Pulling forward thanks to our knowledge.

Pulling forward thanks to our knowledge.

December 2012

Basel 2.5 and Basel III: a brief guide through the maze

The financial crisis has highlighted the need to reform the Basel II capital framework and to complement it with a liquidity risk framework. This document summarizes the main revisions and enhancements introduced with Basel 2.5 and Basel III, the key documents issued by the Basel Committee on Banking Supervision and the Swiss regulator, and the implementation dates.

November 2012

Introducing Alea.CUDA at Zurich F# Users

The meetup will be about F# computation expressions (also referred to as workflow expressions or monads) in practice. I will begin with a brief overview. After that, James Litsios will present an example related to modular pure state management. Finally, Daniel Egloff will present a case study related to Alea.Cuda, a new F# product for processing on the GPU, which Daniel's company, QuantAlea, has created in the context of a client project.

For more information visit:

Zurich F# Users

November 2012

Introducing Alea.CUDA at Functional Londoners

F# and GPUs are two trailblazing yet unrelated technologies. F# is a uniquely productive language to solve complex problems in a clear and concise way. On the other hand GPUs offer an immense computational power to solve large number crunching tasks fast and efficiently.

Our presentation shows how to wed the two technologies F# and GPUs with the help of Alea.CUDA. Alea.CUDA is our new framework and compiler service for GPU computing. It extends F# with the key CUDA concepts and allows to compile F# code quotations to an executable GPU code. I will briefly introduce Alea.CUDA and show you – by means of several live coding examples – how it can be used to develop GPU algorithms entirely in F# with the full flexibility of CUDA-C.

Besides getting an understanding of the main features of Alea.CUDA you will become familiar with some of the basic GPU computing paradigms. To round off the presentation I shall reveal some of the implementational aspects of Alea.CUDA.

Podcast

July 2012

EMIR: new challenges for financial institutions

Overview of the requirements introduced with the European Market Infrastructure Regulation (EMIR) and their challenges to financial institutions.

May 2012

New Generation GPU Accelerated Financial Quant Libraries

Presenting "New Generation GPU Accelerated Financial Quant Libraries" at NVIDIA Global Technology Conference 2012, San José, California.

New generation GPU accelerated solutions for derivative pricing, hedging, and risk management can be build more efficiently with modern technology and functional programming languages like F# on .NET or Scala on the Java VM. As a concrete example we report from a large derivative pricing project developed in F# on .NET.

We will introduce the key design concepts and parallelization strategies, which lead to an efficient and transparent GPU acceleration. Several examples will illustrate the benefit of functional as compared to the classical object oriented approach.

March 2012

Pricing Financial Derivatives with High Performance Finite Difference Solvers on GPUs

Abstract:

The calculation of the fair value and the sensitivity parameters of a financial derivative requires special numerical methods, which are often computationally very demanding. In this chapter we discuss the design and implementation of efficient GPU solvers for the partial differential equations (PDEs) of derivative pricing problems.

For derivatives on a single asset like a stock or an index we consider a massively parallel PDE solver which simultaneously prices a large collection of similar or related derivatives with finite difference schemes. We achieve a speedup of a factor of 25 on a single GPU and up to a factor of 40 on a dual GPU configuration against an optimized CPU version.

Often derivatives are written on multiple underlying assets, e.g. baskets, or the future asset price evolution is modeled with additional risk factors, like for instance stochastic volatilities. The resulting PDE is defined on a multidimensional state space. For these kind of derivatives it is not necessary to pool multiple pricing calculations: alternating direction implicit (ADI) schemes for PDEs on two or more state variables have enough parallelism for an efficient GPU implementation. We benchmark a specific ADI solver for the Heston stochastic volatility model against a fully multi-threaded and optimized CPU implementation. On a recent C2050 Fermi GPU we attain a speedup of a factor of 70 and more for a sufficiently large problem size.

Our results demonstrate the importance of the effective use of GPU resources such as fast on-chip memory and registers.

For more information visit: 

GPU Computing Gems Jade Edition (Applications of GPU Computing Series), Wen-mei W. Hwu (Editor), 2012, p. 309-322

November 2011

Feeling partial: tackling the challenges of PDEs in the brave new world of GPUs in finance

Wilmott Magazine interview with Dr. Daniel Egloff. Beyond huge advantages in terms of efficiency and long-term costs the steady adoption of GPU architecture in finance is bringing with it a shift, not only in the way the industry thinks about hardware, but also the thought given to the logical flow of the computational process and, potentially, the kinds of models utilized in quantitative finance.

March 2011

GPUs in financial computing part III:

The paper looks at the design and implementation of efficient GPU solvers for two factor models with a focus on stochastic volatility models. The resulting partial differential equations of two state variables are solved with alternating direction implicit (ADI) schemes. The paper shows that ADI-style schemes can be parallelized very efficiently on a GPU. Already a single pricing problem can utilize the full GPU capacity, a pooling of multiple pricing calculations to generate more parallelism is not necessary anymore.

Wilmott Magazine, March 2011

December 2010

American options with stopping time constraints

This paper concerns the pricing of American options with stochastic stopping time constraints expressed in terms of the states of a Markov process. A transformation is applied to express the contract as a generalized barrier option. The valuation problem of the barrier option leads to a stochastic Cauchy-Dirichlet problem which we numerically solve with a suitable extension of the Longstaff-Schwartz algorithm.

Applied Mathematical Finance, Volume 16, Issue 3, 2009, p. 287-305.

November 2010

GPUs in financial computing part II: massively parallel PDE solvers on GPUs (Wilmott Technical Paper)

Computing a large number of option prices with finite difference schemes in parallel leads to enough data-parallel work to fully load a modern GPU. The paper proposes a massively parallel PDE solver which simultaneously prices a large collection of similar or related derivatives with finite difference schemes. The performance analysis shows a remarkable speedup by a factor of 25 on a single GPU and up to a factor of 40 on a dual - GPU configuration against an optimized CPU version.

Wilmott Magazine, November 2010

October 2010

The term structure of variance swap rates and optimal investing in variance swaps

We study the optimal investment decision on the variance swap contract and the stock index. We find that two factors are needed to capture the term structure variation of the variance swap rates. Also the presence of variance swap contracts alters the investor’s optimal portfolio decision.

Journal of Financial and Quantitative Analysis, volume 45, issue 05, 2010, pp. 1279-1310.

September 2010

GPUs in financial computing part I: high-performance tridiagonal solvers on GPUs (Wilmott Technical Paper)

The financial industry starts to adopt GPUs more and more. The main application fields as of today are Monte Carlo simulations. They fall into the category of embarrassingly parallel problems and can be implemented on a GPU in a relatively straightforward manner, once a good random number generator is available. Speedups of a factor of 50 to 100 are within reach.

Wilmott Magazine, September 2010

March 2010

Mind your language - Python takes a bite

Interview with Dr. Daniel Egloff in the Wilmott Magazine on the use of Python in financial applications and software architectures.

August 2009

Quantile estimation with adaptive importance sampling

We introduce new quantile estimators with adaptive importance sampling. The adaptive estimators are based on weighted samples that are neither independent nor identically distributed. Using a new law of iterated logarithm for martingales, we prove the convergence of the adaptive quantile estimators for general distributions with nonunique quantiles, thereby extending the work of Feldman and Tucker. We illustrate the algorithm with an example from credit portfolio risk analysis

April 2009

American options with stochastic stopping time constraints

This paper concerns the pricing of American options with stochastic stopping time constraints expressed in terms of the states of a Markov process. We apply a transformation to express the contract as a generalized barrier option. The valuation problem of the barrier option leads to a stochastic Cauchy-Dirichlet problem which we numerically solve with a suitable extension of the Longstaff-Schwartz algorithm.

Applied Mathematical Finance, Volume 16, Issue 3, 2009, p. 287-305

April 2008

Teraflops for Games and Derivative Pricing

Financial computing continuously demands higher computing performance, which can no longer be accomplished by simply increasing clock speed. Cluster and grid infrastructures grow, their cost of ownership explodes. On the other hand, the latest GPU (Graphics Processing Unit) boards show impressive performance metrics. This leads to the questions if and how one can harness this power to bring financial computing to the next level. We analyze the pricing of equity basket options with a local volatility model implemented on a GPU. Our performance gains are very impressive.

January 2007

A dynamic look-ahead Monte Carlo algorithm for pricing Bermudan options

Under the assumption of no-arbitrage, the pricing of American and Bermudan options can be casted into optimal stopping problems. This paper proposes a new adaptive simulation based algorithm for the numerical solution of optimal stopping problems in discrete time.

Annals of Applied Probability Volume 17, Number 4, 2007, p. 1138-1171.

February 2006

A simple model of credit contagion

The paper proposes a simple model of credit contagion in which macro- and micro-structural interdependencies among the debtors within a credit portfolio are included. The microstructure captures interdependencies between debtors that go beyond their exposure to common factors, e.g., business or legal interdependencies. We show that even for diversified portfolios, moderate micro-structural interdependencies have a significant impact on the tails of the loss distribution. This impact increases dramatically for less diversified microstructures.

Journal of Banking & Finance, Volume 31, Issue 8, August 2007, Pages 2475–2492.

This paper won the STOXX 2004 Gold Award of the annual meeting of the European Financial Management Association.

May 2005

Monte Carlo algorithms for optimal stopping and statistical learning

We extend the Longstaff–Schwartz algorithm for approximately solving optimal stopping problems on high-dimensional state spaces. We reformulate the optimal stopping problem for Markov processes in discrete time as a generalized statistical learning problem. Within this setup we apply deviation inequalities for suprema of empirical processes to derive consistency criteria, and to estimate the convergence rate and sample complexity. Our results strengthen and extend earlier results obtained by Clément, Lamberton and Protter [Finance and Stochastics 6 (2002) 449–471].

Annals of Applied Probability Volume 15, Number 2, 2005, p. 1396-1432.