Abstract
In this chapter we will introduce a general framework of financial market. In the first section we present some basic concepts and fundamental results on martingale methods in the pricing and hedging of European contingent claims under the Itô process setting. In Sect. 7.2 we show that within the diffusion process framework, the pricing and hedging of European contingent claims can be done through a PDE approach. In Sect. 7.3 we present two probabilistic methods for closed-form pricing of European options and illustrate these methods through examples. In the fourth section we briefly address the problem of pricing American contingent claims in diffusion models.
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References
Davis, M.H.A.: On Margrabe’s Formula. Mitsubishi Capital, London (1994)
Goldenberg, D.H.: A unified method for pricing options on diffusion processes. J. Financ. Econ. 29, 3–34 (1991)
Jacod, J., Yor, M.: Etude des solutions extrémales et representation integrable de solutions pour certains problèmes de martingales. Z.W. 38, 83–125 (1977)
Jiang, L.: Mathematical Models and Methods of Option Pricing. High Education Press, Beijing (2003, in Chinese)
Karatzas, I.: On the pricing of American options. Appl. Math. Optim. 17, 37–60 (1988)
Karatzas, I.: Lectures on the Mathematics of Finance. CRM Monograph Series, vol. 8. American Mathematical Society, Providence (1997)
Margrabe, W.: The value of an option to exchange one asset for another. J. Financ. 33, 177–186 (1978)
Musiela, M., Rutkowski, M.: Martingale Methods in Financial Modeling. Springer, Berlin/Heidelberg/New York (1997)
Wilmott, P., Dewynne, J., and Howison, S.: Option Pricing: Mathematical Models and Computations. Oxford Financial Press, and Oxford (1993)
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Yan, JA. (2018). Itô Process and Diffusion Models. In: Introduction to Stochastic Finance. Universitext. Springer, Singapore. https://doi.org/10.1007/978-981-13-1657-9_7
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DOI: https://doi.org/10.1007/978-981-13-1657-9_7
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