Archives for April, 2012

How Do Efficient PDE Solvers for Barrier Options Look Like?

Besides European and American Options, another challenge in option pricing is the valuation of Barrier Options. We will see that simply applying the algorithms from the previous posts does not converge well. Especially, pricing a long-term up-and-out barrier option is hard, due to the discontinuity of the payoff. 

How Can I Implement Early Exercise in a PDE Method pricing an American Put Option?

An American option is an option which the owner can exercise at any time during its lifetime. That means the option’s value cannot drop below the exercise value, i.e. the option value  of an American put option satisfies . (1) We use the above condition in the PDE solver (How Can I Price an Option with a PDE Method in Matlab?) to price an American […]

How Can I Price an Option with a PDE Method in Matlab?

Values of European Put Option computed using a PDE solver

In this article, we build a very simple PDE solver for the Black-Scholes Equation. Using the Finite Volume Discretization Method, we derive the equations required for an efficient implementation in Matlab. The implicit Euler time-stepping of the solver guarantees a stable behavior and convergence. All posts in this series: Basics of a PDE solver in Matlab Pricing American options with […]

Expect the Unexpected: Risk Management Must Be Creative

A flying spinning top

Modern risk management is a real challenge. Today, I played with my levitation device. I noticed that most people do not believe that levitation is real. In fact there is a formal proof that levitation in a static magnetic field cannot be stable. This situation is similar to common believes in financial markets. In the […]