Voir la notice de l'article provenant de la source Math-Net.Ru
@article{CHFMJ_2018_3_4_a0, author = {M. M. Dyshaev and V. E. Fedorov and A. S. Avilovich and D. A. Pletnev}, title = {Simulation of feedback effects for futures-style options pricing on {Moscow} {Exchange}}, journal = {\v{C}el\^abinskij fiziko-matemati\v{c}eskij \v{z}urnal}, pages = {379--394}, publisher = {mathdoc}, volume = {3}, number = {4}, year = {2018}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/CHFMJ_2018_3_4_a0/} }
TY - JOUR AU - M. M. Dyshaev AU - V. E. Fedorov AU - A. S. Avilovich AU - D. A. Pletnev TI - Simulation of feedback effects for futures-style options pricing on Moscow Exchange JO - Čelâbinskij fiziko-matematičeskij žurnal PY - 2018 SP - 379 EP - 394 VL - 3 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/CHFMJ_2018_3_4_a0/ LA - ru ID - CHFMJ_2018_3_4_a0 ER -
%0 Journal Article %A M. M. Dyshaev %A V. E. Fedorov %A A. S. Avilovich %A D. A. Pletnev %T Simulation of feedback effects for futures-style options pricing on Moscow Exchange %J Čelâbinskij fiziko-matematičeskij žurnal %D 2018 %P 379-394 %V 3 %N 4 %I mathdoc %U http://geodesic.mathdoc.fr/item/CHFMJ_2018_3_4_a0/ %G ru %F CHFMJ_2018_3_4_a0
M. M. Dyshaev; V. E. Fedorov; A. S. Avilovich; D. A. Pletnev. Simulation of feedback effects for futures-style options pricing on Moscow Exchange. Čelâbinskij fiziko-matematičeskij žurnal, Tome 3 (2018) no. 4, pp. 379-394. http://geodesic.mathdoc.fr/item/CHFMJ_2018_3_4_a0/
[1] F. Black, M. Scholes, “The pricing of options and corporate liabilities”, Journal of Political Economy, 81 (1973), 637–659 | DOI | MR
[2] F. Black, “The pricing of Commodity Contracts”, Journal of Financial Economics, 3 (1976), 167–179 | DOI
[3] U. Çetin, R. Jarrow, P. Protter, “Liquidity risk and arbitrage pricing theory”, Finance and Stochastic, 8 (2004), 311–341 | DOI | MR
[4] R. Frey, “Market illiquidity as a source of model risk in dynamic hedging”, Model Risk, ed. R. Gibson, Risk Publications, London, 2000., 125–136
[5] R. Frey, P. Patie, “Risk management for derivatives in illiquid markets: a simulation study”, Advances in Finance and Stochastics, eds. K. Sandmann, P. Schönbucher, Springer, Berlin, 2002 | MR
[6] M. Jandaćka, D. Śevćović, “On the risk-adjusted pricing-methodology-based valuation of vanilla options and explanation of the volatility smile”, Journal of Applied Mathematics, 3 (2005), 253–258 | MR
[7] H. Liu, J. Yong, “Option pricing with an illiquid underlying asset market”, Journal of Economic Dynamics and Control, 29:12 (2005), 2125–2156 | DOI | MR | Zbl
[8] R. Frey, A. Stremme, “arket volatility and feedback effects from dynamic hedging”, Mathematical Finance, 7:4 (1997), 351–374 | DOI | MR | Zbl
[9] R. Frey, “Perfect option replication for a large trader”, Finance and Stochastics, 2 (1998), 115–148 | DOI
[10] R. A. Jarrow, “Derivative securities markets, market manipulation and option pricing theory”, Journal of Financial and Quantitative Analysis, 29 (1994), 241–261 | DOI
[11] L. A. Bordag, R. Frey, “Pricing options in illiquid markets: symmetry reductions and exact solutions”, Nonlinear Models in Mathematical Finance: Research Trends in Option Pricing, Chapter 3, ed. M. Ehrhardt, Nova Science Publ., 2008, 83–109 | MR
[12] E. Platen, M. Schweizer, “On feedback effects from hedging derivatives”, Mathematical Finance, 8 (1998), 67–84 | DOI | MR | Zbl
[13] R. Sircar, G. Papanicolaou, “Generalized Black — Scholes models accounting for increased market volatility from hedging strategies”, Applied Mathematical Finance, 5:1 (1998), 45–82 | DOI | MR | Zbl
[14] R. K. Gazizov, N. H. Ibragimov, “Lie symmetry analysis of differential equations in finance”, Nonlinear Dynamics, 17 (1998), 387–407 | DOI | MR | Zbl
[15] L. A. Bordag, A. Y. Chmakova, “Explicit solutions for a nonlinear model of financial derivatives”, International Journal of Theoretical and Applied Finance, 10:1 (2007), 1–21 | DOI | MR | Zbl
[16] L. A. Bordag, “On option-valuation in illiquid markets: invariant solutions to a nonlinear model”, Mathematical Control Theory and Finance, eds. A. Sarychev, A. Shiryaev, M. Guerra, M. R. Grossinho, Springer, 2008, 71–94 | DOI | MR | Zbl
[17] P. Schönbucher, P. Wilmott, “The feedback-effect of hedging in illiquid markets”, SIAM Journal on Applied Mathematics, 61 (2000), 232–272 | DOI | MR | Zbl
[18] Dyshaev M.M., “On some models of options pricing on illiquid markets”, Chelyabinsk Physical and Mathematical Journal, 2:1 (2017), 18–19 (In Russ.) | MR
[19] M. Brennan, E. Schwartz, “Finite difference methods and jump processes arising in the pricing of contingent claims: a synthesis”, The Journal of Financial and Quantitative Analysis, 13:3 (1978), 461–474 | DOI | MR
[20] B. Düring, M. Fournié, A. Jüngel, “High order compact finite difference schemes for a nonlinear Black — Scholes equation”, International Journal of Theoretical and Applied Finance, 6:7 (2003), 767–789 | DOI | MR | Zbl
[21] J. Ankudinova, M. Ehrhardt, “On the numerical solution of nonlinear Black — Scholes equations”, Computers Mathematics with Applications, 56:3 (2008), 799–812 | DOI | MR | Zbl
[22] R. Company, E. Navarro, J. R. Pintos, E. Ponsoda, “Numerical solution of linear and nonlinear Black — Scholes option pricing equations”, Computers Mathematics with Applications, 56:3 (2008), 813–821 | DOI | MR | Zbl
[23] R. Company, L. Jódar, E. Ponsoda, C. Ballester, “Numerical analysis and simulation of option pricing problems modeling illiquid markets”, Computers Mathematics with Applications, 59:8 (2010), 2964–2975 | DOI | MR | Zbl
[24] P. Heider, “Numerical methods for non-linear Black — Scholes equations”, Applied Mathematical Finance, 17:1 (2010), 59–81 | DOI | MR | Zbl
[25] A. J. Arenas, G. González-Parra, B. M. Caraballo, “A nonstandard finite difference scheme for a nonlinear Black — Scholes equation”, Mathematical and Computer Modelling, 57:7 (2013), 1663–1670 | DOI | MR | Zbl
[26] J. Guo, W. Wang, “On the numerical solution of nonlinear option pricing equation in illiquid markets”, Computers Mathematics with Applications, 69:2 (2015), 117–133 | DOI | MR | Zbl
[27] D. M. Pooley, P. Forsyth, K. R. Vetzal, “Numerical convergence properties of option pricing PDEs with uncertain volatility”, IMA Journal of Numerical Analysis, 23:2 (2003), 241–267 | DOI | MR | Zbl
[28] B. Düring, M. Fournié, A. Jüngel, “Convergence of a high-order compact finite difference scheme for a nonlinear Black — Scholes equation”, ESAIM: Mathematical Modelling and Numerical Analysis, 38:2 (2004), 359–369 | DOI | MR | Zbl
[29] Moscow Exchage (In Russ.) (accessed 04.09.2017) https://www.moex.com/s204
[30] Dyshaev M.M., Fedorov V.E., “Symmetries and exact solutions of a nonlinear pricing options equation”, Ufa Mathematical Journal, 9:1 (2017), 29–40 | DOI | MR
[31] Dyshaev M.M., Fedorov V.E., “[Symmetry analysis and exact solutions of a nonlinear model of the financial markets theory”, Mathematical Notes of North-Eastern Federal University, 23:1 (89) (2016), 28–45 (In Russ.) | MR | Zbl
[32] Dyshaev M.M., “Group analysis of a nonlinear generalization of the Black — Scholes equiation”, Chelyabinsk Physical and Mathematical Journal, 1:3 (2016), 7–14 (In Russ.) | MR
[33] V. E. Fedorov, M. M. Dyshaev, “Group classification for a general nonlinear model of option pricing”, Ural Mathematical Journal, 2:2 (2016), 37–44 | DOI | Zbl
[34] V. E. Fedorov, M. M. Dyshaev, “Invariant solutions for nonlinear models of illiquid markets”, Mathematical Methods in the Applied Sciences, 2018 | DOI
[35] Kalitkin N.N., Numerical methods, Nauka Publ., Moscow, 1978, 512 pp. (In Russ.)
[36] Richtmyer R., Morton K., Difference Methods for Initial-Value Problems, 2, John Wiley and Sons, New York, 1967, 420 pp. | MR | Zbl
[37] R. Geske, K. Shastri, “Valuation by approximation: a comparison of alternative option valuation techniques”, The Journal of Financial and Quantitative Analysis, 20:1 (1985), 45–71 | DOI
[38] Godunov S.K., Ryaben'kii V.S., Difference schemes (introduction to theory), Nauka Publ., Moscow, 1977, 440 pp. (In Russ.)