Öz
Kaynakça
- 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.
- Y. Aït-Sahalia, Maximum likelihood estimation of discretely sampled diffusions: a closed-form approximation approach, Econometrica, 70, 223–262, 2002.
- F. Black and M. Scholes, The pricing of options and corporate liabilities, J. Political Econ. 81, 637–654, 1973.
- M. Chernov, A.R. Gallant, E. Ghysels and G. Tauchne, Alternative models for stock price dynamics, J. Econometrics, 73, 225–257, 2003.
- J.C. Cox, J.E. Ingersoll and S.A. Ross, A theory of the term structure of interest rates, Econometrica, 53, 385–408, 1985.
- J.-P. Fouque and X. Zhou, Perturbed Gaussian Copula, Adv. Econom. 22, 103–121, 2008.
- J.-P. Fouqu, G. Papanicolaou, R. Sircar and K. Sølna, Multiscale stochastic volatility asymptotics, Multiscale Model. Simul 2, 22–42, 2003.
- 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.
- J.-H. Kim, Y.-K. Ma and C.Y. Park, Joint survival probability via truncated invariant copula, Chaos Solitons Fractals, 85, 68–76, 2016.
- 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.
- O. Vasicek, An equilibrium characterization of the term structure, J. Financial Econ. 5, 177–188, 1977.
Öz
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.
Anahtar Kelimeler
Multi-scale stochastic volatility model transition density function perturbation theory
Kaynakça
- 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.
- Y. Aït-Sahalia, Maximum likelihood estimation of discretely sampled diffusions: a closed-form approximation approach, Econometrica, 70, 223–262, 2002.
- F. Black and M. Scholes, The pricing of options and corporate liabilities, J. Political Econ. 81, 637–654, 1973.
- M. Chernov, A.R. Gallant, E. Ghysels and G. Tauchne, Alternative models for stock price dynamics, J. Econometrics, 73, 225–257, 2003.
- J.C. Cox, J.E. Ingersoll and S.A. Ross, A theory of the term structure of interest rates, Econometrica, 53, 385–408, 1985.
- J.-P. Fouque and X. Zhou, Perturbed Gaussian Copula, Adv. Econom. 22, 103–121, 2008.
- J.-P. Fouqu, G. Papanicolaou, R. Sircar and K. Sølna, Multiscale stochastic volatility asymptotics, Multiscale Model. Simul 2, 22–42, 2003.
- 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.
- J.-H. Kim, Y.-K. Ma and C.Y. Park, Joint survival probability via truncated invariant copula, Chaos Solitons Fractals, 85, 68–76, 2016.
- 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.
- O. Vasicek, An equilibrium characterization of the term structure, J. Financial Econ. 5, 177–188, 1977.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Matematik |
| Bölüm | Matematik |
| Yazarlar | |
| Yayımlanma Tarihi | 15 Haziran 2019 |
| Yayımlandığı Sayı | Yıl 2019 Cilt: 48 Sayı: 3 |