PublicationS
International peer reviewed journals
van der Merwe, C.J., Heyman, D. and de Wet, T., 2018. Approximating risk-free curves in sparse data environments. Finance Research Letters, 26, pp.112-118.
Accounting standards require one to minimize the use of unobservable inputs when calculating fair values of financial assets and liabilities. In emerging markets and less developed countries, zero curves are not as readily observable over the longer term, as data are often more sparse than in developed countries. A proxy for the extended zero curve, calculated from other observable inputs, is found through a simulation approach by incorporating two new techniques, namely permuted integer multiple linear regression and aggregate standardized model scoring. A Nelson Siegel fit, with a mixture of one year forward rates as proxies for the long term zero point, and some discarding of initial data points, was found to perform relatively well in the training and testing data sets.
Local peer reviewed journals
Van der Merwe C.J. & Conradie W.J. 2012. Calculation aspects of the European rebalanced basket option using Monte Carlo methods: Valuation. ORiON, 28(1):1-18.
Extra premiums may be charged to a client to guarantee a minimum payout of a contract on a portfolio that gets rebalanced back to fixed proportions on a regular basis. The valuation of this premium can be seen as that of the pricing of a European put option with underlying rebalanced portfolio. This paper finds the most efficient estimators for the value of this path-dependent multi-asset put option using different Monte Carlo methods. With the help of a refined method, computational time of the value decreased significantly. Furthermore, variance reduction techniques and Quasi-Monte Carlo methods delivered more accurate and faster converging estimates as well.
Other
Van der Merwe C.J. & Van Tonder J. 2012. The risk in your valuation and risk calculations. The South African Treasurer, 2012:26-29.
The effective management of model risk is an increasingly important consideration in reducing the risk associated with it. We provide a brief introduction to the concept of model risk and an associated model risk framework which can be used to minimise this risk significantly.
Van der Merwe, C.J. 2010. Calculation Aspects of the European Rebalanced Basket Option using Monte Carlo methods. Unpublished Masters degree assignment. Stellenbosch: Stellenbosch University.
Life insurance and pension funds offer a wide range of products that are invested in a mix of assets. These portfolios (II), underlying the products, are rebalanced back to predetermined fixed proportions on a regular basis. This is done by selling the better performing assets and buying the worse performing assets. Life insurance or pension fund contracts can offer the client a minimum payout guarantee on the contract by charging them an extra premium (a). This problem can be changed to that of the pricing of a put option with 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 by studying the option’s sensitivities. In this thesis the premium and sensitivities of this put option are calculated, using different Monte Carlo methods, in order to find the most efficient method. Using general Monte Carlo methods, a simplistic pricing method is found which is refined by applying mathematical techniques so that the computational time is reduced significantly. After considering Antithetic Variables, Control Variates and Latin Hypercube Sampling as variance reduction techniques, option prices as Control Variates prove to reduce 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 Pathwise Derivatives Estimates and Finite Difference Approximations for estimating sensitivities of this option are found. Therefore by using the refined pricing method with option prices as Control Variates together with Owen and Faure-Tezuke type randomised Sobol’ sequences as a Quasi-Monte Carlo method, more efficient methods to price this option (compared to simplistic Monte Carlo methods) are obtained.