Browsing by Author "Van Rooyen, Marchand"

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    Constructing volatility surfaces for managed funds
    (2014) Brinkman, Trevor Joseph; Van Rooyen, Marchand; Innocenzi, Paolo
    In this dissertation, a methodology is developed for constructing a volatility surface for a managed fund by extending the work of Bakshi et al. (2003) and Taylor (2014). The power utility assumption (with constant relative risk aversion for a specific maturity) and historical returns series data are used for the identified factors in influencing the return of the fund and the fund itself. The coefficient of relative risk aversion for a specific maturity and market is estimated from quoted option prices on a market index. This is used in combination with the identified factors and fund return series to estimate the risk-neutral skewness of the fund. An optimisation procedure is then used to determine the volatility smile of the fund for a specific maturity. Thereafter, the volatility surface of the fund is constructed by repeating each step for different maturities. Although this methodology produces sensible results, the optimisation routine used is sensitive to initial values and constraints.
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    Open Access
    Efficient implementation of the Heston-Hull & White model
    (2014) Maze, Sheldon; Dos Santos, Moses; Van Rooyen, Marchand
    A model with a stochastic interest rate process correlated to a stochastic volatility process is needed to accurately price long- dated contingent claims. Such a model should also price claims efficiently in order to allow for fast calibration. This dissertation explores the approximations for the characteristic function of the Heston-Hull&White model introduced by Grzelak and Oost- erlee (2011). Fourier-Cosine expansion pricing, due to Fang and Oosterlee (2008), is then used to price contingent claims under this model, which is implemented in MATLAB. We find that the model is efficient, accurate and has a relatively simple calibration procedure. In back-tests, it is determined that the Heston- Hull&White model produces better hedging profit and loss results than a Heston (1993) or a Black and Scholes (1973) model.