Browsing by Author "Fuh, Cheng-Der"

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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
;
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
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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.
Reading between the ratings: Modeling residual credit risk and yield overlap
(2017-08-01)
Chang, Charles
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Fuh, Cheng-Der
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Kao, Chu-Lan Michael
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統計學研究所
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Institute of Statistics
Credit ratings group firms by risk, yet yields are shown to overlap between firms of adjacent ratings. We model this by considering the residual risk arising from differences in the parameters of each firm's value process for firms with the same rating. To do so, our framework simultaneously incorporates jump default with Markov-governed likelihoods and continuous defaults in a default-barrier framework. We provide closed-form approximations for expected default time and tail probabilities, and empirically fit the S-shaped yield curve, intra-rating spread, and inter-rating overlap. Results are robust to time period, rating system, sub-rating, and common characteristics such as liquidity. (C) 2017 Published by Elsevier B.V.
Simulating false alarm probability in K-distributed sea clutter
(1970-01-01)
Teng, Huei-Wen
;
Fuh, Cheng-Der
;
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.