SavedAdd your journal

Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 48 Issue: 3

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

Yong-ki Ma0000-0002-4590-763X
Pages
—
Publication Date
2019-06-15
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

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 explaining the dynamics of the stochastic process.
📊
Key Findings & Data:We propose an approach which can be used for the analytic approximation of the transition density related to a multi-scale stochastic volatility model.
💡
Conclusion & Impact:A numerical test also confirms the effectiveness of the model.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Multi-scale stochastic volatility model · transition density function · perturbation theory

Abstract

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

🔖

Cite This Article

Ma, Y. (2019). Analytic approximation of the transition density function under a multi-scale volatility model. Hacettepe Journal of Mathematics and Statistics, Volume: 48 Issue: 3. https://ajindex.com/articles/1402783

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (11)

  1. T. Adrian and J. Rosenberg, Stock returns and volatility: pricing the short-run and long-run components of market risk, J. Finance, 63, 2997–3030, 2008.
  2. Y. Aït-Sahalia, Maximum likelihood estimation of discretely sampled diffusions: a closed-form approximation approach, Econometrica, 70, 223–262, 2002.
  3. F. Black and M. Scholes, The pricing of options and corporate liabilities, J. Political Econ. 81, 637–654, 1973.
  4. M. Chernov, A.R. Gallant, E. Ghysels and G. Tauchne, Alternative models for stock price 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 interest rates, 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 volatility asymptotics, Multiscale Model. Simul 2, 22–42, 2003.
  8. A.R. Gallant, C.-T. Hsu and G. Tauchen, Using daily range data to calibrate volatility diffusions 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 invariant copula, Chaos Solitons Fractals, 85, 68–76, 2016.
  10. Y.-K. Ma and J.-H. Kim, Pricing the credit default swap rate for jump diffusion default 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.