Pricing derivatives under jump-diffusion model in the underlying in markets with stochastic liquidity

One failure of the Black-Scholes valuation model is to assume that the trading activities of agents have no effect on prices, an assumption that it can only be fulfilled in perfectly liquid markets, making the model very restrictive. This element has already been considered in some studies that inco...

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Autor Principal: Moreno Trujillo, John Freddy
Formato: Artículo (Article)
Lenguaje:Español (Spanish)
Publicado: Facultad de Finanzas, Gobierno y Relaciones Internacionales 2022
Acceso en línea:https://revistas.uexternado.edu.co/index.php/odeon/article/view/7838
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recordtype ojs
institution Universidad Externado de Colombia
collection OJS
language Español (Spanish)
format Artículo (Article)
author Moreno Trujillo, John Freddy
spellingShingle Moreno Trujillo, John Freddy
Pricing derivatives under jump-diffusion model in the underlying in markets with stochastic liquidity
author_facet Moreno Trujillo, John Freddy
author_sort Moreno Trujillo, John Freddy
title Pricing derivatives under jump-diffusion model in the underlying in markets with stochastic liquidity
title_short Pricing derivatives under jump-diffusion model in the underlying in markets with stochastic liquidity
title_full Pricing derivatives under jump-diffusion model in the underlying in markets with stochastic liquidity
title_fullStr Pricing derivatives under jump-diffusion model in the underlying in markets with stochastic liquidity
title_full_unstemmed Pricing derivatives under jump-diffusion model in the underlying in markets with stochastic liquidity
title_sort pricing derivatives under jump-diffusion model in the underlying in markets with stochastic liquidity
description One failure of the Black-Scholes valuation model is to assume that the trading activities of agents have no effect on prices, an assumption that it can only be fulfilled in perfectly liquid markets, making the model very restrictive. This element has already been considered in some studies that incorporate the effect of agents’ trading activities assuming a continuous process for price dynamics, however, financial markets show that a better description of the price dynamics of Risky assets must incorporate random jumps. The contribution of this document is to consider the problem of the valuation of derivatives in illiquid markets where the price of the underlying asset follows a diffusion process with jumps. The corresponding non-linear partial differential equation of valuation is presented and the trading strategy that minimizes the variance of the hedge is described.
publisher Facultad de Finanzas, Gobierno y Relaciones Internacionales
publishDate 2022
url https://revistas.uexternado.edu.co/index.php/odeon/article/view/7838
_version_ 1741870955688361984
spelling ojs-article-78382022-06-07T14:28:03Z Pricing derivatives under jump-diffusion model in the underlying in markets with stochastic liquidity Valoración de derivados bajo un modelo de difusión con saltos del subyacente en mercados con liquidez estocástica Moreno Trujillo, John Freddy valuation of derivatives; diffusion with jumps; illiquidity valoración de derivados; difusión con saltos; iliquidez One failure of the Black-Scholes valuation model is to assume that the trading activities of agents have no effect on prices, an assumption that it can only be fulfilled in perfectly liquid markets, making the model very restrictive. This element has already been considered in some studies that incorporate the effect of agents’ trading activities assuming a continuous process for price dynamics, however, financial markets show that a better description of the price dynamics of Risky assets must incorporate random jumps. The contribution of this document is to consider the problem of the valuation of derivatives in illiquid markets where the price of the underlying asset follows a diffusion process with jumps. The corresponding non-linear partial differential equation of valuation is presented and the trading strategy that minimizes the variance of the hedge is described. Una de las fallas del modelo Black-Scholes de valoración es asumir que las actividades de negociación de los agentes no tienen efecto sobre los precios, supuesto que solo puede cumplirse en mercados perfectamente líquidos, lo que hace que el modelo sea muy restrictivo. Este elemento ya ha sido considerado en algunos trabajos que incorporan el efecto de las actividades de negociación de los agentes asumiendo un proceso continuo para la dinámica de los precios, sin embargo, los mercados financieros muestran que una mejor descripción de la dinámica de los precios de activos riesgosos debe incorporar saltos aleatorios. La contribución de este documento es considerar el problema de la valoración de derivados en mercados ilíquidos en donde el precio del activo subyacente sigue un proceso de difusión con saltos. Se presenta la ecuación diferencial parcial no lineal de valoración correspondiente y se describe la estrategia de negociación que minimiza la varianza de la cobertura. Facultad de Finanzas, Gobierno y Relaciones Internacionales 2022-06-07 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion application/pdf https://revistas.uexternado.edu.co/index.php/odeon/article/view/7838 Odeon; No. 20 (2021): Enero-Junio; 123-137 Odeon; Núm. 20 (2021): Enero-Junio; 123-137 2346-2140 1794-1113 spa https://revistas.uexternado.edu.co/index.php/odeon/article/view/7838/11405 /*ref*/Alexander, G. J., Sharpe, W. F., y Bailey, J. V. (2001). Fundamentals of investments. Pearson Education. /*ref*/Black, F., y Scholes, M. (1973). The valuation of options and corporate liabilities. Journal of Political Economy, 81(3), 637-654. /*ref*/Chan, L. K., y Lakonishok, J. (1995). The behavior of stock prices around institutional trades. The Journal of Finance, 50(4), 1147-1174. /*ref*/Dritschel, M., y Protter, P. (1999). Complete markets with discontinuous security price. Finance and Stochastics, 3(2), 203-214. /*ref*/El-Khatib, Y., y Hatemi-J, A. (2013). On option pricing in illiquid markets with jumps. International Scholarly Research Notices, 2013. /*ref*/El-Khatib, Y., y Privault, N. (2003). Hedging in complete markets driven by normal martingales. Applicationes Mathematicae, 2(30), 147-172. /*ref*/Keim, D. B., y Madhavan, A. (1997). Transactions costs and investment style: An inter-exchange analysis of institutional equity trades. Journal of Financial Economics, 46(3), 265-292. /*ref*/Liu, H., y Yong, J. (2005). Option pricing with an illiquid underlying asset market. Journal of Economic Dynamics and Control, 29(12), 2125-2156. /*ref*/Merton, R. C. (1976). Option pricing when underlying stock returns are discontinuous. Journal of financial economics, 3(1-2), 125-144. /*ref*/Moreno Trujillo, J. F. (2020). Din´amica de precios y valoraci´on de activos contingentes en mercados con riesgo de liquidez. ODEON-Observatorio de Economía y Operaciones Numerical (19). Derechos de autor 2022 John Freddy Moreno Trujillo http://creativecommons.org/licenses/by-nc-sa/4.0
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