Options, Pricing, and Risk Management Part II

In this second part we will focus on numerical methods to price options and on the replication and the risk management of exotic options.

This quantitative finance training course is composed of many videos, quizzes, applications and tutorials in Python.

A certificate of achievements will be delivered once the course has been completed with success.

In the first week, we will introduce Monte Carlo simulations and see how to apply this method to price different kinds of options and to estimate option Greeks. We will also analyse different ways to accelerate the computation speed with quasi-Monte Carlo, variance reduction methods or code optimisation.

In the second week, we will review finite difference methods to price options. We will see how to solve numerically the Black-Scholes partial differential equation with these approaches. We will present the three main methods: explicit, implicit and Crank-Nicolson. We will show that the explicit method is equivalent to the trinomial tree approach and discuss the pros and cons of each method in terms of stability, accuracy of the estimate and computation speed with concrete examples.

In the third week, we will focus on the replication and the risk management of exotic options. We will discuss on the limits of the dynamic replication for some options such as binary or barrier options and present different ways to replicate such options statically with several concrete examples. We will finally highlight the need of pricing models taking into account the volatility surface to price such options.