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Pricing and hedging catastrophe equity put options under a Markov-modulated jump diffusion model
1. | Department of Financial Engineering, Ningbo University, Ningbo, 315211, China |
2. | School of Finance and Statistics, East China Normal University, 500 Dongchuan Road, Shanghai, 200241, China |
3. | School of Science, Nanjing Audit University, Nanjing, 210029, China |
References:
[1] |
A. Ang and G. Bekaert, Regime switches in interest rates,, Journal of Business and Economic Statistics, 20 (2002), 163.
doi: 10.1198/073500102317351930. |
[2] |
L. J. Bo, Y. J. Wang and X. W. Yang, Markov-modulated jump-diffusions for currency option pricing,, Insurance: Mathematics and Economics, 46 (2010), 461.
doi: 10.1016/j.insmatheco.2010.01.003. |
[3] |
J. Buffington and R. J. Elliott, American options with regime switching,, International Journal of Theoretical and Applied Finance, 5 (2002), 497.
doi: 10.1142/S0219024902001523. |
[4] |
J. Campbell and L. Hentschel, No news is good news: An asymmetric model of changing volatility in stock returns,, Journal of Financial Economics, 31 (1992), 281. Google Scholar |
[5] |
C. C. Chang, S. K. Lin and M. T. Yu, Valuation of catastrophe equity puts with Markov-modulated Poisson processes,, The Journal of Risk and Insurance, 78 (2011), 447. Google Scholar |
[6] |
L. F. Chang and M. W. Huang, Analytical valuation of catastrophe equity options with negative exponential jumps,, Insurance: Mathematics and Economics, 44 (2009), 59.
doi: 10.1016/j.insmatheco.2008.09.009. |
[7] |
S. H. Cox and H. W. Pedersen, Catastrophe risk bonds,, North American Actuarial Journal, 4 (2000), 56.
doi: 10.1080/10920277.2000.10595938. |
[8] |
S. H. Cox, J. Fairchild and H. W. Pedersen, Valuation of structured risk management products,, Insurance: Mathematics and Economics, 34 (2004), 259. Google Scholar |
[9] |
A. Dassios, J. W. Jang, Pricing of catastrophe reinsurance and derivatives using the Cox process with short noise intensity,, Finance and Stochastics, 7 (2003), 73.
doi: 10.1007/s007800200079. |
[10] |
J. C. Duan, I. Popova and P. Ritchken, Option pricing under regime switching,, Quantitative Finance, 2 (2002), 116.
doi: 10.1088/1469-7688/2/2/303. |
[11] |
R. J. Elliott, L. L. Chan and T. K. Siu, Option pricing and Esscher transform under regime switching,, Annals of Finance, 1 (2005), 423. Google Scholar |
[12] |
R. J. Elliott and C. J. U. Osakwe, Option pricing for pure jump processes with Markov switching compensators,, Finance and Stochastics, 10 (2006), 250.
doi: 10.1007/s00780-006-0004-6. |
[13] |
R. J. Elliott, T. K. Siu, L. L. Chan and J. W. Lau, Pricing options under a generalized Markov-modulated jump-diffusion model,, Stochastic Analysis and Applications, 25 (2007), 821.
doi: 10.1080/07362990701420118. |
[14] |
H. F$\ddoto$llmer and M. Schweizer, Hedging of contingent claims under incomplete information,, In Applied Stochastic Analysis (Eds. M.H.A. Davis and R.J. Elliot)(London, (1991), 389.
|
[15] |
M. K. Ghosh, A. Arapostathis and S. I. Marcus, Ergodic control of switching diffusions,, SIAM Journal on Control and Optimization, 35 (1997), 1952.
doi: 10.1137/S0363012996299302. |
[16] |
X. Guo, Information and option pricings,, Quantitative Finance, 1 (2001), 38.
doi: 10.1080/713665550. |
[17] |
H. Gründl and H. Schmeiser, Pricing double-trigger reinsurance contracts: Financial versus actuarial approach,, The Journal of Risk and Insurance, 69 (2002), 449. Google Scholar |
[18] |
S. Jaimungal and T. Wang, Catastrophe options with stochastic interest rates and compound poisson losses,, Insurance: Mathematics and Economics, 38 (2006), 469.
doi: 10.1016/j.insmatheco.2005.11.008. |
[19] |
K. Lee and S. Song, Insiders' hedging in a jump diffusion model,, Quantitative Finance, 5 (2007), 537.
doi: 10.1080/14697680601043191. |
[20] |
K. Lee and P. Protter, Hedging claims with feedback jumps in the price process,, Communications on Stochastic Analysis, 2 (2008), 125.
|
[21] |
J. Lewellen, Predicting returns with financial ratios,, Journal of Financial Economics, 74 (2004), 209. Google Scholar |
[22] |
S. K. Lin, C. C. Chang and M. R. Powers, The valuation of contingent capital with catastrophe risks,, Insurance: Mathematics and Economics, 45 (2009), 65.
doi: 10.1016/j.insmatheco.2009.03.005. |
[23] |
R. C. Merton, Option pricing when underlying stock returns are discontinuous,, Journal of Financial Economics, 3 (1976), 125. Google Scholar |
[24] |
Y. Shen and T. K. Siu, Pricing variance swaps under a stochastic interest rate and volatility model with regime-switching,, Operations Research Letters, 41 (2013), 180.
doi: 10.1016/j.orl.2012.12.008. |
[25] |
T. K. Siu, H. L. Yang and J. W. Lau, Pricing currency options under two-factor Markov-modulated stochastic volatility models,, Insurance: Mathematics and Economics, 43 (2008), 295.
doi: 10.1016/j.insmatheco.2008.05.002. |
[26] |
M. Schweizer, A guided tour through quadratic hedging approaches,, in Option Pricing, (2001), 538.
doi: 10.1017/CBO9780511569708.016. |
[27] |
J. H. Yoon, B. G. Jang and K. H. Roh, An analytic valuation method for multivariate contingent claims with regime-switching volatilities,, Operations Research Letters, 39 (2011), 180.
doi: 10.1016/j.orl.2011.02.010. |
show all references
References:
[1] |
A. Ang and G. Bekaert, Regime switches in interest rates,, Journal of Business and Economic Statistics, 20 (2002), 163.
doi: 10.1198/073500102317351930. |
[2] |
L. J. Bo, Y. J. Wang and X. W. Yang, Markov-modulated jump-diffusions for currency option pricing,, Insurance: Mathematics and Economics, 46 (2010), 461.
doi: 10.1016/j.insmatheco.2010.01.003. |
[3] |
J. Buffington and R. J. Elliott, American options with regime switching,, International Journal of Theoretical and Applied Finance, 5 (2002), 497.
doi: 10.1142/S0219024902001523. |
[4] |
J. Campbell and L. Hentschel, No news is good news: An asymmetric model of changing volatility in stock returns,, Journal of Financial Economics, 31 (1992), 281. Google Scholar |
[5] |
C. C. Chang, S. K. Lin and M. T. Yu, Valuation of catastrophe equity puts with Markov-modulated Poisson processes,, The Journal of Risk and Insurance, 78 (2011), 447. Google Scholar |
[6] |
L. F. Chang and M. W. Huang, Analytical valuation of catastrophe equity options with negative exponential jumps,, Insurance: Mathematics and Economics, 44 (2009), 59.
doi: 10.1016/j.insmatheco.2008.09.009. |
[7] |
S. H. Cox and H. W. Pedersen, Catastrophe risk bonds,, North American Actuarial Journal, 4 (2000), 56.
doi: 10.1080/10920277.2000.10595938. |
[8] |
S. H. Cox, J. Fairchild and H. W. Pedersen, Valuation of structured risk management products,, Insurance: Mathematics and Economics, 34 (2004), 259. Google Scholar |
[9] |
A. Dassios, J. W. Jang, Pricing of catastrophe reinsurance and derivatives using the Cox process with short noise intensity,, Finance and Stochastics, 7 (2003), 73.
doi: 10.1007/s007800200079. |
[10] |
J. C. Duan, I. Popova and P. Ritchken, Option pricing under regime switching,, Quantitative Finance, 2 (2002), 116.
doi: 10.1088/1469-7688/2/2/303. |
[11] |
R. J. Elliott, L. L. Chan and T. K. Siu, Option pricing and Esscher transform under regime switching,, Annals of Finance, 1 (2005), 423. Google Scholar |
[12] |
R. J. Elliott and C. J. U. Osakwe, Option pricing for pure jump processes with Markov switching compensators,, Finance and Stochastics, 10 (2006), 250.
doi: 10.1007/s00780-006-0004-6. |
[13] |
R. J. Elliott, T. K. Siu, L. L. Chan and J. W. Lau, Pricing options under a generalized Markov-modulated jump-diffusion model,, Stochastic Analysis and Applications, 25 (2007), 821.
doi: 10.1080/07362990701420118. |
[14] |
H. F$\ddoto$llmer and M. Schweizer, Hedging of contingent claims under incomplete information,, In Applied Stochastic Analysis (Eds. M.H.A. Davis and R.J. Elliot)(London, (1991), 389.
|
[15] |
M. K. Ghosh, A. Arapostathis and S. I. Marcus, Ergodic control of switching diffusions,, SIAM Journal on Control and Optimization, 35 (1997), 1952.
doi: 10.1137/S0363012996299302. |
[16] |
X. Guo, Information and option pricings,, Quantitative Finance, 1 (2001), 38.
doi: 10.1080/713665550. |
[17] |
H. Gründl and H. Schmeiser, Pricing double-trigger reinsurance contracts: Financial versus actuarial approach,, The Journal of Risk and Insurance, 69 (2002), 449. Google Scholar |
[18] |
S. Jaimungal and T. Wang, Catastrophe options with stochastic interest rates and compound poisson losses,, Insurance: Mathematics and Economics, 38 (2006), 469.
doi: 10.1016/j.insmatheco.2005.11.008. |
[19] |
K. Lee and S. Song, Insiders' hedging in a jump diffusion model,, Quantitative Finance, 5 (2007), 537.
doi: 10.1080/14697680601043191. |
[20] |
K. Lee and P. Protter, Hedging claims with feedback jumps in the price process,, Communications on Stochastic Analysis, 2 (2008), 125.
|
[21] |
J. Lewellen, Predicting returns with financial ratios,, Journal of Financial Economics, 74 (2004), 209. Google Scholar |
[22] |
S. K. Lin, C. C. Chang and M. R. Powers, The valuation of contingent capital with catastrophe risks,, Insurance: Mathematics and Economics, 45 (2009), 65.
doi: 10.1016/j.insmatheco.2009.03.005. |
[23] |
R. C. Merton, Option pricing when underlying stock returns are discontinuous,, Journal of Financial Economics, 3 (1976), 125. Google Scholar |
[24] |
Y. Shen and T. K. Siu, Pricing variance swaps under a stochastic interest rate and volatility model with regime-switching,, Operations Research Letters, 41 (2013), 180.
doi: 10.1016/j.orl.2012.12.008. |
[25] |
T. K. Siu, H. L. Yang and J. W. Lau, Pricing currency options under two-factor Markov-modulated stochastic volatility models,, Insurance: Mathematics and Economics, 43 (2008), 295.
doi: 10.1016/j.insmatheco.2008.05.002. |
[26] |
M. Schweizer, A guided tour through quadratic hedging approaches,, in Option Pricing, (2001), 538.
doi: 10.1017/CBO9780511569708.016. |
[27] |
J. H. Yoon, B. G. Jang and K. H. Roh, An analytic valuation method for multivariate contingent claims with regime-switching volatilities,, Operations Research Letters, 39 (2011), 180.
doi: 10.1016/j.orl.2011.02.010. |
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