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Pricing Catastrophe Bond by esscher transform

Journal of Systems Science and Information 2008年第1期6卷 35-44页

作者： Jianxiang Shi Ruiguang Gong Financial School Zhejiang Gongshang University Hangzhou 310018 China

This paper developed a model for pricing catastrophe bond whose trigger is loss index. In the model esscher transform which is a facility usually used in actuarial science now provides an easy way to calculate Radon-Nikodym derivative so that the whole pricing process becomes easier to understand. At the end of this paper we use this model to price a China typhoon catastrophe bond which is also designed by us.

关键词： esscher transform catastrophe bond pricing

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Option Pricing when the Regime-Switching Risk is Priced

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Acta Mathematicae Applicatae Sinica 2009年第3期25卷 369-388页

作者： Tak Kuen Siu Hailiang Yang Department of Mathematics and Statistics Curtin University of Technology Perth W.A. 6845 Australia Department of Statistics and Actuarial Science the University of Hong Kong Pokfulam Road Hong Kong

We study the pricing of an option when the price dynamic of the underlying risky asset is governed by a Markov-modulated geometric Brownian motion. We suppose that the drift and volatility of the underlying risky asset are modulated by an observable continuous-time, finite-state Markov chain. We develop a two- stage pricing model which can price both the diffusion risk and the regime-switching risk based on the esscher transform and the minimization of the maximum entropy between an equivalent martingale measure and the real-world probability measure over different states. Numerical experiments are conducted and their results reveal that the impact of pricing regime-switching risk on the option prices is significant.

关键词： Option valuation regime-switching risk two-stage pricing procedure esscher transform martingale restriction min-max entropy problem

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Empirical Study on Option Pricing under Markov Regime Switching Economics

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Annals of Applied Mathematics 2024年第1期40卷 21-42页

作者： Lianfeng(David)Liu Department of Financial and Actuarial Mathematics Xi'an Jiaotong-Liverpool UniversitySuzhouJiangsu 215123China

In this research,we summarize the results of a practical study of index options based on the option valuation model which was proposed by Siu and Yang(Acta ***.,25(3)(2009),pp.339{388),where an EMM kernel is integrated which takes into account all risk components of a regime-switching ***,the regime-switching risk of an economy in the options is priced using a hidden Markov regime-switching model with the risky underlying asset being modulated by a discrete-time,nite-state,hidden Markov chain whose states represent the hidden states of an *** apply such a model to the pricing of Hang Seng Index options based on the real-world nancial data from October 2009 to October 2010(i.e.,for the year in which the model was proposed).We employed the entropy martingale measure(EMM)approach proposed by Siu and Yang(Acta ***.,25(3)(2009),pp.339{388)to determine the optimal martingale measure for the Markov-modulated *** addition,we have proposed a numerical technique called the weighted di erence method to compliment the EMM *** have also veri ed the extended jump-di usion model under regime-switching that we proposed recently(***.,6(4)(2019),1950038)using the 50ETF options which are obtained from Shanghai Stock Exchange covering a time span from January 2018 to December ***,we have highlighted the challenges for the EMM kernel-based Markov regime-switching model for pricing the out-of-the-money index options in the real world.

关键词： Option pricing EMM regime-switching hidden Markov model esscher transform weighted difference method

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An EPMS Price Estimator for Multi-Asset Financial Derivatives

An EPMS Price Estimator for Multi-Asset Financial Derivative...

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第十届海峡两岸统计与概率研讨会

作者：黄士峰邱冠智 Institute of Statistics "National University of Kaohsiung"

This study proposes an empirical martingale simulation(EMS) and an empirical P-martingale simulation(EPMS) price estimators for multi-asset financial derivatives. Under mild assumptions on the payoff functions, the strong consistency and asymptotic normality of the proposed estimators are established. Several simulation scenarios are conducted to investigate the performance of the proposed price estimators under multivariate geometric Brownian motion and multivariate GARCH models. Numerical results indicate that the multi-asset EMS and EPMS price estimators are capable of improving the efficiency of their Monte Carlo counterparts. In addition, the asymptotic distribution serves as a persuasive approximation to the finite-sample distribution of the EPMS price estimator, which helps to reduce the computation time of finding confidence intervals for the prices of multi-asset derivatives.

关键词： Empirical martingale simulation esscher transform Multi-asset derivatives pricing

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