Options, coverage and diffusion-jump processes: An application to GCARSO titles

  • Francisco Venegas Martínez Oxford University
Keywords: GCARSO shares
JEL Classification: G10

Abstract

We present two models for hedging European options on an underlying asset driven by a mixed diffusion-jump process. The first model, values the option as the average of option prices hedging sequential jumps. In the second model, the option price is determined by minimizing the variance of the portfolio value. In particular, we develop hedging strategies for the case of GCARSO shares.

 

References

Ahn, C. M. y H. E. Thompson (1988). “Jump-Diffusion Processes and the Term Structure of Interest Rates”, Journal of Finance, 43, pp. 155-174.

Arrow, K. J. (1963). “The Role of Securities in the Optimal Allocation of Risk-Bearing”, Review of Economic Studies, 31, pp. 91-96.

Avellaneda, M., A. Levy y A. Parás (1995). “Pricing and Hedging Derivate Securities in Markets with Uncertain Volatilities”, Applied Mathematical Finance, 2, pp. 73-88.

Ball, C. y A. Roma (1994). “Stochastic Volatility Option Prices”, Journal of Financial and Quantitative Analysis, 24 (4), pp. 589-607.

Bingham, N. H. y R. Kiesel (1998). Risk-Neutral Valuation: Pricing and Hedging of Financial Derivates, Springer-Verlag.

Bjerksund, P. y G. Stensland (1993). “Closed-Form Approximation of American Options”, Scandinavian Journal of Management, 9, pp. 87-99.

Bjork, T. (1999). Arbitrage Theory in Continuous Time, Oxford University Press.

Black, F. E. Derman y W. Toy (1990). “A One-Factor Model of Interest Rates and Its Applications to Treasury Bond Options”, Financial Analysts Journal, enero-febrero, pp. 33-39.

Black, F. and M. Scholes (1973). “The Pricing of Options and Corporate Liabilities”, Journal of Political Ecoonomy, 81, pp. 637-654.

Bouleau, N. y D. Lamberton (1989). “Residual Risk and Hedging Strategies in Markovian Markets”, Stochastic Processes and Their Applications, 33, pp. 131-150.

Cox, J. C., J. E. Ingersoll y S. A. Ross (1985). “A Theory of the Term Structure of Interest Rates”, Econometrica, 53, pp. 385-407.

Cox, J. C. y S. Ross (1976). “The Valuation of Options for Alternative Stochastic Processes”, Journal of Financial Economics, 3, pp. 145-166.

Fama, E. (1970). “Efficient Capital Markets: A Review of Theory and Empirical Work”, Journal of Finance, 25, pp. 383-417.

Fölmer, H. y D. Sonderman (1990). “Hedging of Contingent Claims under Incomplete Information, Applied Stochastic Analysis”, en M. H. A. Davis y R. J. Elliot (eds.), Gordon y Breach.

Fouque, J. P., G. Papanicolaou y K. R. Sircar (2000). Derivatives in Financial Markets with Stochastic Volatility, Cambridge University Press.

Gihman, I. y A. V. Skorohod (1972). Stochastic differential equations, Springer-Verlag.

Hanselman, D. y Littlefield (1998). Mastering MATLAB 5: A Comprehensive Tutorial and Reference, Prentice Hall.

Heath, D., R. Jarrow y A. Morton (1992). “Bond Pricing and the Term Structure of Interest Rates: A New Methodology”, Econometrica, 60, pp. 77-105.

Heston, S. (1993). “A Closed-form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options”, Review of Financial Studies, 6 (2), pp. 327-343.

Ho, T. S. y S. B. Lee (1986). “Term Structure Movements and Pricing Interest Rate Contingent Claims”, Journal of Finance, 41, pp. 1011-1029.

Hull, J. y A. White (1993). “One-Factor Interest Rate Models and the Valuation of Interest Rate Derivate Securities”, Journal of Financial and Quantitative Analysis, 28, pp. 235-354.

Hull, J. y A. White (1990). “Pricing Interest Rate-Derivative Securities”. Review of Financial Studies, 3, pp. 573-592.

Hull, J. y A. White (1987). “The Pricing of Option on Assets with Stochastic Volatility”, journal of Finance, 42 (2), pp. 281-300.

Jarrow, R. A. y E. R. Rosenfeld (1984). “Jump Risks and the Intertemporal Capital Asset Pricing Model”, Journal of Business, 57, pp. 337-351.

Kloeden P. E. y P. Eckhard (1992). Numerical Solution of Stochastic Differential Equations, Springer Verlag.

Lamberton, D. y Lapeyre, B. (1996). Introduction to Stochastic Calculus Applied to Finance, Chapman & Hall.

Malliaris, A. G. y W. A. Brock (1982). Stochastic Methods in Economic and Finance, North-Holland.

Merton, R. C. (1976). “Option Pricing when Underlying Stock Returns are Discontinuous”, Journal of Financial Economics, 3, pp. 125-144.

Merton, R. C. (1971). “Optimum Consumption and Portfolio Rules in a Continuous- Time Model”, Journal of Economic Theory, 3, pp. 373-413.

Nelson, C. R. y A. F. Siegel (1987). “Parsimonious Modeling of Yield Curves”, Journal of Business, 60, núm. 4, pp. 473-489.

Naik, V. (1993). “Options, Valuations, and Hedging Strategies with Jumps in the Volatility of Assets Returns”, Journal of Finance, vol. 48, pp. 1969-1984.

Penati, A. y G. Pennacchi (1989). “Optimal Portfolio Choice and the Collapse of a Fixed-Exchange Rate Regime”, Journal of International Economics, 27, pp. 1-24.

Ramírez Sánchez, J. C. (2001). Los problemas más comunes en el pronóstico de rendimientos de activos con distribuciones no normales, Documento de Trabajo, CIDE.

Reiner, E. y M. Rubistein, (1991). “Breaking Down the Barriers”, Risk Magazine, 4 (8).

Renault, E. y N. Touzi, (1996). “Option Hedging and Implied Volatility in a Stochastic Volatility Model”, Mathematical Finance, 6 (3), pp. 279-302.

Rendleman, R y B. Bartter (1980). “The Pricing of Options on Debt Securities”, Journal of Financial and Quantitative Analysis, 15, pp. 11-24.

Samuelson, P. A. (1965). “Proof that Properly Anticipated Prices Fluctuate Randomly”, Industrial Mangement Review, 6, pp. 41-49.

Shaw, W. T. (1998). Modelling Financial Derivatives with Mathematica, Cambridge University Press.

Stein, E. J. Stein, (1991). “Stock Price Distribution with Stochastic Volatility: An Analytic Approach”, Review of Financial Studies, 4 (4), pp. 727-752.

Svensson, L. E. O. (1992). “The Foreign Exchange Risk Premium in a Target Zone with Devaluation Risk”, Journal of International Economics, 33, pp. 21-40.

Tapiero, C. S. (1998). Applied Stochastic Models and Control for Finance and Insurance, Kluwer Academic Publisher.

Turnbull, S. M. y L. M. Wakerman (1991). “A Quick Algorithm for Pricing European Average Options”, Journal of Financial and Quantitative Analysis, 26, pp. 377-389.

Venegas Martínez, F. (2001). “Temporary Stabilization: A Stochastic Analysis”, Journal of Economic Dynamics and Control, 25, núm 9, pp. 1429-1449.

Venegas Martínez, F. (2000a). “On Consumption, Investment, and Risk”, Economía Mexicana, 9, núm. 2, pp. 227-244.

Venegas Martínez, F. y B. González-Aréchiga (2000). “Mercados incompletos y su impacto en los programas de estabilización de precios: El caso mexicano”, Momento Económico, 111, pp. 20-27.

Wiggins J. (1996). “Option Values under Stochastic Volatility”, Journal of Financial Economics, 9 (2), pp. 351-372.

Wilmott, P. (1998). Derivatives: The Theory and Practice of Financial Engineering, John Wiley and Sons.

Wilmott, P., J. N. Dewynne y S. D. Howison (1993). Option Pricing: Mathematical Models and Computation, Oxford Financial Press.

Published
01-07-2001
How to Cite
Venegas MartínezF. (2001). Options, coverage and diffusion-jump processes: An application to GCARSO titles. Estudios Económicos, 16(2), 203-226. https://doi.org/10.24201/ee.v16i2.204
  • Abstract viewed - 317 times
  • PDF (Spanish) downloaded: 766 times