East Asian mathematical journal

  • 제37권5호
  • /
  • Pages.553-566
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  • 2021
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  • 1226-6973(pISSN)
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  • 2287-2833(eISSN)
영남수학회 (The Youngnam Mathematical Society)
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PRICING VULNERABLE POWER OPTION UNDER A CEV DIFFUSION

  • Ha, Mijin (Department of Mathematics, Pusan National University) ;
  • Kim, Donghyun (Department of Mathematics, Pusan National University) ;
  • Yoon, Ji-Hun (Department of Mathematics, Pusan National University)
  • 투고 : 2021.05.03
  • 심사 : 2021.09.16
  • 발행 : 2021.09.30
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초록

In the over-the-counter market, option's buyers could have a problem for default risk caused by option's writers. In addition, many participants try to maximize their benefits obviously in investing the financial derivatives. Taking all these circumstances into consideration, we deal with the vulnerable power options under a constant elasticity variance (CEV) model. We derive an analytic pricing formula for the vulnerable power option by using the asymptotic analysis, and then we verify that the analytic formula can be obtained accurately by comparing our solution with Monte-Carlo price. Finally, we examine the effect of CEV on the option price based on the derived solution.

키워드

과제정보

This work was supported by a 2-Year Research Grant of Pusan National University.

참고문헌

  1. F. Black and M. Scholes, The pricing of options and corporate liabilities, J. Polit. Econ. 81 (1973), no. 3, 637-654. https://doi.org/10.1086/260062
  2. J. C. Cox, The constant elasticity of variance option pricing model, J. Portf. Manag. (1996), 15-17.
  3. H. Geman and Y. F. Shih, Modeling commodity prices under the CEV model, J. Altern. Invest. 11 (2008), no. 3, 65-84. https://doi.org/10.3905/JAI.2009.11.3.065
  4. R. C. Heynen and H. M. Kat, Pricing and hedging power options, Financ. Eng. Jpn. Mark. 3 (1996), no. 3, 253-261. https://doi.org/10.1007/BF02425804
  5. M. Ha, Q. Li, D. Kim, and J.-H. Yoon, The pricing of vulnerable power options with double mellin transforms, J. Appl. Math. Informatics 39 (2021), no. 5-6, 1-12.
  6. M. W. Hung and Y. H. Liu, Pricing vulnerable options in incomplete markets, J. Futures Markets 25 (2005), 135-170. https://doi.org/10.1002/fut.20136
  7. H. Johnson and R. Stulz, The pricing of options with default risk, J. Finance 42 (1987), no. 2, 267-280. https://doi.org/10.1111/j.1540-6261.1987.tb02567.x
  8. J. Jeon, J.-H. Yoon, M. Kang, Pricing vulnerable path-dependent options using integral transforms, J. Comput. Appl. Math. 313 (2017), 259-272. https://doi.org/10.1016/j.cam.2016.09.024
  9. P. Klein, Pricing Black-Scholes options with correlated credit risk, J. Banking Finance 20 (1996), no. 7, 1211-1229. https://doi.org/10.1016/0378-4266(95)00052-6
  10. D. Kim, S.-Y. Choi, and J.-H. Yoon, Pricing of vulnerable options under hybrid stochastic and local volatility, Chaos Soliton. Fract. 146 (2021), 110846. https://doi.org/10.1016/j.chaos.2021.110846
  11. B. Oksendal, Stochastic Differential Equations, Springer, New York, 2003.
  12. S.-H. Park and J.-H. Kim, Asymptotic option pricing under the CEV diffusion, J. Math. Anal. Appl. 375 (2011), no. 2, 490-501. https://doi.org/10.1016/j.jmaa.2010.09.060
  13. S.-J. Yang, M.-K. Lee, and J.-H. Kim, Pricing vulnerable options under a stochastic volatility model, Appl. Math. Lett. 34 (2014), 7-12. https://doi.org/10.1016/j.aml.2014.03.007
  14. J.-H. Yoon and J.-H. Kim, The pricing of vulnerable options with double Mellin transforms, J. Math. Anal. Appl. 422 (2015), no. 2, 838-857. https://doi.org/10.1016/j.jmaa.2014.09.015
  15. Z. Zhang, Z, W. Liu and Y. Sheng, Valuation of power option for uncertain financial market, Appl. Math. Comput. 286 (2016), 257-264. https://doi.org/10.1016/j.amc.2016.04.032