Stochastic Volatility Jump-Diffusion Model for Option Pricing
Nonthiya Makate, Pairote Sattayatham
DOI: 10.4236/jmf.2011.13012   PDF   HTML     5,029 Downloads   11,287 Views   Citations


An alternative option pricing model is proposed, in which the asset prices follow the jump-diffusion model with square root stochastic volatility. The stochastic volatility follows the jump-diffusion with square root and mean reverting. We find a formulation for the European-style option in terms of characteristic functions of tail probabilities.

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N. Makate and P. Sattayatham, "Stochastic Volatility Jump-Diffusion Model for Option Pricing," Journal of Mathematical Finance, Vol. 1 No. 3, 2011, pp. 90-97. doi: 10.4236/jmf.2011.13012.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] [1] J. M. Reinhard, “On a Class of Semi-Markov Risk Models Obtained as Classical Risk Models in a Markovian Environment,” ASTIN Bulletin, Vol. 14, 1984, pp. 23-43.
[2] S. Asmussen, “Risk Theory in a Markovian Environment,” Scandinavian Actuarial Journal, Vol. 2, 1989, pp. 69-100.
[3] Y. Lu and S. Li, “On the Probability of Ruin in a Markov-modulated Risk Model,” Insurance: Mathemat- ics and Economics, Vol. 37, No. 3, 2005, pp. 522-532. doi:10.1016/j.insmatheco.2005.05.006
[4] A. Ng and H. Yang, “Lundberg-Type Bounds for the Joint Distribution of Surplus Immediately before and after Ruin under a Markov-modulated Risk Model,” Astin Bulletin, Vol. 35, 2005, pp. 351-361. doi:10.2143/AST.35.2.2003457
[5] A. Ng and H. Yang, “On the Joint Distribution of Surplus Prior and Immediately after Ruin under a Markovian Re- gime Switching Model,” Stochastic Processes and Their Applications, Vol. 116, No. 2, 2006, pp. 244-266. doi:10.1016/
[6] S. M. Li and Y. Lu, “Moments of the Dividend Payments and Related Problems in a Markov-Modulated Risk Mo- del,” North American Actuarial Journal, Vol. 11, No. 2, 2007, pp. 65-76.
[7] Y. Lu and S. Li, “The Markovian Regime-switching Risk Model with a Threshold Dividend Strategy,” Insurance: Mathematics and Economics, Vol. 44, No. 2, 2009, pp. 296-303. doi:10.1016/j.insmatheco.2008.04.004
[8] J. Liu, J. C. Xu and H. C. Hu, “The Markov-Dependent Risk Model with a Threshold Dividend Strategy,” Wuhan University Journal of Natural Sciences, Vol. 16, No. 3, 2011, pp. 193-198. doi:10.1007/s11859-011-0736-9
[9] J. Zhu and H. Yang, “Ruin Theory for a Markov Regime-Switching Model under a Threshold Dividend Stra- tegy,” Insurance: Mathematics and Economics, Vol. 42, No. 1, 2008, pp. 311-318. doi:10.1016/j.insmatheco.2007.03.004
[10] J. Q. Wei, H. L. Yang and R. M. Wang, “On the Markov -Modulated Insurance Risk Model with Tax,” Blaetter der DGVFM, Vol. 31, No. 1, 2010, pp. 65-78. doi:10.1007/s11857-010-0104-4
[11] M. Zhou and C. Zhang, “Absolute Ruin under Classical Risk Model,” Acta Mathematicae Applicate Sinica, Vol. 28, No. 4, 2005, pp. 57-80.
[12] J. Cai, “On the Time Value of Absolute Ruin with Debit Interest,” Advances in Applied Probability, Vol. 39, No. 2, 2007, pp. 343-359. doi:10.1239/aap/1183667614
[13] H. L. Yuan and Y. J. Hu, “Absolute Ruin in the Compound Poisson Risk Model with Constant Dividend Barrier,” Statistics and Probability Letter, Vol. 78, No. 14, 2008, pp. 2086-2094. doi:10.1016/j.spl.2008.01.076
[14] C. W. Wang and C. C. Yin, “Dividend Payments in the Classical Risk Model under Absolute Ruin with Debit In- terest,” Applied stochastic models in business and Indus- try, Vol. 25, No. 3, 2009, pp. 247-262. doi:10.1002/asmb.722
[15] C. W. Wang, C. C.Yin and E. Q. Li, “On the Classical Risk Model with Credit and Debit Interests under Absolute Ruin,” Statistics and Probability Letters, Vol. 80, No. 15, 2010, pp. 427-436. doi:10.1016/j.spl.2009.11.020

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