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Quantil Hedging for telegraph markets and its applications to a pricing of equity-linked life insurance contracts

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  • Nikita Ratanov

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Abstract

In this paper we develop a financial market model based on continuous time random motions with alternating constant velocities and with jumps occurrng when the velocity switches. If jump directions are in the certain correspondence with the velocity directions of the underlyig random motion with respect to the interest rate, the model is free of arbitrage and complete. Closed form formulas for the option prices and perfect hedging strategies are obtained.The quantile hedging strategies for options are constructed. This methodology is applied to the pricing and risk control of insurance instruments.************************************************************************************************************En este documento está desarrollado un modelo de mercado financiero basado en movimientos aleatorios con tiempo continuo, con velocidades constantes alternates y saltos cuando hay cambios en la velocidad. Si los saltos en la dirección tienen correspondencia con la dirección de la velocidad del comportamiento aleatorio subyacente, con respecto a la tasa interés, el modelo no presenta arbitraje y es completo. Se contruye en detalle las estrategias replicables para opciones y se obtiene una representación cerrada para el precio de las opciones.Las estrategias de cubrimiento quantile para opciones son construidas. Esta metodología es aplicada al control de riesgo y fijación de precios de instrumentos de seguros.

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Bibliographic Info

Paper provided by UNIVERSIDAD DEL ROSARIO in its series BORRADORES DE INVESTIGACIÓN with number 003410.

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Length: 21
Date of creation: 01 Apr 2005
Date of revision:
Handle: RePEc:col:000091:003410

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Related research

Keywords: jump telegraph model; perfect hedging; quantile hedging; pure endowment; equity-linked life insurance;

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References

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  1. Nikita Ratanov, 2004. "Option Pricing Model Based on Telegraph Processes with Jumps," BORRADORES DE INVESTIGACIÓN, UNIVERSIDAD DEL ROSARIO 004330, UNIVERSIDAD DEL ROSARIO.
  2. Elisa Nicolato & Emmanouil Venardos, 2003. "Option Pricing in Stochastic Volatility Models of the Ornstein-Uhlenbeck type," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 13(4), pages 445-466.
  3. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, Elsevier, vol. 3(1-2), pages 125-144.
  4. Hans FÃllmer & Peter Leukert, 1999. "Quantile hedging," Finance and Stochastics, Springer, vol. 3(3), pages 251-273.
  5. Brennan, Michael J. & Schwartz, Eduardo S., 1976. "The pricing of equity-linked life insurance policies with an asset value guarantee," Journal of Financial Economics, Elsevier, Elsevier, vol. 3(3), pages 195-213, June.
  6. Nikita Ratanov, 2007. "A jump telegraph model for option pricing," Quantitative Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 7(5), pages 575-583.
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Cited by:
  1. Alessandro De Gregorio & Stefano M. Iacus, 2007. "Change point estimation for the telegraph process observed at discrete times," Papers 0705.0503, arXiv.org.
  2. Alessandro Gregorio & Stefano Iacus, 2008. "Parametric estimation for the standard and geometric telegraph process observed at discrete times," Statistical Inference for Stochastic Processes, Springer, Springer, vol. 11(3), pages 249-263, October.

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