ОСОБЛИВОСТІ МОДЕЛЮВАННЯ ЦІНОВОЇ ДИНАМІКИ НА ОСНОВІ МОДЕЛІ CEV
Анотація
Розглянуто застосування відомої стохастичної моделі постійної еластичності дисперсії (CEV) до визначення ціни опціону. Знайдена густина умовної ймовірності випадкової величини (ціни активу) моделі для довільного значення параметра еластичності дисперсії β. Показано, що в залежності від параметра β існують два розв’язки для густини умовної ймовірності, які нормовані на одиницю. Один з них належить додатній області зміни параметра β, інший – від’ємній області зміни β. Для β<0 вказаний розв’язок описує лише інтервал -1<β<-1/2 . Визначені ціна європейського опціону кол для значення параметра β=-1/2 моделі для двох зазначених розв’язків густини умовної ймовірності. При цьому використано також розв’язок для густини умовної ймовірності процесу Феллера, який в границі співпадає з моделлю CEV для β=-1/2. Проведено порівняльний аналіз чисельних розрахунків цін опціону.
Посилання
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Tim Bollerslev, Julia Litvinova, and George Tauchen. Leverage and volatility feedback effects in highfrequency data. Journal of Financial Econometrics, 4(3):353–384, 2006.
Jens Carsten Jackwerth and Mark Rubinstein. Recovering probability distributions from option prices. The Journal of Finance, 51(5):1611–1631, 1996.
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John C Cox. Notes on option pricing i: Constant elasticity of variance diffusions. Working paper, Stanford University, 1975.
John C Cox. The constant elasticity of variance option pricing model. The Journal of Portfolio Management, 23(5):15–17, 1996.
VK Singh and N Ahmad. Forecasting performance of constant elasticity of variance model: Empirical evidence from India. International Journal of Applied Economics and Finance, 5(1):87–96, 2011.
KC Yuen, H Yang and KL Chu. Estimation in the constant elasticity of variance model. British Actuarial Journal, 7(2):275–292, 2001.
P. Carr, A. Itkin and D. Muravey, Semi-closed form prices of barrier options in the time dependent CEV and CIR models, Journal of Derivatives, 28 (2020), 26–50.
John C Cox and Stephen A Ross. The valuation of options for alternative stochastic processes. Journal of financial economics, 3(1-2):145–166, 1976.
C. F. Lo and p. H. Yuen. Constant elasticity of variance option pricing model with time-dependent parameters. International Journal of Theoretical and Applied Finance Vol. 3, No. 4 (2000) 661–674.
Y. L. Hsua, T. I. Lina, C. F. Leebc. Constant elasticity of variance (CEV) option pricing model: Integration and detailed derivation. Mathematics and Computers in Simulation. Volume 79, Issue 1, October 2008, Pages 60–71.
Stan Beckers. The constant elasticity of variance model and its implications for option pricing. The Journal of Finance, Vol. 35, N 3, p. 661–673, 1980.
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Dan Pirjol and Iingjiong Zhu. Short maturity Asian options for the CEV model. Preprint. Arxiv:1702.03382 v1 [q-fin.pr] 11 feb. 2017.
