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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The fork in the Hedge Fund industry

Today I return here to Insight Corporation posts. This time with a nice, informative and helpful article in Financial Times about what is going on in the so often mysterious or misunderstood Hedge Fund industry.

To wit here they are some of the best  pasts from the article:

M&A arbitrage is a good example of a highly specialised hedge fund strategy that the “quants” now say they can mimic. “Arbs” place bets on whether corporate acquisitions will fail or succeed. When a company makes an offer for a rival, it will typically offer a premium price — but there is always a danger that the deal collapses, so the shares typically trade slightly below the offer price.

Skilled arb funds — typically stuffed with corporate lawyers, antitrust experts and former investment bankers — buy the shares of targets when they think the deal will go through, and short the ones where they think the deal will fizzle. The risk is in practice binary, and the better the fund, the more accurate its predictions.

Enough deals go through that even average M&A arbitrageurs should make money over time, as they capture what Mr Romahi calls the “deal failure risk premium”.

But quants now think they can do even better than simply systematically buying acquisition targets, by studying history for what deals go through and which fail, and automatically weighing their bets accordingly.

 

And the bifurcation in the industry appears to happen on different approaches and strategies. Some with the quant computer driven models and others just involving Human Intuition and business acumen. But is there really a battle of paradigms, or a diversity of ecosystems not mutually exclusive?:

But he has identified a multitude of factors that affect the M&A strategy’s success rate, using the same statistical techniques that doctors use to determine how long a cancer patient has to live.

As is often the case with quants, they are confident that their mathematical approach produces better results than human intuition. The traditional M&A arbitrageurs are “good but often not very accurate. Our model has actually proven more accurate than the arbitrage funds”, Mr Luo says.

M&A arbitrage is just one of many popular hedge fund strategies whose secrets quants say they are now deciphering. Others include global macro — betting on the ebb and flow of international interest rates and currencies — and even activist strategies pursued by the likes of Dan Loeb’s Third Point, Bill Ackman’s Pershing Square and Carl Icahn.

I will honestly bet that a somewhat healthy co-existence of all the strategies to be in the interests of everyone. An in academia sometimes the theoretical view isn’t so that far off reality:

While the quants have crunched their numbers through supercomputers their models for what works are based virtually entirely on “backtesting” against historical data. The financial crisis showed how a slavish adherence to modelling can spectacularly blow up in real-life markets, either immediately or eventually.

“I have very little regard for these hedge fund replicators,” says Robert Frey, chief investment officer at FQS, a fund-of-hedge funds and a quantitative finance professor at Stony Brook University. “They all fail miserably when the market regime shifts.”

 

I wish you all good trades and strategies: be they quantitative or intuitive!

” #Hedge #fund managers are arguably the celebrity chefs of the money management industry. They are best able to whip up…

Posted by Insight Corporation on Friday, February 19, 2016

Featured Image: BusinessWeek Slams “The Hedge Fund Myth”

 

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.

Probabilistic Momentum with Intraday data – Edgar’s share of the day

The link in the post today is from the blog Systematic Investor and is concerned with Asset Allocation, Portfolio Contruction, Intraday Trading and Probabilistic Momentum Strategies.

With the codes needed to implement the strategies, it may well be a must see for the Algorithmic Traders community that are interested to build strong portfolios.

Probabilistic Momentum with Intraday data.

 

Multi-Asset Market Regimes

Recently discovered Blog on Quantitative Trading. In a single word: excellent!

Quantivity

An astute reader suggested reproducing the results from a recent article on regime analysis by Kritzman et al., Regime Shifts: Implications for Dynamic Strategies in FAJ (May / June 2012). This is a fun exercise to be conducted over a series of posts, as doing so illustrates several important economic principles and some elegant mathematics.

This post begins by identifying macroeconomic market regimes arising from multi-asset economic activity.

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