Category archives for Pricing and Hedging Tutoriual

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 […]

Early Exercise: Curse or Blessing

Many financial contracts come with the right of exercising a right prematurely. Such early exercise rights are a clear advantage for the option holder. But, these rights create optimal stopping problems for the contract parties. Is this really an advantage? In the following, I will show you a little example from my last shopping trip and […]

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 Model Risk and What Can I Do About it?

Falling Tower of Bricks

Model risk is the risk that the market models in investment banking do not properly reflect the reality. This risk is often neglected or simply ignored. But, it is one of the most important risks as we could see in the mispricing of CDO, ABS, MBS etc at the beginning of the financial crisis (early […]

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 optimize my quantitative trading strategy, e.g. MACD signal?

In the previous post, we saw how to backtest a quantitative trading strategy. The result was, that we suspected that we should be able to find better constants for the MACD trading signal strategy. Now, we will use Matlab and Theta Suite in order to create an efficient optimization. Furthermore, we create a simple visualization […]

How can I backtest my quantitative trading strategy, e.g. MACD signal?

Many popular quantitative trading strategies are public for quite a while. Now, if you like to utilize such a strategy with real money, you must make sure that your strategy performs well. For simple strategies, MS Excel is perfect for this task. But, since we would like to use an optimization and a specific visualization […]

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.