Hostname: page-component-cb9f654ff-plnhv Total loading time: 0.001 Render date: 2025-08-16T21:28:24.712Z Has data issue: false hasContentIssue false
  • English
  • Français

Valuing vulnerable Asian options with liquidity risk under Lévy processes

Published online by Cambridge University Press:  07 February 2022

Chengyou Cai  and
Xingchun Wang Open the ORCID record for Xingchun Wang [Opens in a new window]
Chengyou Cai
Affiliation:
School of International Trade and Economics, University of International Business and Economics, Beijing 100029, China. E-mails: xchwangnk@aliyun.com, wangx@uibe.edu.cn
Xingchun Wang
Affiliation:
School of International Trade and Economics, University of International Business and Economics, Beijing 100029, China. E-mails: xchwangnk@aliyun.com, wangx@uibe.edu.cn
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper, we study the pricing of vulnerable Asian options with liquidity risk. We employ general Lévy processes to capture the changes in the liquidity discount factors and the information processes of all assets. In the proposed pricing model, we obtain the closed-form pricing formula of vulnerable Asian options using the Fourier transform methods. Finally, the derived pricing formula is used to illustrate the effects of asymmetric jump risk, and the effects are relatively stable on (vulnerable) Asian options with different moneynesses.

Keywords

Asian optionsDefault riskLévy processesLiquidity discount factorLiquidity risk

Information

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 37 , Issue 3 , July 2023 , pp. 653 - 673
Copyright
© The Author(s), 2022. Published by Cambridge University Press

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.)

Article purchase

Temporarily unavailable

References

Antonelli, F., Ramponi, A., & Scarlatti, S. (2021). CVA and vulnerable options pricing by correlation expansions. Annals of Operation Research 299: 401–427.10.1007/s10479-019-03367-zCrossRefGoogle Scholar
Ballotta, L. & Kyriakou, I. (2014). Monte Carlo simulation of the CGMY process and option pricing. Journal of Futures Markets 34: 1095–1121.10.1002/fut.21647CrossRefGoogle Scholar
Brigo, D., Morini, M., & Pallavicini, A. (2013). Counterparty credit risk, collateral and funding: with pricing cases for all asset classes. New York: Wiley.10.1002/9781118818589CrossRefGoogle Scholar
Brunetti, C. & Caldarera, A. (2006). Asset prices and asset correlations in illiquid markets. Working Paper.Google Scholar
Cai, N. & Kou, S. (2012). Pricing Asian options under a hyper-exponential jump diffusion model. Operations Research 60: 64–77.10.1287/opre.1110.1006CrossRefGoogle Scholar
Cai, N., Song, Y., & Kou, S. (2015). A general framework for pricing Asian options under Markov processes. Operations Research 63: 540–554.10.1287/opre.2015.1385CrossRefGoogle Scholar
Carr, P. & Madan, D. (1999). Option valuation using the fast fourier transform. Journal of Computational Finance 2: 61–73.10.21314/JCF.1999.043CrossRefGoogle Scholar
Carr, P., Geman, H., Madan, D., & Yor, M. (2002). The fine structure of asset returns: an empirical investigation. Journal of Business 75: 305–332.CrossRefGoogle Scholar
Cont, R. & Tankov, P. (2004). Non-parametric calibration of jump-diffusion option pricing models. Journal of Computational Finance 7: 1–49.CrossRefGoogle Scholar
Cruz, J. & Ševčovič, D. (2018). Option pricing in illiquid markets with jumps. Applied Mathematical Finance 25: 395–415.10.1080/1350486X.2019.1585267CrossRefGoogle Scholar
Elliott, R., Chan, L., & Siu, T. (2005). Option pricing and Esscher transform under regime switching. Annals of Finance 1: 423–432.10.1007/s10436-005-0013-zCrossRefGoogle Scholar
Figueroa-López, J., Gong, R., & Houdré, C. (2017). Third-order short-time expansions for close-to-the-money option prices under the CGMY model. Applied Mathematical Finance 24: 547–574.10.1080/1350486X.2018.1429935CrossRefGoogle Scholar
Frame, S. & Ramezani, C. (2014). Bayesian estimation of asymmetric jump-diffusion processes. Annals of Financial Economics 9: 1450008.10.1142/S2010495214500080CrossRefGoogle Scholar
Fusai, G. & Kyriakou, I. (2016). General optimized lower and upper bounds for discrete and continuous arithmetic Asian options. Mathematics of Operations Research 41: 531–559.10.1287/moor.2015.0739CrossRefGoogle Scholar
Fusai, G. & Meucci, A. (2008). Pricing discretely monitored Asian options under Lévy processes. Journal of Banking and Finance 32: 2076–2088.10.1016/j.jbankfin.2007.12.027CrossRefGoogle Scholar
Jeon, J., Yoon, J., & Kang, M. (2016). Valuing vulnerable geometric Asian options. Computers and Mathematics with Applications 71: 676–691.10.1016/j.camwa.2015.12.038CrossRefGoogle Scholar
Klein, P. (1996). Pricing Black-Scholes options with correlated credit risk. Journal of Banking and Finance 20: 1211–1229.CrossRefGoogle Scholar
Klein, P. & Inglis, M. (1999). Valuation of European options subject to financial distress and interest rate risk. Journal of Derivatives 6: 44–56.10.3905/jod.1999.319118CrossRefGoogle Scholar
Klein, P. & Inglis, M. (2001). Pricing vulnerable European options when the option's payoff can increase the risk of financial distress. Journal of Banking and Finance 25: 993–1012.10.1016/S0378-4266(00)00109-6CrossRefGoogle Scholar
Kou, S. & Wang, H. (2004). Option pricing under a double exponential jump diffusion model. Management Science 50: 1178–1192.CrossRefGoogle Scholar
Leippold, M. & Schärer, S. (2017). Discrete-time option pricing with stochastic liquidity. Journal of Banking and Finance 75: 1–16.10.1016/j.jbankfin.2016.11.014CrossRefGoogle Scholar
Li, Z., Zhang, W., & Liu, Y. (2018). Analytical valuation for geometric Asian options in illiquid markets. Physica A: Statistical Mechanics and its Applications 507: 175–191.10.1016/j.physa.2018.05.069CrossRefGoogle Scholar
Li, Z., Zhang, W., Liu, Y., & Zhang, Y. (2019). Pricing discrete barrier options under jump-diffusion model with liquidity risk. International Review of Economics and Finance 59: 347–368.10.1016/j.iref.2018.10.002CrossRefGoogle Scholar
Liang, G. & Ren, X. (2007). The credit risk and pricing of OTC options. Asia-Pacific Financial Markets 14: 45–68.CrossRefGoogle Scholar
Liang, G. & Wang, X. (2021). Pricing vulnerable options in a hybrid credit risk model driven by Heston-Nandi GARCH processes. Review of Derivatives Research 24: 1–30.CrossRefGoogle Scholar
Liao, S. & Huang, H. (2005). Pricing Black-Scholes options with correlated interest rate risk and credit risk: an extension. Quantitative Finance 5: 443–457.10.1080/14697680500362718CrossRefGoogle Scholar
Liu, H. & Yong, J. (2005). Option pricing with an illiquid underlying asset market. Journal of Economic Dynamics and Control 29: 2125–2156.CrossRefGoogle Scholar
Madan, D. & Cherny, A. (2010). Markets as a counterparty: an introduction to conic finance. International Journal of Theoretical and Applied Finance 13: 1149–1177.10.1142/S0219024910006157CrossRefGoogle Scholar
Madan, D. & Schoutens, W. (2016). Applied conic finance. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Madan, D. & Yor, M. (2008). Representing the CGMY and Meixner Lévy processes as time changed Brownian motions. Journal of Computational Finance 12: 27–47.CrossRefGoogle Scholar
Merton, R. (1976). Option pricing when underlying stock returns are discontinuous. Journal of Financial Economics 3: 125–144.10.1016/0304-405X(76)90022-2CrossRefGoogle Scholar
Niu, H. & Wang, D. (2016). Pricing vulnerable options with correlated jump-diffusion processes depending on various states of the economy. Quantitative Finance 16: 1129–1145.10.1080/14697688.2015.1090623CrossRefGoogle Scholar
Pasricha, P. & Goel, A. (2019). Pricing vulnerable power exchange options in an intensity based framework. Journal of Computational and Applied Mathematics 355: 106–115.10.1016/j.cam.2019.01.019CrossRefGoogle Scholar
Song, Y., Cai, N., & Kou, S. (2018). Computable error bounds of Laplace inversion for pricing Asian options. Informs Journal on Computing 30: 634–645.CrossRefGoogle Scholar
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: 957–979.10.1002/fut.21629CrossRefGoogle Scholar
Tsao, C. & Liu, C. (2012). Asian options with credit risks: pricing and sensitivity analysis. Emerging Markets Finance and Trade 48: 96–115.10.2753/REE1540-496X4805S306CrossRefGoogle Scholar
Wang, X. (2017). Differences in the prices of vulnerable options with different counterparties. Journal of Futures Markets 37: 148–163.CrossRefGoogle Scholar
Wang, X. (2020). Analytical valuation of Asian options with counterparty risk under stochastic volatility models. Journal of Futures Markets 40: 410–429.10.1002/fut.22064CrossRefGoogle Scholar
Wang, X. (2020). Valuation of Asian options with default risk under GARCH models. International Review of Economics and Finance 70: 27–40.10.1016/j.iref.2020.06.019CrossRefGoogle Scholar
Wang, X. (2021). Pricing vulnerable options with jump risk and liquidity risk. Review of Derivatives Research 24: 243–260.10.1007/s11147-021-09177-5CrossRefGoogle Scholar
Wang, G., Wang, X., & Zhou, K. (2017). Pricing vulnerable options with stochastic volatility. Physica A: Statistical Mechanics and its Applications 485: 91–103.10.1016/j.physa.2017.04.146CrossRefGoogle Scholar
Xu, G., Shao, X., & Wang, X. (2019). Analytical valuation of power exchange options with default risk. Finance Research Letters 28: 265–274.10.1016/j.frl.2018.05.007CrossRefGoogle Scholar
Yang, S., Lee, M., & Kim, J. (2014). Pricing vulnerable options under a stochastic volatility model. Applied Mathematics Letters 34: 7–12.CrossRefGoogle Scholar
Yang, Q., Ching, W., He, W., & Siu, T. (2019). Pricing vulnerable options under a Markov-modulated jump-diffusion model with fire sales. Journal of Industrial and Management Optimization 15: 293–318.CrossRefGoogle Scholar