Abstract
This chapter provides the tools which are used in option pricing. The field of stochastic processes in continuous time which are defined as solutions of stochastic differential equations plays an important role. To illustrate these notions we use repeatedly approximations by stochastic processes in discrete time and refer to the results from Chapter 4.
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Bollerslev, T. P. (1990). Modelling the coherence in short-run nominal exchange rates: A multivariate generalized arch model, Review of Economics and Statistics 72: 498–505.
Bollerslev, T. P. (1990). Modelling the coherence in short-run nominal exchange rates: A multivariate generalized arch model, Review of Economics and Statistics 72: 498–505.
Hull, J. and White, A. (1990). Pricing interest rate derivatives., The Review of Financial Studies 3: 573–592.
Melino, A. and Turnbull, S. M. (1990). Pricing foreign currency options with stochastic volatility, Journal of Econometrics 45: 239–265.
von Weizsäcker, H. and Winkler, G. (1990). Stochastic integrals, Vieweg, Braunschweig.
Briys, E., Bellalah, M., Mai, H. and de Varenne, F. (1998). Options, futures and exotic derivatives, John Wiley and Sons, Chichester.
Briys, E., Bellalah, M., Mai, H. and de Varenne, F. (1998). Options, futures and exotic derivatives, John Wiley and Sons, Chichester.
Fan, J. and Yao, Q. (1998). Efficient estimation of conditional variance functions in stochastic regression., Biometrika 85: 645–660.
Jeantheau, T. (1998). Strong consistency of estimators for multivariate arch models, Econometric Theory 14: 70–86.
Lubrano, M. (1998). Smooth transition GARCH models: A Bayesian perspective, Technical report, CORE, Louvain-la-Neuve.
Mikosch, T. (1998). Elementary stochastic calculus with finance in view, World Scientific, Singapore.
Embrechts, P., McNeil, A. and Straumann, D. (1999a). Correlation and dependence in risk management: Properties and pitfalls, Preprint ETH Zürich.
Embrechts, P., McNeil, A. and Straumann, D. (1999b). Correlation: Pitfalls and alternatives, RISK May: 69–71.
Franke, J. (1999). Nonlinear and nonparametric methods for analyzing financial time series, in P. Kall and H.-J. Luethi (eds), Operation Research Proceedings 98, Springer-Verlag, Heidelberg.
Franke, J. and Klein, M. (1999). Optimal portfolio management using neural networks - a case study, Technical report, Department of Mathematics, University of Kaiserslautern.
Franke, J. (1999). Nonlinear and nonparametric methods for analyzing financial time series, in P. Kall and H.-J. Luethi (eds), Operation Research Proceedings 98, Springer-Verlag, Heidelberg.
Franke, J. and Klein, M. (1999). Optimal portfolio management using neural networks - a case study, Technical report, Department of Mathematics, University of Kaiserslautern.
He, C. and Teräsvirta, T. (1999). Properties of moments of a family of GARCH processes, Journal of Econometrics 92: 173–192.
Karatzas, I. and Shreve, S. (1999). Brownian motion and stochastic calculus, Springer-Verlag, Heidelberg.
Korn, R. (1999). Optimal portfolios: stochastic models for optimal investment and risk management in continuous time, World Scientific, Singapore.
Korn, R. and Korn, E. (1999). Optionsbewertung und Portfolio-Optimierung, Vieweg, Braunschweig.
Yang, L., Härdle, W. and Nielsen, J. (1999). Nonparametric autoregression with multiplicative volatility and additive mean, Journal of Time Series Analysis 20 (5): 579–604.
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Franke, J., Härdle, W., Hafner, C.M. (2004). Stochastic Integrals and Differential Equations. In: Statistics of Financial Markets. Universitext. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-10026-4_5
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DOI: https://doi.org/10.1007/978-3-662-10026-4_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-21675-9
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