Financial Valuation Methodology

Aim

The course aims to develop an understanding of the valuation of financial derivatives, both through analytical expressions and numerical methods. Upon completion of the course, the student should be able to:

• Explain stochastic processes and related terminology, and solve simple stochastic differential equations.
• Demonstrate an understanding of stochastic calculus and its application in the valuation of financial derivatives.
• Describe and apply the fundamental theory of martingale pricing.
• Describe and apply methods for the numerical valuation of financial derivatives.
• Explain and apply models for the valuation of interest rate derivatives.

Content

• Stokastic processes and stochastic calculus.
• The Black-Scholes-Merton pde and alternative option pricing models (e.g., stochastic volatiliity).
• Numerical methods for derivatives valuation: Finite difference method and Monte Carlo simulation.
• Change of probability measure (Girsanov's theorem), risk neutral valuation and Feynman-Kac's theorem.
• Models for the term structure of interest rates (short rate models, affine term structure models and HJM) and valuation of interest rate derivatives.