Option Pricing in the Presence of Operational Risk

محورهای موضوعی : Financial Mathematics

Alireza Bahiraie ¹ (Department of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, Semnan 35131-19111, Iran)
Mohammad Alipour ² (Department of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, Semnan 35131-19111, Iran)
Rehan Sadiq ³ (School of Engineering, University of British Columbia (Okanagan), 3333 University Way, Kelowna, Canada)

تاریخ دریافت : 1399/06/02 تاریخ پذیرش : 1399/06/02 تاریخ انتشار : 1399/07/10

کلید واژه: Operational Risk, Hedging, Option pricing,

چکیده مقاله :

In this paper we distinguish between operational risks depending on whether the operational risk naturally arises in the context of model risk. As the pricing model exposes itself to operational errors whenever it updates and improves its investment model and other related parameters. In this case, it is no longer optimal to implement the best model. Generally, an option is exercised in a jump-diffusion model, if the stock price either exactly hits the early exercise boundary or the price jumps into the exercise price region. However paths of the diffusion process are continuous. In this paper the impact of operational risk on the option pricing through the implementation of Mitra’s model with jump diffusion model is presented. A partial integral differential equation is derived and the impact of parameters of Merton’s model on operational risk and option value by operational value at risk measure is employed. The option values in the presence of operational risk on data set are computed and some of the results are presented.

منابع و مأخذ:

[1] Acharya, V., Pedersen, L., Asset pricing with liquidity risk, Journal of Financial Economics,
2005, 77, P. 375-410, Doi:10.1016/j.jfineco.2004.06.007

 

[2] Bahiraie, A. and Alipour, M., Jump OpVaR with operational risk, International Journal of Computing Science and Mathematics, 2020, 12)3(, P. 213-225, Doi:10.1504/IJCSM.2019.10025236

 

[3] Bahiraie, A., Azhar, A.K.M. and Ibrahim, A. A new dynamic geometric approach for empirical analysis of financial ratios and bankruptcy, Journal of Industrial and Management Optimization, 2011, 7)4(, P. 947–965, Doi:10.3934/jimo.2011.7.947

 

[4] Bahiraie, A., Abbasi, B., Omidi, F., Hamzah, N.A. and Yaakub, A.H. Continuous time portfolio optimization, International Journal of Nonlinear Analysis and Applications, 2015, 6(2), P. 103–112.

 Doi:10.22075/IJNAA.2015.258

 

[5] Black, F., Scholes, M., The Pricing of Options and Corporate Liabilities, Journal of Political
Economy, 1973, 81, P. 637-654, Doi:10.1086/260062

 

[6] Chavez-Demoulin, V., Embrechts, P., Neslehova, J., Quantitative models for operational
risk:Extremes, dependence and aggregation, Journal of Banking & Finance, 2006, 30(206), P.
2635-2658, Doi:10.1016/j.jbankfin.2005.11.008

 

[7] Chorafas, D., Operational Risk Control with Basel II: Basic Principles and Capital Requirements,
Butterworth-Heinemann, Oxford, 2004, Doi:10.1007/978-3-642-15923-7

 

[8] Cont, R., Tankov, P., Financial Modelling with Jump Processes, second printing. Chapman and
Hall/CRC Press, London, 2004, Doi:10.1201/9780203485217

 

[9] Eshaghi, M., Askari, G., Hyper-Rational Choice and Economic Behaviour, Advances in Mathematical Finance and Applications, 2018, 3(3), P. 69-76, Doi:10.22034/AMFA.2018.544950

[10] Elandt, R., The folded normal distribution: two methods of estimating parameters from moments, Journal of Technimetrics, 1961, 3, P. 551-562, Doi:10.2307/ 1266561

 

[11] Fenga, S. P., Hung, M. W., Wang, Y. H, Option pricing with stochastic liquidity risk: Theory
and evidence, Journal of Financial Markets, 2014, 18, P. 77-95.

 

[12] Hanson, F. B., Westman, J. J, Jump-Diffusion Stock Return Models in Finance: Stochastic
Process Density with Uniform-Jump Amplitude, working paper, University of Illinois at Chicago,
2002, Doi:10.1016/j.finmar.2013.05.002

 

[13] Hull,J., White, A., The impact of default risk on the prices of options and other derivative
securities, Journal of Banking &Finance, 1995, 19, P. 299-322, Doi:10.1016/0378-4266(94)00050

 

[14] Izadikhah, M., Improving the Banks Shareholder Long Term Values by Using Data Envelopment Analysis Model, Advances in Mathematical Finance and Applications, 2018, 3(2), P.27-41.

Doi: 10.22034/amfa.2018.540829

 

[15] Jackson, P., Maude, D. J., Perraudin, W., Bank capital and value at risk, Journal of Derivatives, 1997, 4, P. 73-90, Doi:10.3905/jod.1997.407972

 

[16] Klein. P., Pricing Black-Scholes options with correlated credit risk, Journal of Banking & Finance, 1996, 20, P.1211-1129, Doi:10.1016/0378-4266(95)00052

 

[17] Merton, R. C., Option pricing when underlying stock returns are discontinuous, Journal of Financial Economics. 1976, 3, P. 125-144, Doi:10.1016/0304-405 (76)90022-2

 

[18] Mitra, S., Operational risk of option hedging, Journal of Economic Modelling, 2013, 33,
P. 194-203, Doi:10.1016/j.econmod.2013.04.031

 

[19] Su, X., Wang, W., Pricing options with credit risk in a reduced form model, Journal of the
Korean Statistical Society, 2012, 41, P. 437-444, Doi: 10.1016/j.jkss.2012.01.006

 

[20] Suleyman, B., Andrea M. B., A Theory of Operational Risk, SSRN, Society for Economic Dynamics, 2016, Meeting Papers, 352, Doi:10.2139/ssrn.2737178