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EQUILIBRIUM VALUATION OF CURRENCY OPTIONS UNDER A DISCONTINUOUS MODEL WITH CO-JUMPS

Published online by Cambridge University Press:  20 January 2020

Yu Xing Open the ORCID record for Yu Xing [Opens in a new window] ,
Yuhua Xu  and
Huawei Niu Open the ORCID record for Huawei Niu [Opens in a new window]
Yu Xing
Affiliation:
School of Finance, Nanjing Audit University, Nanjing 211815, China; Jiangsu Key Laboratory of Financial Engineering (Nanjing Audit University), Nanjing 211815, China E-mail: [email protected]
Yuhua Xu
Affiliation:
School of Finance, Nanjing Audit University, Nanjing 211815, China
Huawei Niu
Affiliation:
School of Finance, Nanjing Audit University, Nanjing 211815, China
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Abstract

In this paper, we study the equilibrium valuation for currency options in a setting of the two-country Lucas-type economy. Different from the continuous model in Bakshi and Chen [1], we propose a discontinuous model with jump processes. Empirical findings reveal that the jump components in each country's money supply can be decomposed into the simultaneous co-jump component and the country-specific jump component. Each of the jump components is modeled with a Poisson process whose jump intensity follows a mean reversion stochastic process. By solving a partial integro-differential equation (PIDE), we get a closed-form solution to the PIDE for a European call currency option. The numerical results show that the derived option pricing formula is efficient for practical use. Importantly, we find that the co-jump has a significant impact on option price and implied volatility.

Keywords

co-jumpcurrency optionequilibrium valuationpartial integro-differential equation
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 35 , Issue 3 , July 2021 , pp. 432 - 450
Copyright
© Cambridge University Press 2020

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References

1.Bakshi, G. & Chen, Z. (1997). Equilibrium valuation of foreign exchange claims. Journal of Finance 52: 799–826.CrossRefGoogle Scholar
2.Bakshi, G. & Madan, D. (2000). Spanning and derivative-security valuation. Journal of Financial Economics 55(2): 205–238.CrossRefGoogle Scholar
3.Bakshi, G. & Panayotov, G. (2013). Predictability of currency carry trades and asset pricing implications. Journal of Financial Economics 110(1): 139–163.Google Scholar
4.Barndorff-Nielsen, O.E. & Shephard, N. (2006). Econometrics of testing for jumps in financial economics using bipower variation. Journal of Financial Econometrics 4(1): 1–30.CrossRefGoogle Scholar
5.Barunik, J. & Vacha, L. (2018). Do co-jumps impact correlations in currency markets? Journal of Financial Markets 37: 97–119.CrossRefGoogle Scholar
6.Bates, D. (1996). Jumps and stochastic volatility: exchange rate processes implicit in Deutsche mark options. Review of Financial Studies 9: 69–107.CrossRefGoogle Scholar
7.Caporin, M., Kolokolov, A., & Renò, R. (2016). Systemic co-jumps. Journal of Financial Economics 126: 563–591.CrossRefGoogle Scholar
8.Carr, P. & Madan, D. (1999). Option valuation using the fast Fourier transform. Journal of Computational Finance 2: 61–73.CrossRefGoogle Scholar
9.Carr, P. & Wu, L. (2007). Stochastic skew in currency options. Journal of Financial Economics 86: 213–247.CrossRefGoogle Scholar
10.Daal, E. & Madan, D. (2005). An empirical examination of the variance-gamma model for foreign currency options. Journal of Business 78(6): 2121–2152.CrossRefGoogle Scholar
11.Das, S. & Uppal, R. (2004). Systemic risk and international portfolio choice. Journal of Finance 59(6): 2809–2834.CrossRefGoogle Scholar
12.Du, D. (2013). General equilibrium pricing of currency and currency options. Journal of Financial Economics 110(3): 730–751.CrossRefGoogle Scholar
13.Duffie, D., Pan, J., & Singleton, K. (2000). Transform analysis and asset pricing for affine jump-diffusions. Econometrica 68(6): 1343–1376.Google Scholar
14.Fu, J. & Yang, H. (2012). Equilibrium approach of asset pricing under Lévy process. European Journal of Operational Research 223(3): 701–708.CrossRefGoogle Scholar
15.Garman, M. & Kohlhagen, S. (1983). Foreign currency option values. Journal of International Money & Finance 2(3): 231–237.CrossRefGoogle Scholar
16.Heston, S. (1993). A closed-form solution for options with stochastic volatility with application to bond and currency options. Review of Financial Studies 6: 327–343.CrossRefGoogle Scholar
17.Keddad, B. (2019). How do the Renminbi and other East Asian currencies co-move? Journal of International Money & Finance 91: 49–70.CrossRefGoogle Scholar
18.Kou, S.G. (2002). A jump-diffusion model for option pricing. Management Science 48(8): 1086–1101.CrossRefGoogle Scholar
19.Lucas, R.E. (1982). Interest rates and currency prices in a two-country world. Journal of Monetary Economics 10: 335–359.CrossRefGoogle Scholar
20.Merton, R.C. (1976). Option pricing when underlying stock returns are discontinuous. Journal of Financial Economics 3(1): 125–144.CrossRefGoogle Scholar
21.Santa-Clara, P. & Yan, S. (2010). Crashes, volatility, and the equity premium: lessons from S&P 500 options. The Review of Economics and Statistics 92(2): 435–451.CrossRefGoogle Scholar
22.Xing, Y. & Yang, X-P. (2015). Equilibrium valuation of currency options under a jump-diffusion model with stochastic volatility. Journal of Computational and Applied Mathematics 280: 231–247.CrossRefGoogle Scholar