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

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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From QuantLabs.net 2: “Scanning hot sectors for market trading within Europe “

The second installment from Quantlabs.net. This time on trading opportunities within European Union:

 

Scanning hot sectors for market trading within Europe

A quick run down on which market sectors could get hot within what country of the Euro Area. These could be very useful to break down trading opportunities by country and economic trading for ETF or indices.

 

10530873-european-union-logo-600x300

 

 

From QuantLabs.net: “Scanning US markets for hot sectors to pair trade or arbitrage “

I recommend followers of Insight Corporation to check this Blog and this post in particular. Why?  It is about the list of Videos and the supporting material found in there to help the interested get a grip on Algorithmitic Trading:

Scanning US markets for hot sectors to pair trade or arbitrage

Here are my first set of call with this potential Pair Trading/Arbitrage strategy. This will be part of my Algo Trading Course in Python which you can find here

These are my ‘market calls’ as explained in my video. Just remember my disclaimer that I am not a register financial advisor and these are only for research purposes!

I will check back in a few weeks to see how these did

First call Mar 7:

 

REIT-Residential

 

Long EQR Short OAKS

 

Mortgage Invesment

 

Long LEN Short BZH

Mortgage Investment

Long HTGC Short JGW

 

And here it is Bryan Downing – the founder – talk about the issue in the post: the strategy of pair of stocks trading: ” Scanning US markets for hot sectors to pair trade:



 

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.

Repost – Exchange Traded Derivatives in an Automated World

A repost from the Blog The Bull Run. Worth the read, especially this paragraph:

The potential benefits of outsourcing middle and back-office functions to assist in the ETD trading process have been well documented over the years. However, the financial crisis and changing regulations that are still being discussed have forced financial services firms to reassess their operations and outsourcing plans. It is no longer just about cost savings and flexibility, but also about complying with regulations and improving competitive positions in difficult business conditions. Those that adopt new, more sophisticated and automated solutions can differentiate their offering from their competitors.”

Exchange Traded Derivatives in an Automated World.

via Exchange Traded Derivatives in an Automated World.