This module is not currently running in 2022 to 2023.
The aim of this module is to offer hands-on training in computational finance. Given proliferation of new financial products, finding their theoretical prices are now routine in financial industry. Hence, just knowing the theoretical foundations is, although indispensable, not enough for the students who seek their career as financial professionals. The module discusses two lines of computation ideas. The first approach is Martingale asset pricing, in which the students are expected to perform Monte Carlo simulations and use tree models to compute the theoretical prices of a wide range of financial derivatives. The second technique is finite difference methods to solve the Hamilton-Jacobi-Bellman pricing equations numerically. Both computational approaches are the acknowledged standards in a variety of modern quantitative finance suites used worldwide. The module starts with the theoretical foundations of each line of computation ideas and a short introduction to programming.
Total contact hours: 32
Private study hours: 118
Total study hours: 150
This is a compulsory module for the:
* MSc in Quantitative Finance and Econometrics
Technical notes (4000 words) (50%)
Take-home exam: (50%)
Reassessment Instrument: 100% coursework
Core reading
* Evans, Gwynne, Blackledge, Jonathan and Peter Yardley. Numerical methods for partial differential equations. Springer, 2000.
* Evans, Gwynne, Blackledge, Jonathan and Peter Yardley. Analytic methods for partial differential equations. Springer, 1999.
* Wilmott, Paul, Howison, Sam and Jeff Dewynne. The mathematics of financial derivatives: a student introduction. Cambridge University Press, 1995.
Recommended reading
* Björk, Thomas. Arbitrage theory in continuous time. 3rd Edition. Oxford University Press, 2009.
* Pliska, Stanley. Introduction to Mathematical Finance: Discrete Time Models. Blackwell, 1997.
This list will be augmented by the chapters from the Handbook of the Economics of Finance and articles from such journals as American Economic Review, Econometrica, Journal of Finance, Journal of Financial Economics, and Review of Economic Studies among others.
See the library reading list for this module (Canterbury)
On successfully completing the module students will be able to:
8.1. comprehensively understand martingale measure theory and dynamic optimization theory
8.2. critically understand and systematically apply Monte Carlo Method and Feynman-Kac's stochastic representation to quantify martingale measure problems
8.3. critically understand and systematically apply Tree Model and Finite Difference Method to quantify dynamic programming solutions of investor’s optimal choice
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