no. 4, pp. 1-48.View/Download from: UTS OPUS or Publisher's site
We present two models for the fair value of a self-funding instalment warrant. In both models we assume the underlying stock process follows a geometric Brownian motion. In the first model, we assume that the underlying stock pays a continuous dividend yield and in the second we assume that it pays a series of discrete dividend yields. We show that both models admit similarity reductions and use these to obtain simple finite-difference and Monte Carlo solutions. We use the method of multiple scales to connect these two models and establish the first-order correction term to be applied to the first model in order to obtain the second, thereby establishing that the former model is justified when many dividends are paid during the life of the warrant. Further, we show that the functional form of this correction may be expressed in terms of the hedging parameters for the first model and is, from this point of view, independent of the particular payoff in the first model. In two appendices we present approximate solutions for the first model which are valid in the small volatility and the short time-to-expiry limits, respectively, by using singular perturbation techniques. The small volatility solutions are used to check our finite-difference solutions and the small time-to-expiry solutions are used as a means of systematically smoothing the payoffs so we may use pathwise sensitivities for our Monte Carlo 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.View/Download from: UTS OPUS or Publisher's site
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, MJ & 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.View/Download from: UTS OPUS or Publisher's site
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.View/Download from: UTS OPUS or Publisher's site
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.
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.View/Download from: UTS OPUS or Publisher's site
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.
El-Hassan, N 2005, 'Use of credit VAR models for measuring risk', Asia Risk Conference, Asia Risk Conference, -, Singapore.
Chiarella, C, Craddock, MJ & El-Hassan, N 2002, 'A short time expansion of the volatility function for the calibration of option pricing models', Society of Computational Economics Conference, Society of Computational Economics Conference, Aix-en-Provence, France.
Chiarella, C & El-Hassan, N 2001, 'Evaluating barrier options using Fourier-Hermite expansions', 8th Annual Asia-Pacific Finance Association Conference, Bangkok, Thailand.
Chiarella, C & El-Hassan, N 2000, 'The evaluation of point barrier options in a path integral framework', 4th Columbia-JAFFEE Conference Proceedings, Columbia-JAFFEE Conference, JAFFEE, Tokyo, Japan, pp. 103-126.
Chiarella, C, El-Hassan, N & Kucera, A 2000, 'The evaluation of multiasset European and American options via Fourier-Hermite series expansions', Sixth International Conference on Computing in Economics and Finance, Barcelona, Spain.
Chiarella, C, El-Hassan, N & Kucera, A 2000, 'The evaluation of point barrier options in a path integral framework', Seventh International Conference on Computational Finance/Forecasting Financial Markets, London, UK.
Chiarella, C, El-Hassan, N & Kucera, A 1997, 'Evaluation of derivative security prices in a path integral framework using Fourier-Hermite series expansions', JIC97, Japanese Association of Financial Econometrics and Engineering, Tokyo, Japan, pp. 350-372.
Colwell, DB, El-Hassan, N & Kwon, OK 2019, 'Variance minimizing strategies for stochastic processes with applications to tracking stock indices'.
© 2019 International Review of Finance Ltd. 2019 This paper extends the notion of variance optimal hedging of contingent claims under the incomplete market setting to the hedging of entire processes and applies the results to the problem of tracking stock indices. Sufficient conditions under which this is possible are given, along with the corresponding variance minimizing strategy. The performances of tracking error variance (TEV) minimizing, locally risk minimizing, and variance minimizing strategies in tracking stock indices are investigated using both simulated and historical market data. In particular, it is shown using S&P500 data over the period 2000 and 2015 that the TEV of the variance minimizing strategy is statistically lower than other strategies at the 95% confidence level for 6-month holding periods.
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.
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, Craddock, MJ & 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.
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'.