Tag archives for Option Pricing

VDAX revisited – Implied volatility return vs. Index Return

Last time we looked at implied volatility, we found a close relationship between historical volatility and implied volatility. This time, we want to look at the relative changes of DAX and VDAX and their relationship. Advertisements

Financial Modelling (with Matlab Source): A great new book

Book Cover

Joerg Kienitz and Daniel Wetterau present “Financial Modelling: Theory, Implementation and Practice with MATLAB Source”, a great resource on state-of-the-art models in financial mathematics. The authors try to bridge the gap between current research topics and an implementation which can be applied in the real world. That means the authors are neither afraid of practical […]

Post Crisis Financial Modelling – What changes?

I recently stumbled upon an interesting book about post-crisis interest-rate modelling. Besides future changes in the LIBOR and possible EURIBOR fixing after the manipulations of the past few years, counter-party default and collateral become important. Changes in Interest-Rate and Credit Instrument Pricing Pre-crisis, there was a risk-free rate on which the market agreed. This way, different […]

What is Historical Volatility and Why Do We Need Implied Volatilities?

Chart of VDAX and DAX volatility

Looking at financial instruments, one often finds the term implied volatility. In this post, we want to describe what it is and what you can do with it. We start refreshing the term historical volatility and then we explain the implied volatility. An example of German DAX with real data concludes this post. Historical Volatility […]

Matlab GPU toolbox: Benchmarking Accelereyes vs. MathWorks vs. GP-YOU?

Graphics Card

There is a great option for speed-up of your Matlab code: Use your graphics card. If you have an Nvidia graphics card, there is a whole universe of optimized code for these cards. The underlying technology is called CUDA and many of the required functions for a transparent usage from Matlab already exist. There are […]

Feedback: What is the Effect of Hedging Options on the Underlying?

Plot from Theta Suite Result Explorer

More and more investors insist on guarantees on the investments. Theses investments are often created using options or dynamic strategies like CPPI. Recently, these strategies were made available in secularized form: Leveraged Exchange Traded Funds   (LETF) and Exchange Traded Notes (ETN). Also, life insurance instruments often include guarantees on funds like Variable Annuities. In this […]

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 […]

What is the Difference Between Risk-Neutral Valuation and Real-World Valuation?

Open door to new life

In option pricing, two technical terms often create confusion. One term is “risk-neutral” and the other “real-word”. You hear these terms in the context of option pricing, backtesting, risk management and hedging. In this article I try to clarify the terminology. Background First, we start with “risk-neutral”. The term risk-neutral refers to option pricing: The […]

How can I implement Monte-Carlo Simulations in MS Excel?

Monte-Carlo simulation is a very import tool for assessing all kinds of risks and chances. It it widely used in project management, option pricing and business valuation. Often, the input data and the reporting should be placed in MS Excel. This article presents the different options available for combining Monte-Carlo simulation and MS Excel.

Theta Proxy promises speed-up of MS Excel UDFs — How fast is it?

Car in Plasma

Theta Proxy XL is a new product from my company Thetaris. It promises speed-ups of several orders of magnitude. Here, I present some benchmark results. These will help you to decide when to apply Theta Proxy XL and when to stay with plain MS Excel. Test Case 1: European Option VBA Monte-Carlo Code (2 free […]

What is a Good Design for a Pricing Library? Use a Payoff Description Language

3d lamp with jigsaw puzzle isolated on the white background

A good library design requires a separation of the functionality into modules with an appropriate API. The size of the modules is determined by the application. While for a simple trading application a good API might contain everything from fitting the stochastic processes to pricing an option under a single function, this is completely insufficient for assessing model […]

Pricing and Hedging 101

One of the main methods required in option pricing is the Black-Scholes framework. This theory is very appealing and somewhat convincing as we will see in the following.