Paper review series – Error analysis in Fourier methods for option pricing

I will start a new series of posts here in Insight Corporation. It will feature a review of papers about Financial Engineering and Risk Management.

The first paper in this new series is about option pricing, a central Financial Engineering topic. This series will mostly feature posts in the leading publication in this field  Risk.net. From now and then I will also publish some other relevant paper reviews from other source as well, and if the occasion is the right one.

Error analysis in Fourier methods for option pricing

 

The main points and abstract follows. Further download and reading of the paper is fully recommended:

  • We present an error analysis in using Fourier methods for pricing European options when the underlying asset follows an exponential Levy process.
  • The derived bound is minimised to achieve optimal parameters for the numerical method.
  • We propose a scheme to use the error bound in choosing parameters in a systematic fashion to meet a pre-described error tolerance at minimal cost.
  • Using numerical examples, we present results comparable to or superior to relevant points of comparison

 

 

Abstract

We provide a bound for the error committed when using a Fourier method to price European options, when the underlying follows an exponential Lévy dynamic. The price of the option is described by a partial integro-differential equation (PIDE). Applying a Fourier transformation to the PIDE yields an ordinary differential equation (ODE) that can be solved analytically in terms of the characteristic exponent of the Lévy process. Then, a numerical inverse Fourier transform allows us to obtain the option price. We present a bound for the error and use this bound to set the parameters for the numerical method. We analyze the properties of the bound and demonstrate the minimization of the bound to select parameters for a numerical Fourier transformation method in order to solve the option price efficiently.

 Featured Image: Black-Scholes Model Wiki at OptionTradingpedia.com

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Strategy Replication – Evolutionary Optimization based on Financial Sentiment Data

Mintegration with this interesting post on Evolutionary Optimization applied to Portfolio Management :

STRATEGY REPLICATION – EVOLUTIONARY OPTIMIZATION BASED ON FINANCIAL SENTIMENT DATA

mintegration blog

Wow, I enjoyed replicating this neatly written paper by Ronald Hochreiter.
Ronald is an Assistant Professor at the Vienna University of Economics and Business (Institute for Statistics and Mathematics).

In his paper he applies evolutionary optimization techniques to compute optimal rule-based trading strategies based on financial sentiment data.

The evolutionary technique is a general Genetic Algorithm (GA).

The GA is a mathematical optimization algorithm drawing inspiration from the processes of biological evolutionto breed solutions to problems. Each member of the population (genotype) encodes a solution (phenotype) to the problem. Evolution in the population of encodings is simulated by means of evolutionary processes; selection, crossover and

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More attention to be paid to Quantlabs.net in Insight Corporation

I would like to say that I must pay more attention to a fellow Blogger here at Insight Corporation. His name is Bryan Downing and he is from England, but lives in Toronto, Canada. He is a Software geek and expert with a knowledge base in Trading and Financial Markets.

Without a regular schedule I will post and re-post editions of Bryan’s Blog: Quantlabs.net. Specially on these topics: Quantitative Investment Strategies, Markets Infrastructure, Trading Algorithms and Risk Management technologies, which are ones where I see to be of mine and Bryan’s interest and expertise. I recommend also everyone to follow and check the Youtube video channel for the Blog.

Today’s post:

Smart beta crucial to measure trading risk

Smart beta crucial to measure trading risk

This is an import risk metric I use to assess when choosing a long vs short in my upcoming Abritrage Phase of upcoming trading course. See video below to see detail of this next phase which should start early May

 

risk

 

Quant at Risk – Risk Management with Pawel Lachowicz

A post today about Pawel Lachowicz and his Website Quant at Risk. The important topic of Risk Management now and then here at the Digital Edge.

covv

This is a picture of Pawel’s book: Applied Portfolio Optimization with Risk Management using MATLAB.

The OTC Space weekly round-up

This week round up from The OTC Space. As always it is a great source of good posts on matters related to cutting edge Financial Markets, platforms derivatives and all the Risk Management, technological, regulatory and scientific issues related with Finance. Worthy….!!

Single-Dealer Platforms evolve and remain relevant

Excellent blog on trading platforms, dealing in the markets and the modern era of Digital Investment Management!

SingleDealerPlatforms.Org

The evolving global regulatory landscape is fundamentally changing how banks operate, the returns available, the business lines and markets in which they can effectively compete, and the way in which they interact with and service their clients via their Single-Dealer Platforms.

For example, under Dodd Frank, standardised swaps trading with clients will migrate from OTC bilateral trading, over to regulated venues such as SEFs. This will see the value proposition and revenue generated for banks likewise shift from a

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