Hostname: page-component-76fb5796d-x4r87 Total loading time: 0 Render date: 2024-04-25T20:40:46.427Z Has data issue: false hasContentIssue false
  • English
  • Français

ANALYTICAL VALUATION OF VULNERABLE OPTIONS IN A DISCRETE-TIME FRAMEWORK

Published online by Cambridge University Press:  13 September 2016

Xingchun Wang
Xingchun Wang*
Affiliation:
School of International Trade and Economics, University of International Business and Economics, Beijing 100029, People's Republic of China E-mail: xchwangnk@aliyun.com; wangx@uibe.edu.cn
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper, we present a pricing model for vulnerable options in discrete time. A Generalized Autoregressive Conditional Heteroscedasticity process is used to describe the variance of the underlying asset, which is correlated with the returns of the asset. As for counterparty default risk, we study it in a reduced form model and the proposed model allows for the correlation between the intensity of default and the variance of the underlying asset. In this framework, we derive a closed-form solution for vulnerable options and investigate quantitative impacts of counterparty default risk on option prices.

Keywords

mathematical finance
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 31 , Issue 1 , January 2017 , pp. 100 - 120
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. Anderson, R. & Sundaresan, S. (2000). A comparative study of structural models of corporate bond yields: an exploratory investigation. Journal of Banking and Finance 24: 255–269.Google Scholar
2. Arora, N., Gandhi, P., & Longstaff, F. (2012). Counterparty credit risk and the credit default swap market. Journal of Financial Economics 103: 280–293.Google Scholar
3. Artzner, P. & Delbaen, F. (1995). Default risk insurance and incomplete markets. Mathematical Finance 5: 187–195.CrossRefGoogle Scholar
4. Black, F. & Cox, J. (1976). Valuing corporate securities: some effects of bond indenture provisions. Journal of Finance 31: 351–367.CrossRefGoogle Scholar
5. Black, F. & Scholes, M. (1973). The valuation of options and corporate liabilities. Journal of Political Economy 8: 637–659.CrossRefGoogle Scholar
6. Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics 81: 301–327.Google Scholar
7. Cao, M. & Wei, J. (2001). Vulnerable options, risky corporate bond, and credit spread. Journal of Futures Markets 21: 301–327.3.0.CO;2-K>CrossRefGoogle Scholar
8. Christoffersen, P., Jacobs, K., & Ornthanalai, C. (2012). Dynamic jump intensities and risk premiums: evidence from S&P500 returns and options. Journal of Financial Economics 106: 447–472.CrossRefGoogle Scholar
9. Christoffersen, P., Jacobs, K., Ornthanalai, C., & Wang, Y. (2008). Option valuation with long-run and short-run volatility components. Journal of Financial Economics 90: 272–297.Google Scholar
10. Duan, J. (1995). The GARCH option pricing model. Mathematical Finance 5: 13–32.Google Scholar
11. Duffie, D. & Singleton, K. (1999). Modeling term structures of defaultable bonds. Review of Financial Studies 12: 687–720.Google Scholar
12. Duffie, D. & Zhu, H. (2011). Does a central clearing counterparty reduce counterparty risk? Review of Asset Pricing Studies 1: 74–95.CrossRefGoogle Scholar
13. Fard, F. (2015). Analytical pricing of vulnerable options under a generalized jump-diffusion model. Insurance: Mathematics and Economics 60: 19–28.Google Scholar
14. Heston, S. & Nandi, S. (2000). A closed-form GARCH option valuation model. Review of Financial Studies 13: 585–625.Google Scholar
15. Hull, J. (2012). Options, futures, and other derivatives. 8th ed., New Jersey: Pearson–Prentice Hall.Google Scholar
16. Hull, J. & White, A. (1995). The impact of default risk on the prices of options and other derivative securities. Journal of Banking and Finance 19: 299–322.CrossRefGoogle Scholar
17. Jarrow, R., Lando, D., & Turnbull, S. (1997). A Markov model for the term structure of credit risk spreads. Review of Financial Studies 10: 481–523.CrossRefGoogle Scholar
18. Jarrow, R. & Turnbull, S. (1995). Pricing derivatives on financial securities subject to credit risk. Journal of Finance 50: 53–85.Google Scholar
19. Johnson, H. & Stulz, R. (1987). The pricing of options with default risk. Journal of Finance 42: 267–280.Google Scholar
20. Kendall, M. & Stuart, A. (1977). The advanced theory of statistics Vol. 1, New York: Macmillan.Google Scholar
21. Klein, P. (1996). Pricing Black–Scholes options with correlated credit risk. Journal of Banking and Finance 20: 1211–1229.Google Scholar
22. Lando, D. (1998). On Cox processes and credit risky securities. Review of Derivatives Research 2: 99–120.Google Scholar
23. Leland, H. (1994). Corporate debt value, bond covenants, and optimal capital structure. Journal of Finance 49: 1213–1252.Google Scholar
24. Leland, H. & Toft, K. (1996). Optimal capital structure, endogenous bankruptcy, and the term structure of credit spreads. Journal of Finance 51: 987–1019.CrossRefGoogle Scholar
25. Merton, R. (1974). On the pricing of corporate debt: the risk structure of interest rates. Journal of Finance 29: 449–470.Google Scholar
26. Shephard, N. (1991). From characteristic function to a distribution function: a simple framework for theory. Econometric Theory 7: 519–529.CrossRefGoogle Scholar
27. 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.CrossRefGoogle Scholar
28. Wang, G. & Wang, X. (2016). Pricing vulnerable options with stochastic volatility. European Journal of Finance, under second round.Google Scholar
29. Wang, X. (2016). Differences in the prices of vulnerable options with different counterparties. Journal of Futures Markets DOI: 10.1002/fut.21789, forthcoming.Google Scholar
30. Yang, S., Lee, M., & Kim, J. (2014). Pricing vulnerable options under a stochastic volatility model. Applied Mathematics Letters 34: 7–12.Google Scholar