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 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




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

Interview in OpalesqueTV: ” Melvyn Teo, Singapore Management University, Director BNP Paribas Hedge Fund Centre “

From the page on the OpalesqueTV youtube channel. This is video from 2010, but I thought it still carries relevance and long-term logic:

Opalesque’s first CAMPUS series features Melvyn Teo, Associate Professor of Finance at Singapore Management University. Teo is also Director of the BNP Paribas Hedge Fund Centre at the Singapore Management University.

In this Opalesque CAMPUS, Teo shares his findings that hedge funds charging lower than average performance fees tend to have a higher liquidity risk, which will translate into problems for investors, when they try to pull money out of the fund. One example of such a problem is the “return impact” of redemptions, when the return of the fund tends to fall in the next month.

Teo also gives specific recommendations what investors can do to better understand the liquidity risk a fund may carry.


More attention to be paid to 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: 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




Merger Arbitrage: the Puzzle Capital example

Opalesque TV – Backstage

Set up as a family office by renowned French hedge fund entrepreneurs, Jean-Louis Juchault and David Obert, Puzzle Capital launched the Abrax Merger Arbitrage Fund in 2011. The fund is managed by Xavier Robinson, a merger arb manager with a strong pedigree and extensive experience of the strategy over the last 20 years. Since launch in May 2011, the fund has had no negative years and has generated double digit annualized net returns. As of the end of November 2015, the fund is up 21% YTD. The fund will look to soft close at $350/400m and to hard close at $500m.

Xavier says the single most important aspect of merger arb is to avoid “deal breaks”, as it takes ten successful investments to make up the performance loss caused by one deal break. Xavier and his team have invested in over 600 deals, but have only experienced one (!) deal break since launch. This stellar track record is in part a team effort and also a reflection of Xavier’s deep skills in prop trading, portfolio management, and investment banking.

In this Opalesque.TV BACKSTAGE video, hear Xavier and Jean-Louis speak about: The criteria employed by Abrax to filter deals with examples of deals that were correctly avoided How the failed merger between SHIRE and ABBVIE in Oct. 2014 is still impacting markets today, contributing to pricing inefficiencies in spreads and creating attractive opportunities A review of Puzzle’s best month and worst months The strategy outlook for merger arb

Puzzle Capital was founded by Jean-Louis Juchault and David Obert in 2009 as their family office and is regulated by the AMF in France. The two have worked together since 1989 (as MD & CEO, MD & CIO) at Barep Asset Management, a $5bn multi-strategy hedge fund. In 2001 they co-founded Systeia Capital Management which they sold in early 2008 to Credit Agricole.

Xavier Robinson has managed the Abrax fund since inception and has extensive experience of merger arbitrage investing. Xavier started his career in 1995 with BNP and then worked with Citigroup, Lehman and Dexia as a proprietary trader, fund manager and M&A banker. Xavier holds a Civil Engineering Degree from the Ecole Supérieure des Travaux Publics and an MSc in Finance from ESSEC (Paris).

Recent eVestment Data Detail Asset Distribution Among Global Hedge Funds

The link in this post relates to analysis of the global Assets Under Management (AUM) of the Hedge Fund industry done by Managed Funds Assotiation. Revealing the proeminence of the United States as the global leader in the asset class with 70% of the total AUM.


Recent eVestment Data Detail Asset Distribution Among Global Hedge Funds.