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    National Tsing Hua University Institutional Repository > 科技管理學院  > 計量財務金融學系 > 博碩士論文  >  GPU-Based Monte Carlo Calibration to Implied Volatility Surfaces under Multi-Factor Stochastic Volatility Model


    Please use this identifier to cite or link to this item: http://nthur.lib.nthu.edu.tw/dspace/handle/987654321/83273


    Title: GPU-Based Monte Carlo Calibration to Implied Volatility Surfaces under Multi-Factor Stochastic Volatility Model
    Authors: 陳靜
    Han, Chuan-Hsiang
    Chen, Ching
    教師: 韓傳祥
    Date: 2013
    Keywords: volatility
    model calibration
    Monte Carlo simulation
    multi-factor Stochastic Volatility Model (SVM)
    Martingale Control Variate (MCV)
    (Corrected) Fourier transform method
    Graphics Processing Unit (GPU)
    Abstract: Financial markets comprise of the spot market and its derivative market. The spot market contains information that is backward-looking. On the other hand, the derivative market uses a forward-looking concept. Model calibration, which is the focus of this paper, is a crucial tool to analyze forward information, which is frequently utilize when regarding pricing, hedging, and risk management.

    A model calibration problem is mainly about solving a nonlinear optimization problem to find the best fit of implied volatility surface. This kind of problem can be solved by many different methods, including Fourier transform, perturbation methods, numerical PDEs, etc. The above methods are based on deterministic approaches, which are restricted to simple models; these lack flexibility and are inapplicable in high-dimensional models. Hence Monte Carlo simulation is employ to solve complex high-dimensional models.

    We propose a multi-factor Stochastic Volatility Model (SVM) that takes different frequency data into account. Literatures find the dynamic of implied volatilities is better fitted under multi-factor SVM. The accuracy of the Monte Carlo simulation can be improved using a variance reduction method, known as, the Martingale Control Variate (MCV). The advantage of better fitting comes with the problem of massive computation. We involve parallel computing on the Graphics Processing Unit (GPU) to help solve this problem. GPUs are first used for computer graphing, which turn increasingly programmable and computationally powerful especially on calculations that are carried out simultaneously. Combining GPU parallel computing with the Martingale Control Variate method will result in a model calibration of multi-factor SVM that is even more precise and more feasible to analyze option data in real time.

    After developing the model, the time dependent volatility model is used to calculate the Volatility Index (VIX) with the use of the term structure of VIX published by the Chicago Board Options Exchange (CBOE) we can solve the identification problem that we faced in multi-factor SVM.
    URI: http://nthur.lib.nthu.edu.tw/dspace/handle/987654321/83273
    Source: http://thesis.nthu.edu.tw/cgi-bin/gs/hugsweb.cgi?o=dnthucdr&i=sGH02100071502.id
    Appears in Collections:[計量財務金融學系] 博碩士論文

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