Resumen
Usando el concepto de leyes de conservación, estudiamos ciertos modelos financieros similares al modelo de Black–Scholes. Demostramos que sin limitaciones complementarias tales modelos pueden tener dos o más volatilidades. Este hecho impone varias limitaciones intrínsecas para los parámetros de sistemas dinámicos con fines de garantizar la definición correcta de dichos sistemas.
Citas
Blenman, L.P.; Clark, S.P. (2005) “Options with constant underlying elasticity in strikes”, Review of Derivatives Research 8: 67–83.
Cathcart, L.; El-Jahel, L. (1998) “Valuation of defaultable bonds”, Journal of Fixed Income 8: 65–78.
Cané de Estrada, M.; Cortina, E.; Ferro Fontán, C.; Di Fiori, J. (2001) “Defaultable bonds with log-normal spread: an application of the model to Argentinean and Brazilian bonds during the Argentine crisis”, Preprint, Instituto Argentino de Matemática, Buenos Aires
Cané de Estrada, M.; Cortina, E.; Ferro Fontán, C; Di Fiori, J. (2005) “Pricing of defaultable bonds with log-normal spread: development of the model and an application to Argentinean and Brazilian bonds during the Argentine crisis”, Review of Derivatives Research 8(1): 40–60.
Hui, C.H.; Lo, C.F. (2002) “Valuation Model of Defaultable Bond Values in Emerging Markets”, Asia-Pacific Financial Markets 9(1): 45–60.
Lo, C.F.; Hui, C.H. (2000) “Valuation of defaultable bonds using signaling process –An extension”, Preprint, Chinese University of Hong Kong, Hong Kong
Sukhomlin, N. (2006) “Conservation law of strike price in the Black–Scholes model”, Economı́a 17-18: 147–161, Universidad de los Andes, Venezuela.
Sukhomlin, N.; Jacquinot, Ph. (2006) “Symmetries and conservation laws in the Black–Scholes model of financial markets”, The XVth International Symposium on Mathematical Methods Applied to Sciences, 153–154. In: E. Piza & J. Trejos (Eds.), The University of Costa Rica, Costa Rica.
Sukhomlin, N.; Jacquinot, Ph. (2006) “Conservation laws and the Black–Scholes model”, The International Conference on the Mathematics of Optimization and Decision Making, University of Antilles and Guyana, Point-à-Pitre, Guadeloupe, France.
Sukhomlin, N.; Jacquinot, Ph. (2006) “Explicit formulation of the volatility in the Black-Scholes-Merton model: theory and application”, Journal of Future Markets (in publication).
Wilmott, P.; Howison, S.; Dewynne, J. (1995) The Mathematics of Financial Derivatives. Cambridge University press, Cambridge