This is an interim project I did in the period June 2011- Jan 2012 at a Dutch Bank.
The implementation of a new treasury and risk management system at a bank called for a formal validation of the both the system output, as well as the system configuration.
Validation / Configuration:
Defining swap curves, contributing rates and interpolation method. Validate discount curves and pricing models on linear products: deposits and loans bonds, interest rate swaps, forward, cross currency swaps
Validate VAR calculations and risk reports: replicate the VAR calculation of various deal types.
Development:
Develop liquidity management and risk management model for maturing and non-maturing accounts.
Various IT tasks: works on Bloomberg and Reuters interfaces, Excel tools, writing SQL Server queries and scrips.
This was a project I did in the period September 2011 – January 2012
European- and State regulations are open to dialogs with industries.
In this study, the financial impact on my client of a wide variety of possible future regulatory scenario’s are examined using quantitative modeling and scenario analysis. The results of the study and condensed into a strategic advice.
Below are some usefull transform invariants for Brownian motion.
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Here we present a new yield curve interpolation method, one that’s based on conditioning a stochastic model on a set of market yields. The concept is closely related to a Brownian bridge where you generate scenario according to an SDE, but with the extra condition that the start and end of the scenario’s must have certain values. In this article we use Gaussian process regression to generalization the Brownian bridge and allows for more complicated conditions. As an example we condition the Vasicek spot interest rate model on a set of yield constraints, and give analytical solution.
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A list of popular binomial and trinomial tree used in finance for pricing options.
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The equations in this category are used to estimate the derivative of functions.
These routines are quite often used in finance to estimate sensitivities like delta,gamma,theta, and the estimation of boundary conditions.
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This list contains the most common stochastic processes used in finance.
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This page gives an overview of some well known probability distributions.
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This equation uses the Gauss-Legendre quadrature to approximate the value of a spread option. The Gauss-Legendre quadrature abscissas (Xi) are rescaled in the range -4 to +4. The equation is unbiased and gives very accurate results, typical 6 digit accuracy with 16 quadrature points. The method was describes by K. Ravindran in his paper “Low-fat spreads” (1993) RISK 6 (10) 56–57.
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A great deal has been written about fixing ‘invalid correlation matrices’ for risk management purposes. Correlation matrices are invalid when it’s mathematically impossible to generate random numbers with those mutual correlations. The most common cause of this problem -as seen in finance- is that the correlation matrices numbers are made up, or are based on historical data with a wrong treatment of missing data. This article will show how to solve the later type of problems by explaining how to do a correct estimation of correlation coefficient for data-sets with missing data. The technique to do so is called ‘expectation maximization’ (EM). We will illustrate the method by solving a practical example.
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This article describes the probability distribution of the high of a geometric Brownian motion.
An equation is given that calculates the probability that the high is above a
certain level H within a given timeframe 0<t<T.
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This article describes a very simple and efficient solution for handling matrices and tensors in C++. The idea is to store the matrix (or tensor) in a standard vector by translating the multidimensional index to a one dimensional index.
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A Dutch energy firm has asked us to run a model validation. The model is designed to optimize the electricity cost of a large industrial plant, and uses hourly electricity prices curves for the cost part, and a mixed integer linear programming model for the plant constrained optimization with the production flexibility limits.
One of the algorithms used in the Probability Engine is a weighted covariance calculation. Instead of using a simple two pass algorithm, we chose for a single pass algorithm that improves both speed and accuracy.
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Digital spread options have a payoff that depends on the difference -spread- between two underlying S1,S2. The payoff is 1 unit (Dollar, Euro) if the spread S1-S2 is greater that a strike K, and zero otherwise. This article gives the pricing formula of the option considering a Black & Scholes world.
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This project involved cost optimization the water transport- and purification process. We looked at the production flexibility, and examined how we can reschedule production to lower electricity cost. Electricity prices are not constant, and the cost reduction strategy involves rescheduling electricity use to cheaper hours. We showed that production costs van be reduced by 20% by (dynamic) re-scheduling the timing of production and water transport based on (real-time) electricity prices.
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In this article I’ll describe two methods for calibrating the model parameters of the Ornstein-Uhlenbeck process to a given dataset.
- The least squares regression method
- maximum likelihood method
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A client has been building some very useful Excel based tools for corporates. For their next release, we have been helping then move the data that is currently stored in Excel to a proper database.
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Together with Maarten van der Kloot Meijburg, we have looked into the risk and trading behavior of farmers who own a CHP (combined heat power cogeneration).
A lot of farmers own CHP’s, and that makes sense -they can use most of their outputs -power, heat, CO2- to grow their crops.
I have completed a consultancy project that I did together with SQ consult for a large West-European energy utility. An interesting project, with interesting results!
The goal of the project was to model the financial and strategic effects of 5 different (national and European) renewable energy regulatory scenariose on its portfolio.
This model looked into the entire value chain (upstream, trading and sales), analysing the risks for the grey portfolio, existing green installations and new asset development with a specific focus on possible movements within the national merit order.
, volatility 
, and has an initial value of 