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Journals / Hacettepe Journal of Mathematics and Statistics / 2019 / Cilt: 48 - Sayı: 3

Analytic approximation of the transition densityfunction under a multi-scale volatility model

Yong-Ki MA
Pages
682–688
Publication Date
2022-10-18
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

A numerical test also confirms the effectiveness of the model.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The transition density function plays an important role in understanding and explainingthe dynamics of the stochastic process.
📊
Key Findings & Data:We propose an approach which can be used forthe analytic approximation of the transition density related to a multi-scale stochasticvolatility model.
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Conclusion & Impact:A numerical test also confirms the effectiveness of the model.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

The transition density function plays an important role in understanding and explainingthe dynamics of the stochastic process. We propose an approach which can be used forthe analytic approximation of the transition density related to a multi-scale stochasticvolatility model. Using perturbation theory, we compute the leading-order term and thefirst-order correction terms. A numerical test also confirms the effectiveness of the model.

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Cite This Article

MA, Y. (2022). Analytic approximation of the transition densityfunction under a multi-scale volatility model. Hacettepe Journal of Mathematics and Statistics, Cilt: 48 - Sayı: 3, 682–688. https://ajindex.com/articles/530117

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References (1)

  1. T. Adrian and J. Rosenberg,Stock returns and volatility: pricing the short-run andlong-run components of market risk, J. Finance,63, 2997–3030, 2008. [2]Y. Aït-Sahalia,Maximum likelihood estimation of discretely sampled diffusions: aclosed-form approximation approach, Econometrica,70, 223–262, 2002. [3]F. Black and M. Scholes,The pricing of options and corporate liabilities, J. PoliticalEcon.81, 637–654, 1973. [4]M. Chernov, A.R. Gallant, E. Ghysels and G. Tauchne,Alternative models for stockprice dynamics, J. Econometrics,73, 225–257, 2003. [5]J.C. Cox, J.E. Ingersoll and S.A. Ross,A theory of the term structure of interestrates, Econometrica,53, 385–408, 1985. [6]J.-P. Fouque and X. Zhou,Perturbed Gaussian Copula, Adv. Econom.22, 103–121,2008. [7]J.-P. Fouqu, G. Papanicolaou, R. Sircar and K. Sølna,Multiscale stochastic volatilityasymptotics, Multiscale Model. Simul2, 22–42, 2003. [8]A.R. Gallant, C.-T. Hsu and G. Tauchen,Using daily range data to calibrate volatilitydiffusions and extract the forward integrated variance, Rev. Econ. Stat.81, 617–631,1999. [9]J.-H. Kim, Y.-K. Ma and C.Y. Park,Joint survival probability via truncated invariantcopula, Chaos Solitons Fractals,85, 68–76, 2016. [10]Y.-K. Ma and J.-H. Kim,Pricing the credit default swap rate for jump diffusiondefault intensity processes, Quant. Finance,10, 809–817, 2010. [11]O. Vasicek,An equilibrium characterization of the term structure, J. Financial Econ.5, 177–188, 1977.