Browsing by Author "Teng, Huei-Wen"

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A SPHERICAL MONTE CARLO APPROACH FOR CALCULATING VALUE-AT-RISK AND EXPECTED SHORTFALL IN FINANCIAL RISK MANAGEMENT
(2017-01-01)
Teng, Huei-Wen
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資訊管理與財務金融系註：原資管所+財金所
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Department of Information Management and Finance
Accurate and efficient calculation for expected values is challenging in finance as well as various disciplines. In general, expected values can be written as high-dimensional integrals. Monte Carlo simulation is an indispensable tool for calculating them, but it is notoriously known for its slow convergence. For spherical distributions, this paper proposes a variance reduction technique and investigates its applications in finance. By using polar transformation, the expected value is written as an integral, and the innermost integral is with respect to the radius and the outermost integral is with respect to the unit sphere. The spherical Monte Carlo estimator is the average of function values of some random points generated by lattice. We consider Value-at-Risk and expected shortfall calculation under heavy-tailed distributions and demonstrate the superiority of the proposed method via numerical studies in terms of variance, computation time, and efficiency.
A systematic and efficient simulation scheme for the Greeks of financial derivatives
(2019-07-03)
Lyuu, Yuh-Dauh
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Teng, Huei-Wen
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Tseng, Yao-Te
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Wang, Sheng-Xiang
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統計學研究所
Greeks are the price sensitivities of financial derivatives and are essential for pricing, speculation, risk management, and model calibration. Although the pathwise method has been popular for calculating them, its applicability is problematic when the integrand is discontinuous. To tackle this problem, this paper defines and derives the parameter derivative of a discontinuous integrand of certain functional forms with respect to the parameter of interest. The parameter derivative is such that its integration equals the differentiation of the integration of the aforesaid discontinuous integrand with respect to that parameter. As a result, unbiased Greek formulas for a very broad class of payoff functions and models can be systematically derived. This new method is applied to the Greeks of (1) Asian options under two popular Levy processes, i.e. Merton's jump-diffusion model and the variance-gamma process, and (2) collateralized debt obligations under the Gaussian copula model. Our Greeks outperform the finite-difference and likelihood ratio methods in terms of accuracy, variance, and computation time.
Efficient Simulation of Value-at-Risk Under a Jump Diffusion Model: A New Method for Moderate Deviation Events
(2018-04-01)
Fuh, Cheng-Der
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Teng, Huei-Wen
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Wang, Ren-Her
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資訊管理與財務金融系註：原資管所+財金所
;
Department of Information Management and Finance
Importance sampling is a powerful variance reduction technique for rare event simulation, and can be applied to evaluate a portfolio's Value-at-Risk (VaR). By adding a jump term in the geometric Brownian motion, the jump diffusion model can be used to describe abnormal changes in asset prices when there is a serious event in the market. In this paper, we propose an importance sampling algorithm to compute the portfolio's VaR under a multi-variate jump diffusion model. To be more precise, an efficient computational procedure is developed for estimating the portfolio loss probability for those assets with jump risks. And the tilting measure can be separated for the diffusion and the jump part under the assumption of independence. The simulation results show that the efficiency of importance sampling improves over the naive Monte Carlo simulation from 9 to 277 times under various situations.
ON SPHERICAL MONTE CARLO SIMULATIONS FOR MULTIVARIATE NORMAL PROBABILITIES
(2015-09-01)
Teng, Huei-Wen
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Kang, Ming-Hsuan
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Fuh, Cheng-Der
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交大名義發表
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National Chiao Tung University
The calculation of multivariate normal probabilities is of great importance in many statistical and economic applications. In this paper we propose a spherical Monte Carlo method with both theoretical analysis and numerical simulation. We start by writing the multivariate normal probability via an inner radial integral and an outer spherical integral using the spherical transformation. For the outer spherical integral, we apply an integration rule by randomly rotating a predetermined set of well-located points. To find the desired set, we derive an upper bound for the variance of the Monte Carlo estimator and propose a set which is related to the kissing number problem in sphere packings. For the inner radial integral, we employ the idea of antithetic variates and identify certain conditions so that variance reduction is guaranteed. Extensive Monte Carlo simulations on some probabilities confirm these claims.
Simulating false alarm probability in K-distributed sea clutter
(1970-01-01)
Teng, Huei-Wen
;
Fuh, Cheng-Der
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資訊管理與財務金融系註：原資管所+財金所
;
Department of Information Management and Finance
Efficient and precise calculation of the probability of false alarms for the K-distributed sea clutter and noise is crucial in radar detection system. We propose efficient and optimal importance sampling algorithms, in which two importance sampling estimators are constructed for both the product form and the compound form of the underlying K distribution. Moreover, we prove the existence and uniqueness of the optimal tilting parameters. Detection accuracy and efficiency are analyzed in simulation studies.