Time subordination represents a simple but powerful tool for modeling asset dynamics. This is theoretically founded on the property of local semi-martingales which can be represented as a time changed Brownian motion as shown by Monroe (1978). Given the non- negativeness of asset prices, here, time-changed geometric Brownian motions are considered. In particular, this formulation allows to represent option prices as averages of Black and Scholes prices. The problem of a non-parametric calibration of the subordinator distribution is focused. In particular, it is shown that a cross section of market option prices imposes a set of linear inequalities that the distribution of the subordinator has to satisfy. This results in an infinite dimensional optimization problem or in a set of semi-infinite dimensional programming models. The advantages with respect to a parametric specification consist of the fact that the problem remains linear in the unknowns. Furthermore, differently from a fully unrestricted non-parametric approach, the return distribution is always continuous. Empirical results are reported by using market option prices on the FTSE index.
Log-normal mixtures in option pricing: non parametric calibration / L. Barzanti; P. Foschi. - ELETTRONICO. - (2008), pp. 29-29. (Intervento presentato al convegno 5th Internazional Conference on Computational Management Science tenutosi a London nel March 26-28, 2008).
Log-normal mixtures in option pricing: non parametric calibration
BARZANTI, LUCA;FOSCHI, PAOLO
2008
Abstract
Time subordination represents a simple but powerful tool for modeling asset dynamics. This is theoretically founded on the property of local semi-martingales which can be represented as a time changed Brownian motion as shown by Monroe (1978). Given the non- negativeness of asset prices, here, time-changed geometric Brownian motions are considered. In particular, this formulation allows to represent option prices as averages of Black and Scholes prices. The problem of a non-parametric calibration of the subordinator distribution is focused. In particular, it is shown that a cross section of market option prices imposes a set of linear inequalities that the distribution of the subordinator has to satisfy. This results in an infinite dimensional optimization problem or in a set of semi-infinite dimensional programming models. The advantages with respect to a parametric specification consist of the fact that the problem remains linear in the unknowns. Furthermore, differently from a fully unrestricted non-parametric approach, the return distribution is always continuous. Empirical results are reported by using market option prices on the FTSE index.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
