Advanced Financial Engineering - Interest Rate Derivatives in C++  Short Courses

What will I learn?

• Different representations of interest rates as zero rates, forward rates and instantaneous forward rates and their equivalence.
• Libor and forward Libor; properties of interest rates
• "Linear" interest rate instruments and their pricing: Forward Rate Agreements, bonds, interest rate swaps.
• Calibrating a yield curve to market prices of linear instruments.
• Designing a C++ framework for the yield curve.
• Basic interest rate derivatives: bond options, swaptions, caps/floors and captions/floortions.
• Derivation of Black formulae for pricing simple cases: swaptions and caps.
• Integrating the yield curve into an extended Pricing Framework (and refactoring) to allow analytic pricing of interest rate derivatives.
• Separation of Instruments and Models and the use of Double Dispatch to bring them together in the Pricing Framework.
• Motivation for using change of probability measure; special case of T-forward measure
• Mathematical concepts: numeraires, martingales, fundamental theorems of asset pricing, Radon-Nikodym derivatives, Girsanov theorem.
• Application of mathematical machinery to affine short rate models with focus on (extended) Vasicek framework.
• Analytic pricing of basic interest rate derivatives (including zero coupon bond options) in affine short rate framework and integration into Pricing Framework.
• Monte Carlo implementation of Vasicek framework, design of a templated Simulation class hierarchy, and integration into Pricing Framework (with more refactoring).
• Extension to pricing of captions/floortions and coupon bond options.
• Bermudan exercise and the advantages of the Hull-White lattice approach.
• Forward rate modelling and the Heath-Jarrow-Morton (HJM) framework.
• Consistency condition for arbitrage-free HJM model calibration.
• HJM volatility term structure.
• Implementation of MC pricing of interest rate derivatives in HJM framework within Pricing Framework.

• Distinguish different mathematical representations of interest rate curves.
• Distinguish different approaches to representing the dynamics of interest rates.
• Price the most important interest rate derivatives under different dynamical assumptions, both analytically and under Monte Carlo simulation.
• Use change of measure and other advanced mathematical techniques to simplify the mathematical expressions derived from interest rate models for option prices.
• Use double dispatch, polymorphism and templated class hierarchies to build a pricing library which allows a diverse hierarchy of instruments to be priced under various modelling assumptions.

Teaching and Assessment

A lectronic copy of lecture notes is provided to all students at the start of the course.

Source code for a C++ library integrating all the software techniques discussed is also made available and can be compiled and used to compare results obtained using different modelling/pricing techniques.