Insegnamento a.a. 2005-2006

Go to class group/s: 31

GM-LS (6 credits - I sem. - AI) - MM-LS (6 credits - I sem. - AI) - OSI-LS (6 credits - I sem. - AI) - AFC-LS (6 credits - I sem. - AI) - CLAPI-LS (6 credits - I sem. - AI) - CLEFIN-LS (6 credits - I sem. - AI) - CLELI-LS (6 credits - I sem. - AI) - CLEACC-LS (6 credits - I sem. - AI) - DES-LS (6 credits - I sem. - AI) - CLEMIT-LS (6 credits - I sem. - AI) - CLG-LS (6 credits - I sem. - AI)

Course Director:
ANNA BATTAUZ

Course Objectives

This course is an introduction to the numerical techniques used in quantitative finance: we study the essential tools to understand and solve the basic issues of computation in financial engineering. Financial problems can be addressed and solved using discrete or continuous-time models. Unfortunately, most of the times we are forced to find a numerical answer to questions arising from practice. In a Black-Scholes market, for example, there is no closed formula for pricing finite-maturity American put options, and if the underlying stock pays some dividend during the life of the option, no formula is available neither for American call options. We face the same problem also in case of Asian options, whose payoff depends on the average value of the underlying asset. In this course we deal with the basic techniques that enable us to solve numerically the financial problems, such as Monte Carlo simulation and the solution of the Black-Scholes partial differential equations via finite-difference schemes. Moreover, we study some extensions and alternatives to the Black and Scholes model, whose importance is crucial for the quantitative analysis of modern financial markets, for example when dealing with credit risk models and the evaluation of defaultable securities.

Course Content Summary

• Pricing of European and American-type derivative securities in discrete time: algorithms and computational issues.
• Monte Carlo simulation and examples of variance reduction techniques.
• Finite difference schemes and the solution of partial differential equations for pricing European options.
• Extensions to the Black-Scholes model (time-varying coefficients, stochastic volatility, jump-diffusion processes).

Beyond these topics, we deal with the evaluation of path-dependent and exotic options; derivatives with several underlying assets; the change of numeraire and the risk-neutral evaluation; the American option problem, analytical approximations and the free-boundary formulation.
Time is devoted to the computer implementation of the discussed numerical methods.

Detailed Description of Assessment Methods

Student evaluation consists of a report and a short written exam.

Textbooks

• P. WILMOTT, Derivatives: the theory and practice of financial engineering, Chichester, John Wiley & Sons, 1998.

Exam textbooks & Online Articles (check availability at the Library)

Last change 10/05/2005 00:00