Asymptotic properties of Monte Carlo estimators of diffusion processes

Detemple, Jérôme; García, René; Rindisbacher, Marcel

doi:10.1016/j.jeconom.2005.06.028

Cited by 21 publications

(7 citation statements)

References 60 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Kurtz and Protter (1991) identify the law of the error of the Euler scheme for discretizing stochastic differential equations, and they characterize the limiting error through a stochastic differential equation driven by a Brownian motion independent of the original driving Brownian motion. Jacod and Protter (1998) extend this analysis to Lévy-driven processes, and Detemple, Garcia, and Rindisbacher (2006) use it to compare alternative discretization methods. Related ideas arise in the convergence of GARCH models to continuous-time limits, as in Duan (1997).…”

Section: The Limit Theoremmentioning

confidence: 99%

Risk Horizon and Rebalancing Horizon in Portfolio Risk Measurement

Glasserman¹

2010

Mathematical Finance

View full text Add to dashboard Cite

This paper analyzes portfolio risk and volatility in the presence of constraints on portfolio rebalancing frequency. This investigation is motivated by the incremental risk charge (IRC) introduced by the Basel Committee on Banking Supervision. In contrast to the standard market risk measure based on a ten-day value-at-risk calculated at 99% confidence, the IRC considers more extreme losses and is measured over a one-year horizon. More importantly, whereas ten-day VaR is ordinarily calculated with a portfolio's holdings held fixed, the IRC assumes a portfolio is managed dynamically to a target level of risk, with constraints on rebalancing frequency. The IRC uses discrete rebalancing intervals (e.g., monthly or quarterly) as a rough measure of potential illiquidity in underlying assets. We analyze the effect of these rebalancing intervals on the portfolio's profit and loss distribution over a risk-measurement horizon. We derive limiting results, as the rebalancing frequency increases, for the difference between discretely and continuously rebalanced portfolios; we use these to approximate the loss distribution for the discretely rebalanced portfolio relative to the continuously rebalanced portfolio. Our analysis leads to explicit measures of the impact of discrete rebalancing under a simple model of asset dynamics.

show abstract

Section: The Limit Theoremmentioning

confidence: 99%

Risk Horizon and Rebalancing Horizon in Portfolio Risk Measurement

Glasserman¹

2010

Mathematical Finance

View full text Add to dashboard Cite

show abstract

“…In a recent paper, Detemple et al (2002) study estimators of the conditional expectation of diffusions. They show that if J is allowed to diverge too fast relative to N; then the bias of their estimator blows up.…”

Section: Article In Pressmentioning

confidence: 99%

Efficient estimation of general dynamic models with a continuum of moment conditions

Carrasco

Chernov

Florens

et al. 2007

Journal of Econometrics

113

View full text Add to dashboard Cite

There are two difficulties with the implementation of the characteristic function-based estimators. First, the optimal instrument yielding the ML efficiency depends on the unknown probability density function. Second, the need to use a large set of moment conditions leads to the singularity of the covariance matrix. We resolve the two problems in the framework of GMM with a continuum of moment conditions. A new optimal instrument relies on the double indexing and, as a result, has a simple exponential form. The singularity problem is addressed via a penalization term. We introduce HAC-type estimators for non-Markov models. A simulated method of moments is proposed for nonanalytical cases. r

show abstract

“…(see [5]) A comparison of (33), (34) and (44), showes that these three methods converge at the same speed N 1 .…”

Section: Euler Scheme On the Transformed State Variablesmentioning

confidence: 96%

Application of Doss Transformation in Approximation of Stochastic Differential Equations

Vajargah¹

2013

JCSCM

View full text Add to dashboard Cite

The solution of the financial application, be it asset pricing, portfolio allocation or risk management, relies on the simulation of discretized versions of the stochastic differential equations(SDEs). The simplest way to confront SDEs in numerical situations is to discretize them and use monte carlo simulation. The Euler scheme is most often used for discretization of SDEs. This discretization involves an approximation error. In this topic at the first we recall an introduction to SDEs and Monte carlo simulation. Then, we study the asymptotic error distribution of Euler approximations of solutions of SDEs. We also study the error distribution associated with a Doss transformation of the state variables. Convergence results for Euler schemes with and without doss transformation and the comparison of them with Milshtein scheme are presented at the end.

show abstract

Asymptotic properties of Monte Carlo estimators of diffusion processes

Cited by 21 publications

References 60 publications

Risk Horizon and Rebalancing Horizon in Portfolio Risk Measurement

Risk Horizon and Rebalancing Horizon in Portfolio Risk Measurement

Efficient estimation of general dynamic models with a continuum of moment conditions

Application of Doss Transformation in Approximation of Stochastic Differential Equations

Contact Info

Product

Resources

About