Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-10T10:45:21.077Z Has data issue: false hasContentIssue false
  • English
  • Français

PRICING VULNERABLE AMERICAN PUT OPTIONS UNDER JUMP–DIFFUSION PROCESSES

Published online by Cambridge University Press:  14 December 2016

Guanying Wang ,
Xingchun Wang  and
Zhongyi Liu
Guanying Wang
Affiliation:
College of Management and Economics, Tianjin University, Tianjin, China Key Laboratory of Computation and Analytics of Complex Management Systems (CACMS), Tianjin, China E-mail: wangguanyingnk@163.com
Xingchun Wang
Affiliation:
School of International Trade and Economics, University of International Business and Economics, Beijing, China E-mail: xchwangnk@aliyun.com
Zhongyi Liu
Affiliation:
School of Management, People's Public Security University of China, Beijing, China E-mail: liuzhongyi@ppsuc.edu.cn
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper evaluates vulnerable American put options under jump–diffusion assumptions on the underlying asset and the assets of the counterparty. Sudden shocks on the asset prices are described as a compound Poisson process. Analytical pricing formulae of vulnerable European put options and vulnerable twice-exercisable European put options are derived. Employing the two-point Geske and Johnson method, we derive an approximate analytical pricing formula of vulnerable American put options under jump–diffusions. Numerical simulations are performed for investigating the impacts of jumps and default risk on option prices.

Keywords

credit riskjump–diffusion processesmulti-exercisable optionsvulnerable american options
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 31 , Issue 2 , April 2017 , pp. 121 - 138
Copyright
Copyright © Cambridge University Press 2016 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Brennan, M. & Schwartz, E. (1977). The valuation of American put options. Journal of Finance 32: 449–462.Google Scholar
2. Bunch, D.S. & Johnson, H. (1992). A simple and numerically efficient valuation method for American puts using a Geske–Johnson approach. Journal of Finance 47: 809–816.Google Scholar
3. Chang, L. & Hung, M. (2006). Valuation of vulnerable American options with correlated credit risk. Review of Derivatives Research 9: 137–165.Google Scholar
4. Chung, S.L. (2002). Pricing American options on foreign assets in a stochastic interest rate economy. Journal of Financial and Quantitative Analysis 37: 667–692.Google Scholar
5. Cox, J. & Ross, S. (1976). The valuation of options for alternative stochastic processes. Journal of Financial Economics 3: 145–166.Google Scholar
6. Eraker, B. (2004). Do stock prices and volatility jump? Reconciling evidence from spot and option prices. Journal of Finance 59: 1367–1403.Google Scholar
7. Geske, R. (1979). The valuation of compound options. Journal of Financial Economics 7: 375–380.Google Scholar
8. Geske, R. & Johnson, H.E. (1984). The American put option valued analytically. Journal of Finance 39: 1511–1524.Google Scholar
9. Ho, T.S., Stapleton, R.C., & Subrahmanyam, M.G. (1997). The valuation of American options with stochastic interest rate: a generalization of the Geske–Johnson technique. Journal of Finance 52: 827–840.Google Scholar
10. Hui, C.H., Lo, C.F., & Lee, H.C. (2003). Pricing vulnerable Black–Scholes options with dynamic default barriers. Journal of Derivatives 10: 62–69.Google Scholar
11. Hung, M. & Liu, Y. (2005). Pricing vulnerable options in incomplete markets. Journal of Futures Markets 25: 135–170.Google Scholar
12. Johnson, H. & Stulz, R. (1987). The pricing of options with default risk. Journal of Finance 42: 267–280.Google Scholar
13. Klein, P. (1996). Pricing Black–Scholes options with correlated credit risk. Journal of Banking & Finance 20: 1211–1229.Google Scholar
14. Klein, P. & Inglis, M. (1999). Valuation of European options subject to financial distress and interest rate risk. Journal of Derivatives 6: 44–56.Google Scholar
15. Klein, P. & Inglis, M. (2001). Pricing vulnerable European options when the option's payoff can increase the risk of financial distress. Journal of Banking & Finance 25: 993–1012.Google Scholar
16. Klein, P. & Yang, J. (2010). Vulnerable American options. Managerial Finance 36: 414–430.Google Scholar
17. Lee, M., Yang, S., & Kim, J. (2016). A closed form solution for vulnerable options with Heston's stochastic volatility. Chaos, Solitons and Fractals 86: 23–27.Google Scholar
18. Longstaff, F.A. & Schwartz, E.S. (2001). Valuing American options by simulations: a simple least-squares approach. Review of Financial Studies 14: 113–147.Google Scholar
19. Merton, R.C. (1973). Theory of rational option pricing. Bell Journal of Economics and Management Science 4: 141–183.Google Scholar
20. Merton, R.C. (1976). Option pricing when underlying stock returns are discontinuous. Journal of Financial Economics 3: 125–144.Google Scholar
21. Tian, L., Wang, G., Wang, X., & Wang, Y. (2014). Pricing vulnerable options with correlated credit risk under jump–diffusion processes. Journal of Futures Markets 34: 957–979.Google Scholar
22. Wang, X. (2016). Analytical valuation of vulnerable options in a discrete-time framework. Probability in the Engineering and Informational Sciences, DOI: https://doi.org/10.1017/S0269964816000292.Google Scholar
23. Yang, S., Lee, M., & Kim, J. (2014). Pricing vulnerable options under a stochastic volatility model. Applied Mathematics Letters 34: 7–12.CrossRefGoogle Scholar