Empirical Martingale Simulation for Asset Prices

Duan, Jin‐Chuan; Simonato, Jean‐Guy

doi:10.1287/mnsc.44.9.1218

Cited by 179 publications

(109 citation statements)

References 15 publications

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“…We then examine the impact of this adjustment on caplet prices. A similar adjustment is proposed in a setting without discretization error by Duan and Simonato [6]; see also the discussion in Boyle et al [4]. Similar adjustments appear to be in widespread use in practice.…”

Section: Finite-sample Adjustmentmentioning

confidence: 82%

Arbitrage-free discretization of lognormal forward Libor and swap rate models

Glasserman

Zhao

2000

Finance and Stochastics

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Abstract. An important recent development in the pricing of interest rate derivatives is the emergence of models that incorporate lognormal volatilities for forward Libor or forward swap rates while keeping interest rates stable. These market models have three attractive features: they preclude arbitrage among bonds, they keep rates positive, and, most distinctively, they price caps or swaptions according to Black's formula, thus allowing automatic calibration to market data. But these features of continuous-time formulations are easily lost when the models are discretized for simulation. We introduce methods for discretizing these models giving particular attention to precluding arbitrage among bonds and to keeping interest rates positive even after discretization. These methods transform the Libor or swap rates to positive martingales, discretize the martingales, and then recover the Libor and swap rates from these discretized variables, rather than discretizing the rates themselves. Choosing the martingales proportional to differences of ratios of bond prices to numeraire prices turns out to be particularly convenient and effective. We can choose the discretization to price one caplet of arbitrary maturity without discretization error. We numerically investigate the accuracy of other caplet and swaption prices as a gauge of how closely a model calibrated to implied volatilities reproduces market prices. Numerical results indicate that several of the methods proposed here often outperform more standard discretizations.

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Section: Finite-sample Adjustmentmentioning

confidence: 82%

Arbitrage-free discretization of lognormal forward Libor and swap rate models

Glasserman

Zhao

2000

Finance and Stochastics

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“…The martingale property fails to hold exactly in simulation because of discretization and sampling errors. We have used the Empirical Martingale Simulation (EMS) technique of Duan and Simonato (1998) in order to achieve variance reduction and ensure that the martingale property is satisfied. The technique is applied as follows for n stock price paths with m sub-intervals each (Chan & Wong, 2013).…”

Section: Ngarch Option Pricing Modelmentioning

confidence: 99%

Empirical Performance of Black-Scholes and GARCH Option Pricing Models during Turbulent Times: The Indian Evidence

Bhat¹,

Arekar²

2016

IJEF

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Exchange-traded currency options are a recent innovation in the Indian financial market and their pricing is as yet unexplored. The objective of this research paper is to empirically compare the pricing performance of two well-known option pricing models -the Black-Scholes-Merton Option Pricing Model (BSM) and Duan"s NGARCH option pricing model -for pricing exchange-traded currency options on the US dollar-Indian rupee during a recent turbulent period. The BSM is known to systematically misprice options on the same underlying asset but with different strike prices and maturities resulting in the phenomenon of the "volatility smile". This bias of the BSM results from its assumption of a constant volatility over the option"s life. The NGARCH option pricing model developed by Duan is an attempt to incorporate time-varying volatility in pricing options. It is a deterministic volatility model which has no closed-form solution and therefore requires numerical techniques for evaluation. In this paper we have compared the pricing performance and examined the pricing bias of both models during a recent period of volatility in the Indian foreign exchange market. Contrary to our expectations the pricing performance of the more sophisticated NGARCH pricing model is inferior to that of the relatively simple BSM model. However orthogonality tests demonstrate that the NGARCH model is free of the strike price and maturity biases associated with the BSM. We conclude that the deterministic BSM does a better job of pricing options than the more advanced time-varying volatility model based on GARCH.

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“…Belief coe cients/A-synchronous updating ratio(? )/Intensity of choice Huisman et al (2010) A B S Q M L B e l i e f c o e c i e n t s / I n t e n s i t y o f c h o i c e Kouwenberg and Zwinkels (2014) ABS QML Belief coe cients/Intensity of choice Kouwenberg and Zwinkels (2015) ABS QML Price elasticity/Belief coe cients/Intensity of choice Lof (2012) A B S N L S B e l i e f c o e c i e n t s / I n t e n s i t y o f c h o i c e Lof (2015) ABS Duan and Simonato (1998), GMM for generalized method of moments, and SMD for simulated minimum distance. '?'…”

Section: A Route To Empirical Estimation Of Fabms: Review Of Existingmentioning

confidence: 99%

Estimation of financial agent-based models with simulated maximum likelihood

Kukačka

Baruník

2017

Journal of Economic Dynamics and Control

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. This paper proposes a general computational framework for empirical estimation of financial agent based models, for which criterion functions do not have known analytical form. For this purpose, we adapt a nonparametric simulated maximum likelihood estimation based on kernel methods. Employing one of the most widely analysed heterogeneous agent models in the literature developed by Brock and Hommes (1998), we extensively test properties of the proposed estimator and its ability to recover parameters consistently and efficiently using simulations. Key empirical findings point us to the statistical insignificance of the switching coefficient but markedly significant belief parameters defining heterogeneous trading regimes with superiority of trend-following over contrarian strategies. In addition, we document slight proportional dominance of fundamentalists over trend following chartists in main world markets. Terms of use: Documents in AbstractThis paper proposes a general computational framework for empirical estimation of financial agent based models, for which criterion functions do not have known analytical form. For this purpose, we adapt a nonparametric simulated maximum likelihood estimation based on kernel methods. Employing one of the most widely analysed heterogeneous agent models in the literature developed by Brock and Hommes (1998), we extensively test properties of the proposed estimator and its ability to recover parameters consistently and e ciently using simulations. Key empirical findings point us to the statistical insignificance of the switching coe cient but markedly significant belief parameters defining heterogeneous trading regimes with superiority of trend-following over contrarian strategies. In addition, we document slight proportional dominance of fundamentalists over trend following chartists in main world markets.JEL: C14, C51, C63, D84, G02, G12

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Empirical Martingale Simulation for Asset Prices

Cited by 179 publications

References 15 publications

Arbitrage-free discretization of lognormal forward Libor and swap rate models

Arbitrage-free discretization of lognormal forward Libor and swap rate models

Empirical Performance of Black-Scholes and GARCH Option Pricing Models during Turbulent Times: The Indian Evidence

Estimation of financial agent-based models with simulated maximum likelihood

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