• Previous Article
    Minimizing total completion time in a two-machine no-wait flowshop with uncertain and bounded setup times
  • JIMO Home
  • This Issue
  • Next Article
    An integrated dynamic facility layout and job shop scheduling problem: A hybrid NSGA-II and local search algorithm
doi: 10.3934/jimo.2019072

Pricing dynamic fund protection under a Regime-switching Jump-diffusion model with stochastic protection level

1. 

Department of Mathematics and Physics, Suzhou University of Science and Technology, Suzhou 215009, China

2. 

College of Applied Mathematics, Shanxi University of Finance and Economics, Taiyuan 030006, China

3. 

Department of Mathematics and Center for Financial Engineering, Soochow University, Suzhou 215006, China

* Corresponding author: Yinghui Dong

Received  February 2018 Revised  March 2019 Published  July 2019

Fund Project: The authors thank the anonymous referees for valuable comments to improve the earlier version of the paper. This work is supported by the NSF of Jiangsu Province (Grant No. BK20170064), the NNSF of China (Grant No. 11771320), QingLan Project, the scholarship of Jiangsu Overseas Visiting Scholar Program, Suzhou Key Laboratory for Big Data and Information Service (SZS201813) and the Graduate Innovation Program (Grant No. KYCX17-2059) of Jiangsu Province of China

In this paper, we investigate the valuation of dynamic fund protections under the assumption that the market value of the basic fund and the protection level follow regime-switching processes with jumps. The price of the dynamic fund protection (DFP) is associated with the Laplace transform of the first passage time. We derive the explicit formula for the Laplace transform of the DFP under the regime-switching, hyper-exponential jump-diffusion process. By using the Gaver-Stehfest algorithm, we present some numerical results for the price of the DFP.

Citation: Chao Xu, Yinghui Dong, Zhaolu Tian, Guojing Wang. Pricing dynamic fund protection under a Regime-switching Jump-diffusion model with stochastic protection level. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2019072
References:
[1]

J. Buffington and R. J. Elliott, American options with regime switching, International Journal of Theoretical and Applied Finance, 5 (2002), 497-514. doi: 10.1142/S0219024902001523. Google Scholar

[2]

C. C. ChangY. H. Lian and M. H. Tsay, Pricing dynamic guaranteed funds under a double exponential jump diffusion model, Academia Economic Papers, 40 (2012), 269-306. Google Scholar

[3]

Y. H. Dong, Pricing dynamic guaranteed funds with stochastic barrier under Vasicek interest rate model, hinese Journal of Applied Probability and Statistics, 29 (2013), 237-245. Google Scholar

[4]

Y. H. DongG. J. Wang and R. Wu, Pricing the zero-coupon bond and its fair premium under a structural credit risk model with jumps, Journal of Applied Probability, 48 (2011), 404-419. doi: 10.1239/jap/1308662635. Google Scholar

[5]

R. J. Elliott, L. Aggoun and J. B. Moore, Hidden Markov Models: Estimation and Control, Springer-Verlag, Berlin-Heidelberg-New York, 1994. Google Scholar

[6]

R. J. ElliottC. Leunglung and T. K. Siu, Option pricing and Esscher transform under regime switching, Annals of Finance, 1 (2005), 423-432. doi: 10.1007/s10436-005-0013-z. Google Scholar

[7]

H. K. Fung and L. K. Li, Pricing discrete dynamic fund protections, North American Actuarial Journal, 7 (2003), 23-31. doi: 10.1080/10920277.2003.10596115. Google Scholar

[8]

H. U. Gerber and G. Pafumi, Pricing dynamic investment fund protection, North American Actuarial Journal, 4 (2000), 28-37. doi: 10.1080/10920277.2000.10595894. Google Scholar

[9]

H. U. Gerber and E. S. Shiu, From ruin theory to pricing reset guarantees and perpetual put options, Insurance: Mathematics and Economics, 24 (1999), 3-14. doi: 10.1016/S0167-6687(98)00033-X. Google Scholar

[10]

H. U. Gerber and E. S. Shiu, Pricing perpetual fund protection with withdrawal option, North American Actuarial Journal, 7 (2003), 60-77. doi: 10.1080/10920277.2003.10596087. Google Scholar

[11]

H. U. Gerber and E. S. W. Shiu, The time value of ruin in a Sparre Andersen model, North American Actuarial Journal, 9 (2005), 49-84. doi: 10.1080/10920277.2005.10596197. Google Scholar

[12]

X. Guo, Information and option pricings, Quantitative Finance, 1 (2001), 38-44. doi: 10.1080/713665550. Google Scholar

[13]

J. D. Hamilton, Rational-expectations econometric analysis of changes in regime: An investigation of the terms tructure of interest rates, Journal of Economic Dynamics and Control, 12 (1998), 385-423. doi: 10.1016/0165-1889(88)90047-4. Google Scholar

[14]

M. R. Hardy, A regime-switching model of long-term stock returns, North American Actuarial Journal, 5 (2001), 41-53. doi: 10.1080/10920277.2001.10595984. Google Scholar

[15]

J. Imai and P. P. Boyle, Dynamic fund protection, North American Actuarial Journal, 5 (2001), 31-47. doi: 10.1080/10920277.2001.10595996. Google Scholar

[16]

Z. JinL. Y. QianW. Wang and R. M. Wang, Pricing dynamic fund protections with regime switching, Journal of Computational and Applied Mathematics, 297 (2016), 13-25. doi: 10.1016/j.cam.2015.11.012. Google Scholar

[17]

S. G. Kou, A jump-diffusion model for option pricing, Management Science, 48 (2002), 1086-1101. Google Scholar

[18]

S. G. Kou and H. Wang, First passage times of a jump diffusion process, Advance in Applied Probability, 35 (2003), 504-531. doi: 10.1239/aap/1051201658. Google Scholar

[19]

S. G. Kou and H. Wang, Option pricing under a double exponential jump diffusion model., Management Science, 50 (2004), 1178-1192. Google Scholar

[20]

V. Naik, Option valuation and hedging strategies with jumps in the volatility of asset returns, Journal of Finance, 48 (1993), 1969-1984. doi: 10.1111/j.1540-6261.1993.tb05137.x. Google Scholar

[21]

C. C. SiuS. C. P. Yam and H. Yang, Valuing equity-linked death benefits in a regime-switching framework, ASTIN Bulletin, 45 (2015), 355-395. doi: 10.1017/asb.2014.32. Google Scholar

[22]

H. Y. Wong and C. M. Chan, Lookback options and dynamic fund protection under multiscale stochastic volatility, Insurance: Mathematics and Economics, 40 (2007), 357-385. doi: 10.1016/j.insmatheco.2006.05.006. Google Scholar

[23]

H. Y. Wong and K. W. Lam, Valuation of discrete dynamic fund protection under Lévy processes, North American Actuarial Journal, 13 (2009), 202-216. doi: 10.1080/10920277.2009.10597548. Google Scholar

[24]

C. Xu and Y. H. Dong, Pricing dynamic fund protections under a stochastic boundary, Journal of Suzhou University of Science and Technology, 2 (2018), 21-25. Google Scholar

show all references

References:
[1]

J. Buffington and R. J. Elliott, American options with regime switching, International Journal of Theoretical and Applied Finance, 5 (2002), 497-514. doi: 10.1142/S0219024902001523. Google Scholar

[2]

C. C. ChangY. H. Lian and M. H. Tsay, Pricing dynamic guaranteed funds under a double exponential jump diffusion model, Academia Economic Papers, 40 (2012), 269-306. Google Scholar

[3]

Y. H. Dong, Pricing dynamic guaranteed funds with stochastic barrier under Vasicek interest rate model, hinese Journal of Applied Probability and Statistics, 29 (2013), 237-245. Google Scholar

[4]

Y. H. DongG. J. Wang and R. Wu, Pricing the zero-coupon bond and its fair premium under a structural credit risk model with jumps, Journal of Applied Probability, 48 (2011), 404-419. doi: 10.1239/jap/1308662635. Google Scholar

[5]

R. J. Elliott, L. Aggoun and J. B. Moore, Hidden Markov Models: Estimation and Control, Springer-Verlag, Berlin-Heidelberg-New York, 1994. Google Scholar

[6]

R. J. ElliottC. Leunglung and T. K. Siu, Option pricing and Esscher transform under regime switching, Annals of Finance, 1 (2005), 423-432. doi: 10.1007/s10436-005-0013-z. Google Scholar

[7]

H. K. Fung and L. K. Li, Pricing discrete dynamic fund protections, North American Actuarial Journal, 7 (2003), 23-31. doi: 10.1080/10920277.2003.10596115. Google Scholar

[8]

H. U. Gerber and G. Pafumi, Pricing dynamic investment fund protection, North American Actuarial Journal, 4 (2000), 28-37. doi: 10.1080/10920277.2000.10595894. Google Scholar

[9]

H. U. Gerber and E. S. Shiu, From ruin theory to pricing reset guarantees and perpetual put options, Insurance: Mathematics and Economics, 24 (1999), 3-14. doi: 10.1016/S0167-6687(98)00033-X. Google Scholar

[10]

H. U. Gerber and E. S. Shiu, Pricing perpetual fund protection with withdrawal option, North American Actuarial Journal, 7 (2003), 60-77. doi: 10.1080/10920277.2003.10596087. Google Scholar

[11]

H. U. Gerber and E. S. W. Shiu, The time value of ruin in a Sparre Andersen model, North American Actuarial Journal, 9 (2005), 49-84. doi: 10.1080/10920277.2005.10596197. Google Scholar

[12]

X. Guo, Information and option pricings, Quantitative Finance, 1 (2001), 38-44. doi: 10.1080/713665550. Google Scholar

[13]

J. D. Hamilton, Rational-expectations econometric analysis of changes in regime: An investigation of the terms tructure of interest rates, Journal of Economic Dynamics and Control, 12 (1998), 385-423. doi: 10.1016/0165-1889(88)90047-4. Google Scholar

[14]

M. R. Hardy, A regime-switching model of long-term stock returns, North American Actuarial Journal, 5 (2001), 41-53. doi: 10.1080/10920277.2001.10595984. Google Scholar

[15]

J. Imai and P. P. Boyle, Dynamic fund protection, North American Actuarial Journal, 5 (2001), 31-47. doi: 10.1080/10920277.2001.10595996. Google Scholar

[16]

Z. JinL. Y. QianW. Wang and R. M. Wang, Pricing dynamic fund protections with regime switching, Journal of Computational and Applied Mathematics, 297 (2016), 13-25. doi: 10.1016/j.cam.2015.11.012. Google Scholar

[17]

S. G. Kou, A jump-diffusion model for option pricing, Management Science, 48 (2002), 1086-1101. Google Scholar

[18]

S. G. Kou and H. Wang, First passage times of a jump diffusion process, Advance in Applied Probability, 35 (2003), 504-531. doi: 10.1239/aap/1051201658. Google Scholar

[19]

S. G. Kou and H. Wang, Option pricing under a double exponential jump diffusion model., Management Science, 50 (2004), 1178-1192. Google Scholar

[20]

V. Naik, Option valuation and hedging strategies with jumps in the volatility of asset returns, Journal of Finance, 48 (1993), 1969-1984. doi: 10.1111/j.1540-6261.1993.tb05137.x. Google Scholar

[21]

C. C. SiuS. C. P. Yam and H. Yang, Valuing equity-linked death benefits in a regime-switching framework, ASTIN Bulletin, 45 (2015), 355-395. doi: 10.1017/asb.2014.32. Google Scholar

[22]

H. Y. Wong and C. M. Chan, Lookback options and dynamic fund protection under multiscale stochastic volatility, Insurance: Mathematics and Economics, 40 (2007), 357-385. doi: 10.1016/j.insmatheco.2006.05.006. Google Scholar

[23]

H. Y. Wong and K. W. Lam, Valuation of discrete dynamic fund protection under Lévy processes, North American Actuarial Journal, 13 (2009), 202-216. doi: 10.1080/10920277.2009.10597548. Google Scholar

[24]

C. Xu and Y. H. Dong, Pricing dynamic fund protections under a stochastic boundary, Journal of Suzhou University of Science and Technology, 2 (2018), 21-25. Google Scholar

Figure 1.  $ DFP_0 $ versus $ T $
Figure 2.  $ DFP_0 $ versus $ F_0 $
Figure 3.  $ DFP_0 $ versus $ K_0 $
Figure 4.  $ DFP_0 $ versus $ a_{12} $
Figure 5.  $ DFP_0 $ versus $ \lambda_{11} $
Figure 6.  $ DFP_0 $ versus $ \sigma_1 $
Figure 7.  For example, if $ k_{i1} = 1,i = 1,\cdots,m, $ $ k_{i2} = 1,i = 0,1,\cdots,m-1, k_{m2} = 2, $ then we have $ h(\tilde{\alpha}_{ij}-) = -\infty, h(\tilde{\alpha}_{ij}+) = +\infty. $ Therefore, there exists at least one root at each of the $ 2m $ intervals, $ (0,\tilde{\alpha}_{11}),(\tilde{\alpha}_{11},\tilde{\alpha}_{12}),(\tilde{\alpha}_{12},\tilde{\alpha}_{21}),\cdots,(\tilde{\alpha}_{m1},\tilde{\alpha}_{m2}) $ and there exists at least two roots at the interval $ (\tilde{\alpha}_{m2},+\infty). $
[1]

Tak Kuen Siu, Yang Shen. Risk-minimizing pricing and Esscher transform in a general non-Markovian regime-switching jump-diffusion model. Discrete & Continuous Dynamical Systems - B, 2017, 22 (7) : 2595-2626. doi: 10.3934/dcdsb.2017100

[2]

Zhuo Jin, George Yin, Hailiang Yang. Numerical methods for dividend optimization using regime-switching jump-diffusion models. Mathematical Control & Related Fields, 2011, 1 (1) : 21-40. doi: 10.3934/mcrf.2011.1.21

[3]

Fuke Wu, George Yin, Zhuo Jin. Kolmogorov-type systems with regime-switching jump diffusion perturbations. Discrete & Continuous Dynamical Systems - B, 2016, 21 (7) : 2293-2319. doi: 10.3934/dcdsb.2016048

[4]

Zhuo Jin, Linyi Qian. Lookback option pricing for regime-switching jump diffusion models. Mathematical Control & Related Fields, 2015, 5 (2) : 237-258. doi: 10.3934/mcrf.2015.5.237

[5]

Isabelle Kuhwald, Ilya Pavlyukevich. Bistable behaviour of a jump-diffusion driven by a periodic stable-like additive process. Discrete & Continuous Dynamical Systems - B, 2016, 21 (9) : 3175-3190. doi: 10.3934/dcdsb.2016092

[6]

Wuyuan Jiang. The maximum surplus before ruin in a jump-diffusion insurance risk process with dependence. Discrete & Continuous Dynamical Systems - B, 2019, 24 (7) : 3037-3050. doi: 10.3934/dcdsb.2018298

[7]

Ishak Alia. A non-exponential discounting time-inconsistent stochastic optimal control problem for jump-diffusion. Mathematical Control & Related Fields, 2019, 9 (3) : 541-570. doi: 10.3934/mcrf.2019025

[8]

Jiaqin Wei. Time-inconsistent optimal control problems with regime-switching. Mathematical Control & Related Fields, 2017, 7 (4) : 585-622. doi: 10.3934/mcrf.2017022

[9]

Mourad Bellassoued, Raymond Brummelhuis, Michel Cristofol, Éric Soccorsi. Stable reconstruction of the volatility in a regime-switching local-volatility model. Mathematical Control & Related Fields, 2019, 0 (0) : 0-0. doi: 10.3934/mcrf.2019036

[10]

Xin Zhang, Hui Meng, Jie Xiong, Yang Shen. Robust optimal investment and reinsurance of an insurer under Jump-diffusion models. Mathematical Control & Related Fields, 2019, 9 (1) : 59-76. doi: 10.3934/mcrf.2019003

[11]

Yinghui Dong, Kam Chuen Yuen, Guojing Wang. Pricing credit derivatives under a correlated regime-switching hazard processes model. Journal of Industrial & Management Optimization, 2017, 13 (3) : 1395-1415. doi: 10.3934/jimo.2016079

[12]

Jiapeng Liu, Ruihua Liu, Dan Ren. Investment and consumption in regime-switching models with proportional transaction costs and log utility. Mathematical Control & Related Fields, 2017, 7 (3) : 465-491. doi: 10.3934/mcrf.2017017

[13]

Ping Chen, Haixiang Yao. Continuous-time mean-variance portfolio selection with no-shorting constraints and regime-switching. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-21. doi: 10.3934/jimo.2018166

[14]

Jiaqin Wei, Zhuo Jin, Hailiang Yang. Optimal dividend policy with liability constraint under a hidden Markov regime-switching model. Journal of Industrial & Management Optimization, 2019, 15 (4) : 1965-1993. doi: 10.3934/jimo.2018132

[15]

Nguyen Huu Du, Nguyen Thanh Dieu, Tran Dinh Tuong. Dynamic behavior of a stochastic predator-prey system under regime switching. Discrete & Continuous Dynamical Systems - B, 2017, 22 (9) : 3483-3498. doi: 10.3934/dcdsb.2017176

[16]

Chuancun Yin, Kam Chuen Yuen. Optimal dividend problems for a jump-diffusion model with capital injections and proportional transaction costs. Journal of Industrial & Management Optimization, 2015, 11 (4) : 1247-1262. doi: 10.3934/jimo.2015.11.1247

[17]

Dan Li, Jing'an Cui, Yan Zhang. Permanence and extinction of non-autonomous Lotka-Volterra facultative systems with jump-diffusion. Discrete & Continuous Dynamical Systems - B, 2015, 20 (7) : 2069-2088. doi: 10.3934/dcdsb.2015.20.2069

[18]

Qing-Qing Yang, Wai-Ki Ching, Wanhua He, Tak-Kuen Siu. Pricing vulnerable options under a Markov-modulated jump-diffusion model with fire sales. Journal of Industrial & Management Optimization, 2019, 15 (1) : 293-318. doi: 10.3934/jimo.2018044

[19]

Fahd Jarad, Thabet Abdeljawad. Generalized fractional derivatives and Laplace transform. Discrete & Continuous Dynamical Systems - S, 2018, 0 (0) : 709-722. doi: 10.3934/dcdss.2020039

[20]

Donny Citra Lesmana, Song Wang. A numerical scheme for pricing American options with transaction costs under a jump diffusion process. Journal of Industrial & Management Optimization, 2017, 13 (4) : 1793-1813. doi: 10.3934/jimo.2017019

2018 Impact Factor: 1.025

Metrics

  • PDF downloads (4)
  • HTML views (136)
  • Cited by (0)

Other articles
by authors

[Back to Top]