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A CLOSED-FORM GARCH VALUATION MODEL FOR POWER EXCHANGE OPTIONS WITH COUNTERPARTY RISK

Published online by Cambridge University Press:  24 January 2019

Xingchun Wang ,
Guangli Xu  and
Dan Li
Xingchun Wang
Affiliation:
School of International Trade and Economics, University of International Business and Economics, Beijing100029, China E-mail: xchwangnk@aliyun.com
Guangli Xu
Affiliation:
School of Statistics, University of International Business and Economics, Beijing100029, China E-mail: xuguangli@uibe.edu.cn; linda9556@163.com
Dan Li
Affiliation:
School of Statistics, University of International Business and Economics, Beijing100029, China E-mail: xuguangli@uibe.edu.cn; linda9556@163.com
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Abstract

In this paper, a discrete-time framework is proposed to value power exchange options with counterparty default risk, where counterparty risk is considered in a reduced-form setting and the variance processes of the underlying assets are captured by GARCH processes. In addition, the proposed model allows for the correlation between the intensity of default and the variances of the underlying assets by breaking down the total risk into systematic and idiosyncratic components. By dint of measure-change techniques and characteristic functions, we obtain the closed-form pricing formula for the value of power exchange options with counterparty default risk. Finally, numerical results are presented to show the power exchange option values.

Keywords

default riskGARCHidiosyncratic riskpower exchange optionssystematic riskG13
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 34 , Issue 2 , April 2020 , pp. 279 - 296
Copyright
Copyright © Cambridge University Press 2019

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References

1.Black, F. & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy 81(3): 637–654.CrossRefGoogle Scholar
2.Blenman, L.P. & Clark, S.P. (2005). Power exchange options. Finance Research Letters 2(2): 97–106.CrossRefGoogle Scholar
3.Bo, L., Wang, Y., & Yang, X. (2013). Stochastic portfolio optimization with default risk. Journal of Mathematical Analysis and Applications 397(2): 467–480.CrossRefGoogle Scholar
4.Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics 31(3): 307–327.CrossRefGoogle Scholar
5.Carr, P. & Ghamami, S. (2015). Derivatives pricing under bilateral counterparty risk. Ssrn Electronic Journal 2015 26: 1–28.Google Scholar
6.Christoffersen, P., Jacobs, K., Ornthanalai, C., & Wang, Y. (2008). Option valuation with long-run and short-run volatility components. Journal of Financial Economics 90(3): 272–297.CrossRefGoogle Scholar
7.Christoffersen, P., Jacobs, K., & Ornthanalai, C. (2011). Dynamic jump intensities and risk premia: evidence from s&p500 returns and options. Journal of Financial Economics 106(3): 447–472.CrossRefGoogle Scholar
8.Crepey, S. (2015a). Bilateral counterparty risk under funding constraints, part I: pricing. Mathematical Finance 25(1): 1–22.CrossRefGoogle Scholar
9.Crepey, S. (2015b). Bilateral counterparty risk under funding constraints, part II: CVA. Mathematical Finance 25(1): 23–50.CrossRefGoogle Scholar
10.Duan, J. (1995). The GARCH option pricing model. Mathematical Finance 5(1): 13–32.CrossRefGoogle Scholar
11.Duffie, D. & Singleton, K.J. (1999). Modeling term structures of defaultable bonds. Review of Financial Studies 12(4): 687–720.CrossRefGoogle Scholar
12.Fard, F.A. (2015). Analytical pricing of vulnerable options under a generalized jumpdiffusion model. Insurance Mathematics & Economics 60: 19–28.CrossRefGoogle Scholar
13.Fischer, S. (1978). Call option pricing when the exercise price is uncertain, and the valuation of index bonds. Journal of Finance 33(1): 169–176.CrossRefGoogle Scholar
14.Heston, S. & Nandi, S. (2000). A closed-form GARCH option valuation model. Review of Financial Studies 13(3): 585–625.CrossRefGoogle Scholar
15.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(2): 299–322.CrossRefGoogle Scholar
16.Jarrow, R.A. & Yu, F. (2001). Counterparty risk and the pricing of defaultable securities. Journal of Finance 56(5): 1765–1799.CrossRefGoogle Scholar
17.Johnson, H. & Stulz, R. (1987). The pricing of options with default risk. Journal of Finance 42(2): 267–280.CrossRefGoogle Scholar
18.Karatzas, I. & Shreve, S.E. (1991). Brownian motion and stochastic calculus. New York: Springer.Google Scholar
19.Kendall, M. & Stuart, A (1977). The advanced theory of statistics. Vol. 1. New York: Macmillan.Google Scholar
20.Klein, P. (1996). Pricing Black–Scholes options with correlated credit risk. Journal of Banking and Finance 20(7): 1211–1229.CrossRefGoogle Scholar
21.Leung, S.Y. & Kwok, Y.K. (2005). Credit default swap valuation with counterparty risk. The Kyoto Economic Review 74(1): 25–45.Google Scholar
22.Margrabe, W. (1978). The value of an option to exchange one asset for another. Journal of Finance 33(1): 177–186.CrossRefGoogle Scholar
23.Merton, R. (1974). On the pricing of corporate debt: the risk structure of interest rates. Journal of Finance 29(2): 449–470.Google Scholar
24.Shephard, N. (1991). From characteristic function to a distribution function: a simple framework for theory. Econometric Theory 7(4): 519–529.CrossRefGoogle Scholar
25.Tompkins, R.G. (2000). Power options: hedging nonlinear risks. Journal of Risk 2(2): 29–45.CrossRefGoogle Scholar
26.Wang, X. (2016). Pricing power exchange options with correlated jump risk. Finance Research Letters 19: 90–97.CrossRefGoogle Scholar
27.Wang, X. (2018). Pricing vulnerable European options with stochastic correlation. Probability in the Engineering and Informational Sciences 32(01): 67–95.CrossRefGoogle Scholar
28.Wang, X., Song, S., & Wang, Y. (2017). The valuation of power exchange options with counterparty risk and jump risk. Journal of Futures Markets 37(5): 499–521.CrossRefGoogle Scholar
29.Yoon, J. & Kim, J. (2015). The pricing of vulnerable options with double Mellin transforms. Journal of Mathematical Analysis and Applications 422(2): 838–857.CrossRefGoogle Scholar