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Title: Model calibration for financial assets with mean-reverting price processes
Keywords: Model calibration, Mean-reverting process, Inverse problem, Optimal control, Distribution correction, Weighted Monte-Carlo simulation.
Issue Date: 18-Dec-2006
Citation: CHEN DIHUA (2006-12-18). Model calibration for financial assets with mean-reverting price processes. ScholarBank@NUS Repository.
Abstract: This thesis discusses the model calibration for financial assets with mean-revertingprice processes, which is an important topic in mathematical finance.The first part focuses on the recovery of local volatility from market data forSchwartz(1997) model. We formulate it as an inverse parabolic problem, and derivethe necessary condition for determining the local volatility under the optimal controlframework. An iterative algorithm is provided to solve the optimality systemand a synthetic numerical example is provided to illustrate the effectiveness.The second part is devoted to the model parameter calibration and distributioncorrection for Hull-White interest rate model. We propose an efficient-yet-precisecalibration technique which uses the analytical tractability of the model. To removethe occurrence of negative rates, a distribution correction method is proposed basedon weighted Monte-Carlo simulation. Our method has a notable advantage that itcan still preserve the calibration to the market data.
Appears in Collections:Master's Theses (Open)

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