On Approximate Pricing of Spread Options via Conditional Value-at-Risk
https://doi.org/10.26794/2308-944X-2021-9-3-27-51
Abstract
It is widely accepted to use conditional value-at-risk for risk management needs and option pricing. As a rule, there are difficulties in exact calculations of conditional value-at-risk. In the paper, we use the conditional value-at-risk methodology to price spread options, extending some approximation approaches for these needs. Our results we illustrate by numerical calculations which demonstrate their effectiveness. We also show how conditional value-at-risk pricing can help with regulatory needs inspired by the Basel Accords.
Keywords
spread options,
conditional value-at-risk,
approximation methods,
capital constraints,
Margrabe market
Supporting agencies: The research was supported by the NSERC Discovery Grants #5901 and RES 0043487.
About the Authors
C. Maksimov
Canadian Western Bank
Canada
Canada
Chingis Maksimov, Edmonton, AB
A. Melnikov
University of Alberta
Canada
Canada
Alexander Melnikov — Professor, DSc from Steklov Mathematical Institute, Russia, PhD from Steklov Mathematical Institute, Russia, MSc from Moscow State University, Russia. Edmonton, AB
References
1. Acerbi, C. (2002). Spectral measures of risk: A coherent representation of subjective risk aversion. Journal of Banking & Finance, 26(7), 1505–1518.
2. Artzner, P., Delbaen, F., Eber, J., & Heath, D. (1999). Coherent measures of risk. Mathematical Finance, 9(3), 203–228.
3. Basel Committee on Banking Supervision. (2016). Minimum capital requirements for market risk. www.bis.org/bcbs/publ/d352.pdf (accessed 4th December 2018).
4. Soubra, A., & Bastidas-Arteaga, E. (2014). Advanced Reliability Analysis Methods. 10.13140/RG.2.1.1697.7124.
5. Bjerksund, P., & Stensland, G. (2006). Closed form spread option valuation. NHH Dept. of Finance & Management Science Discussion Paper No. 2006/20. https://ssrn.com/abstract=1145206
6. Browne, S. (1999). Reaching goals by a deadline: Digital options and continuous-time active portfolio management. Advances in Applied Probability, 31(02), 551–577.
7. Brutti Righi, M., & Ceretta, P. (2016). Shortfall deviation risk: An alternative for risk measurement. The Journal of Risk, 19(2), 81–116.
8. Carmona, R., & Durrleman. (2003). V. Pricing and hedging spread op tions. SIAM Review, 45(4), 627–685.
9. Cobb, B., & Rumi, R. (2012). Approximating the distribution of a sum of log-normal random variables. Sixth European Workshop on Probabilistic Graphical Models, Granada, Spain.
10. El Karoui, N., & Quenez, M. (1995). Dynamic programming and pricing of contingent claims in an incomplete market. SIAM Journal on Control and Optimization, 33(1), 29–66.
11. Fischer, S. (1978). Call option pricing when the exercise price is uncertain, and the valuation of index bonds. The Journal of Finance, 33(1), 169–176.
12. Foellmer, H., & Leukert, P. (1999). Quantile hedging. Finance and Stochastics, 3(3), 251–273.
13. Foellmer, H., & Leukert, P. (2000). Efficient hedging: Cost versus shortfall risk. Finance and Stochastics, 4(2), 117–146.
14. Hcine, M., & Bouallegue, R. (2015). On the approximation of the sum of lognormals by a log skew normal distribution. Intenational Journal of Computer Networks & Communications, 7, 135–151.
15. Kirk, E. (1995). Correlation in the energy markets. In Managing Energy Price Risk, (71–78). London: Risk Publications and Enron Capital & Trade Resources.
16. Kulldorff, M. (1993). Optimal control of favorable games with a time limit. SIAM Journal on Control and Optimization, 31(1), 52–69.
17. Lo, C. F. (2012). The sum and difference of two log-normal random variables. Journal of Applied Mathematics, 2012(Article ID 838397), 1–13. https://doi.org/10.1155/2012/838397
18. Margrabe, W. (1978). The value of an option to exchange one asset for another. The Journal of Finance, 33(1), 177–186.
19. Mehta, N. B., Molisch, A., Wu, J., & Zhang, J. (2007). Approximating a sum of random variables with a lognormal. IEEE Transactions on Wireless Communications, 6(7), 2690–2699.
20. Melnikov, A. (2011). Risk Analysis in Finance and Insurance, 2nd ed. Boca Raton, Florida: Chapman & Hall/CRC.
21. Melnikov, A., & Smirnov, I. (2012). Dynamic hedging of conditional value-at-risk. Insurance: Mathematics and Economics, 51(1), 182–190.
22. Molisch, A. (2013), Wireless Communications. Hoboken, N.J.: Wiley.
23. Rockafellar, R., & Uryasev, S. (2000). Optimisation of conditional value-at-risk. The Journal of Risk, 2(3), 21–41.
24. Shreve, S. (2011). Stochastic Calculus for Finance II. New York: Springer.
Review
For citations:
Maksimov C., Melnikov A. On Approximate Pricing of Spread Options via Conditional Value-at-Risk. Review of Business and Economics Studies. 2021;9(3):27-51. https://doi.org/10.26794/2308-944X-2021-9-3-27-51
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