On Pricing Options with Finite Difference Methods

Posted on 2017-05-24 |

Introduction

In this notes, finite difference methods for pricing European and American options are considered. We test explicit, implicit and Crank-Nicolson methods to price the European options. For American options, we implement intuitive Bermudan approach and apply the Brennan Schwartz algorithm to prevent the error propagation. Results of simple numerical experiments are shown in the end of notes. This project is implemented using Python objected-oriented programming[code].

Calibration of Forward Rate Curve

Posted on 2017-04-08 |

Calibration of Forward Rate Curve

Introduction

Term structure of interest rate describes the relationship between yield and maturity. In practice, the term structure is extensively used by market practitioners to understand conditions in fixed income market and to evaluate various interest rate derivatives. Actually only for several specific maturity the interest rate is known, while the other maturity can be computed by interpolation. To construct the yield curve, many approaches have been proposed. There are parametric methods like Nelson-Siegel model and non-parametric methods such as bootstrapping method and spline methods. The idea of this note is to present all the details of how we have implemented calibration of instantaneous forward rate curve using constrained cubic spline method.