VALUATION OF BEE SCHEMES
We specialise in the valuation of black economic empowerment (BEE) share purchase schemes for audit, mark to market, and hedging purposes. These schemes are often complex and require financial engineering - this applies in either the vendor, institutional or mixed financing cases. See here for a general discussion of our approach.
VALUATION OF EMPLOYEE STOCK OPTIONS
We have a solution for pricing employee stock options that is compliant with the latest IFRS2 regulations. Our model has been applied with audit success to several portfolios of ESOs in South Africa. As a small business, we are able to offer you a competitively priced and tailor-made solution. Our reports will provide all the relevant MtMs of the options and we provide spreadsheets of the cost amortisation schedules that you will need to use. See here for a summary of our approach.
In particular, robust mark to market algorithms for illiquid or thinly traded instruments. This interest has lead us to develop a fairly broad use of the SABR model for volatility skews. We have clients that use our SABR solutions in front office, middle office, and price risk management areas in South Africa and in other emerging markets such as Eastern Europe. See our SABR paper. We have a general interest in pricing under local and stochastic volatility models, and under Lévy models.
Such as the bootstrap of 'difficult' yield curves. We have solutions for building swap and bond curves in the South African market, real (CPI linked) curves, and forward prime curves. Interestingly, most published solutions for yield curve bootstrap, and those implemented in typical trading systems, allow for pathology or arbitrage. See our interpolation papers written with Pat Hagan. There we introduce a new method of interpolation which we call 'monotone convex'. Summary of the key issues involved, and how the monotone convex method succeeds in resolving the key problems of positivity and continuity of forwards. Some ideas on including OISs in the bootstrap (work in progress).
Lydia completed a B.Sc. in Mathematics and Computer Science in 2003 and a B.Sc. Honours in Mathematics in 2004, both with distinction. She then worked at several banks as a contractor until 2006. In 2007 she completed the Mathematics of Finance Honours program at Wits University with distinction; in 2013 she completed her Masters dissertation at the University of Stellenbosch with distinction. She is able to code in Visual Basic, Matlab, C++ and C#.
Dr. Graeme West tragically passed away in September 2011. He was the founder and director of Financial Modelling Agency. He obtained a PhD in Mathematics in 1993, and worked in academia until 1997. He then worked in the banking and finance industry and formed Financial Modelling Agency in 2003. He completed several of the exams of the Mathematics of Finance Honours program at Wits University, and received the FRM (GARP) and the PRM (PRMIA) certification.
CLIENTS IN 2016 AND 2017
Antalis South Africa, Brimstone, Calgro M3 Holdings, KAP Industrial, Logos Advisory Services, Multichoice, Norconsult Africa, Old Mutual Namibia, OMSFIN, PPC, Reunert Management Services, Royal Bafokeng Holdings, Saab Grintek Defence, Spanjaard, Sygnia, Taurus Gold, Teraco and Wiphold.
Patrick S. Hagan and Graeme West
Interpolation Methods for Curve Construction, Applied Mathematical Finance, 2006, 13(2), p 89-129.
Patrick S. Hagan and Graeme West
Methods for constructing a yield curve. Wilmott magazine, p 70-81, May 2008. Spreadsheet demonstrating the monotone convex interpolation method. Summary comparison of the various interpolation methods available. Treatment of the mathematics of the monotone convex method. Clarification of the simultaneous bootstrap algorithm.
A discussion of how to include OIS instruments in the yield curve bootstrap (work in progress - comments very welcome).
Graeme West and Lydia West
The pricing of Black Economic Empowerment share purchase schemes. The Southern African Treasurer, Special Issue on Risk Management. Published by Treasury Management International, p 35-40, Association of Corporate Treasurers of Southern Africa, 2009.
Employee stock options. Equity-Based Compensation Plans - An Introduction, Institute for Chartered Financial Analysts of India.
Employee stock options. Corporate Treasury in South Africa, published by Treasury Management International, p 28-32, Association of Corporate Treasurers of Southern Africa 20th Anniversary Edition, 2008.
A finite difference model for valuation of employee stock options. Preprint.
Better Approximations to Cumulative Normal Functions, Wilmott Magazine, p 70-76, May 2005. Also a zip file which includes a spreadsheet which will generate all of the diagrams and examples in the article, and VB6 code (class module) and C++ code (header and cpp files) for the best univariate, bivariate and trivariate cumulative normal functions. These solutions have been implemented in Espen Haug's 'Complete Guide' 2nd edition.
Calibration of the SABR model in Illiquid Markets, Applied Mathematical Finance, 2005, 12(4), 371-385. Some of the algorithms here have been implemented in Espen Haug's 'Complete Guide' 2nd edition. These are the slides from a presentation at the Maths in Finance conference, Kruger Park, 2005. An executive summary of our SABR approach, including alternative calibration approaches.
Interest rate derivatives in the South African Market based on the prime rate. Journal for Studies in Economics and Econometrics, 2008, 32(1).
Lydia Janse van Rensburg
Empirical and Fitted Estimation of Risk Measures for Hedge Funds. Honours project, Advanced Mathematics of Finance, University of the Witwatersrand, 2007. Matlab code relevant for the project. This code has been slightly modified from that referred to in the project; the proprietary C++ component has been eliminated and the code is now entirely in Matlab. The documentation has not been modified. Relative to the existing documentation, hypergeomSeries.m replaces the Matlab function hypergeom (we think this function has issues) and the Matlab code CPlusPlusPearsonIVCDF.m which calls the C++ code to calculate the Pearson IV CDF has been replaced by (somewhat slower) Matlab code PearsonIVCDFSeries.m.
Peter Ouwehand and Graeme West
Pricing rainbow options, Wilmott Magazine, p 74-80, May 2006.
Coherent VaR-type measures. The Southern African Treasurer, Special Issue on Risk Management, Part 2. Published by Treasury Management International, p 20-23, Association of Corporate Treasurers of Southern Africa, 2010.
American Monte Carlo Pricing under Pure Jump Lévy Models. M.Sc. Thesis, University of Stellenbosch, 2012, supervised by Peter Ouwehand.
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