Estimating expected exposure profiles using biplot interpolation

Abstract

ENGLISH SUMMARY : The accounting standards provides guidelines on how to determine the fair value for a financial asset or liability held at fair value. When considering the fair value of derivative instruments, some additional adjustments need to be made for counterparty credit risk. For interest rate swaps, in particular, one needs to calculate the effective exposure of the swap in order to make these adjustments. One of the most popular methods, albeit computationally intensive, is to calculate these exposures through Monte Carlo simulation. In this study an alternative method of calculating the effective exposure using biplot interpolation is proposed. In this proposed method, an analytical approach in approximating the effective exposure profile is implemented through fitting a beta function. The parameters for this beta function are then estimated through biplot interpolation, which in turn approximates the exposure profile. When the performance of the biplot interpolation approach was tested using a standard interval testing approach, the approximated biplot interpolated profile provided a reasonable approximation of the true profile.

AFRIKAANSE OPSOMMING : Die rekeningkundige standaarde bevat riglyne vir die bepaling van die billike waarde van 'n finansiele bate of las wat teen billike waarde gehou word. Wanneer die billike waarde vir afgeleide instrumente beskoud word, moet verdere aanpassings aangebring word vir die teenparty-kredietrisiko. Vir rentekoersruilkontrakte moet die effektiewe blootstelling van die ruilkontrak bereken word om hierdie aanpassings moontlik te kan aan bring. Een van die gewildste metodes, hoewel berekeningsintensief, is om hierdie blootstellings met behulp van Monte Carlo-simulasie te bereken. In hierdie studie word 'n alternatiewe metode vir die berekening van die effektiewe blootstelling met behulp van bi-stipping-interpolasie voorgestel. In hierdie voorgestelde metode word 'n analitiese benadering gebruik om die effektiewe blootstellingsprofiel te benader deur 'n beta-funksie toe te pas. Die parameters vir hierdie beta-funksie word dan bepaal deur bi-stipping-interpolasie, wat op sy beurt die blootstellingsprofiel benader. Toe die uitvoering van die bi-stipping-interpolasiebenadering met behulp van 'n standaard-interval-toetsbenadering getoets is, het die benaderde bi-stipping-geinterpoleerde profiel 'n redelike benadering van die ware profiel gegee.