Proceedings
Van der Merwe C.J. 2019. K-nearest neighbour triplot classification with polybags. Unpublished paper delivered at the Eight Correspondence Analysis and Related Methods conference. 5 February 2019, South Africa.
Classification techniques have been used in a variety of disciplines and have recently received more attention due to the increasing popularity of big data. One of the shortcomings of these techniques is that the end-user at some point needs to understand them to fully interpret the results, but for some it sometimes comes across as a black box. Through combining these techniques with biplots one is able to classify data, and simultaneously visualise the classification technique resulting in a so-called triplot. Additionally, by incorporating polybags, the ability of limiting the misclassification error is also introduced, allowing for further practical application.
Van der Merwe C.J., de Wet T. & Heyman D. 2017. Approximating risk-free curves in sparse data environments. Unpublished paper delivered at the Sixth International Conference on Mathematics in Finance. 8-12 August, South Africa.
IFRS 13 provides guidance on the classification of inputs used within fair valuation calculations. It further requires one to maximize the level of inputs used, or rather minimize the use of unobservable inputs. In less developed countries, zero curves are not as readily observable over the longer term, as data are often more sparse than in developed countries.
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In this research it was found that a proxy can be used to obtain the full curve through other observable inputs and specified models - allowing the fair value calculation to use inputs calculated from observed values rather than unobservable inputs. The approximations were found through a phased simulation approach which incorporates two new techniques, namely permuted integer multi linear regression (PIMLR) and aggregate standardized model scoring (ASMS).
This is done through fitting various different models to an artificially created sparse environment and comparing it to the actual observed rates. The models were then scored in order to determine the average best performing model across the various datasets.
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A Nelson Siegel fit, with an average forward rate as proxy for the level parameter, and a simple combination of zero rates for the slope and curvature parameters was found to perform relatively well within the training and testing datasets.
Life insurance and pension funds offer a wide range of products that are invested in a mix of assets. The portfolios underlying these contracts are rebalanced on a regular basis back to predetermined fixed proportions. Life insurance or pension fund contracts can offer the client a minimum payout guarantee on the contract by charging them an extra premium. This problem can be changed to that of the pricing of a put option with the rebalanced portfolio as the underlying. It forms a liability for the insurance firm, and therefore needs to be managed in terms of risks as well.
This can be done with the help of the option's sensitivities. The premium and sensitivities of this put option are calculated, using different Monte Carlo methods, in order to find the most efficient estimators.
Using general Monte Carlo methods, a simplistic pricing method is found which is refined by applying mathematical techniques that reduce the computational time significantly. A discussion will be done on different Monte Carlo methods implemented in order to make the simulation more efficient. After considering Antithetic Variables, Control Variates and Latin Hypercube Sampling as variance reduction techniques, option prices as Control Variates reduced the error of the refined method most efficiently. This is improved by considering different Quasi-Monte Carlo techniques, namely Halton, Faure, normal Sobol' and other randomised Sobol' sequences. Owen and Faure Tezuke type randomised Sobol' sequences improved the convergence of the estimator the most efficiently. Furthermore, the best methods between Path-wise Derivatives Estimates and Finite Difference Approximations for estimating sensitivities of this option are found.
National Proceedings
Van der Merwe C.J. 2019. Classifying yield spread movements through triplots: a South African application. Unpublished paper delivered at the 61st annual conference of the South African Statistical Association. 28 November, Johannesburg.
Significant movements in yield spreads from a sparse data environment are classified using various share, interest rate, financial ratio, and economic type covariates in a visually interpretive manner. This allows for a better understanding of how various factors drive the changes in yield spreads. Additionally, this visualisation technique provides the ability to classify whether an unlisted debt instrument's yield spread had significantly changed or stayed stable during a specific observation period. The analysis was implemented in a web-based application as well.
Van der Merwe C.J. 2018. KNN-Triplot classification with polybags. Unpublished paper delivered at the 60th annual conference of the South African Statistical Association. 28 November, Johannesburg.
Classification techniques do not easily allow for visual interpretation, nor do they allow for the limitation of the false negative and positive error rates. For some areas of research and practical applications these shortcomings are important to address. In this paper, k-nearest neighbour classification is combined with biplots allowing for classification, and simultaneously visualizing the classification technique resulting in a so-called triplot. By further incorporating polybags, the ability of limiting misclassification type errors is also introduced. An application to medical research data is provided.
Fair value adjustments for smaller financial institutions
Van der Merwe C.J. 2014. Unpublished paper delivered at the 56th annual conference of the South African Statistical Association. 28 October, Grahamstown.
Given the recent changes in the financial landscape and introduction of IFRS 13 Fair Value Measurement, smaller financial institutions are faced with the difficulty of incorporating fair value adjustments for credit risk in their annual financial statements. A brief outline of how these adjustments can be simplified will be given, together with different solutions of possibly implementing it within the IFRS 13 framework. Different tests will be discuss to see what the impact of the various methodologies on these approach could lead to.
Model risk poses an increasingly higher threat due to the ever more widespread use of models. In essence, mathematical models are used to try and capture an observed phenomenon. At first this risk might seem to be of little importance to corporate treasuries; however it could possibly be a significant risk that is sometimes overlooked. We consider a proposed model risk management framework, and also present results on an international benchmarking survey on model governance and validation.
The International Financial Reporting Standards (IFRS) guidelines provide accountants guidance as to how to set up financial statements. With the increasing amount of academic research done with regards to the valuation of different derivatives and financial instruments, it often lacks the consideration with regards to these guidelines and specifically the inputs used in valuations. A brief summary of the appropriate standards will be provided, with special focus of how this relates to derivative and financial instrument pricing. Also, a discussion on the different inputs that can be used in exotic derivative valuation, and the calculation thereof, will be given. An in depth focus on the bootstrapping and calculation of the term structure of risk-free interest rates (e.g. Bond, Swap, and Money Market zero coupon risk-free curves) and how they relate to different financial instruments will also be provided. Different types of Swap zero coupon risk-free curves also exist, which needs to be considered when valuing certain type of instruments. A comparison will be provided as to how valuations might differ if the different curves are used. Finally, a brief discussion on credit value adjustments will also be made.
Van der Merwe C.J. 2011. Unpublished paper delivered at Colloquium: Department Statistics and Actuarial Science, Stellenbosch University. 29 July, Stellenbosch.
Life insurance and pension funds offer a wide range of products that are invested in a mix of assets. The portfolios underlying these contracts are rebalanced on a regular basis back to predetermined fixed proportions. Life insurance or pension fund contracts can offer the client a minimum payout guarantee on the contract by charging them an extra premium. This problem can be changed to that of the pricing of a put option with the rebalanced portfolio as the underlying. It forms a liability for the insurance firm, and therefore needs to be managed in terms of risks as well.This can be done with the help of the option's sensitivities. The premium and sensitivities of this put option are calculated, using different Monte Carlo methods, in order to find the most efficient estimators. Using general Monte Carlo methods, a simplistic pricing method is found which is refined by applying mathematical techniques that reduce the computational time significantly.
A discussion will be done on different Monte Carlo methods implemented in order to make the simulation more efficient. After considering Antithetic Variables, Control Variates and Latin Hypercube Sampling as variance reduction techniques, option prices as Control Variates reduced the error of the refined method most efficiently. This is improved by considering different Quasi-Monte Carlo techniques, namely Halton, Faure, normal Sobol' and other randomised Sobol' sequences. Owen and Faure Tezuke type randomised Sobol' sequences improved the convergence of the estimator the most efficiently. Furthermore, the best methods between Path-wise Derivatives Estimates and Finite Difference Approximations for estimating sensitivities of this option are found.
Van der Merwe C.J. & Conradie W.J. 2010. Unpublished paper delivered at the 52nd annual conference of the South African Statistical Association. 10 November, Potchefstroom.
Life insurance and pension funds offer a wide range of products that are invested in a mix of assets. The portfolios underlying these contracts are rebalanced on a regular basis back to predetermined fixed proportions. Life insurance or pension fund contracts can offer the client a minimum payout guarantee on the contract by charging them an extra premium. This problem can be changed to that of the pricing of a put option with the rebalanced portfolio as the underlying. It forms a liability for the insurance firm, and therefore needs to be managed in terms of risks as well.This can be done with the help of the option's sensitivities. The premium and sensitivities of this put option are calculated, using different Monte Carlo methods, in order to find the most efficient estimators. Using general Monte Carlo methods, a simplistic pricing method is found which is refined by applying mathematical techniques that reduce the computational time significantly.
A discussion will be done on different Monte Carlo methods implemented in order to make the simulation more efficient. After considering Antithetic Variables, Control Variates and Latin Hypercube Sampling as variance reduction techniques, option prices as Control Variates reduced the error of the refined method most efficiently. This is improved by considering different Quasi-Monte Carlo techniques, namely Halton, Faure, normal Sobol' and other randomised Sobol' sequences. Owen and Faure Tezuke type randomised Sobol' sequences improved the convergence of the estimator the most efficiently. Furthermore, the best methods between Path-wise Derivatives Estimates and Finite Difference Approximations for estimating sensitivities of this option are found.