Dynamics of state price densities

Abstract

Ambiguity, also called Knightian or model uncertainty, is a key feature in financial modeling. A recent paper by Maccheroni et al. (2004) characterizes investor preferences under aversion against both risk and ambiguity. Their result shows that these preferences can be numerically represented in terms of convex risk measures. In this paper we study the corresponding problem of optimal investment over a given time horizon, using a duality approach and building upon the results by Schachermayer (1999, 2001). In many situations this seems to be the only feasible approach among the known techniques, as is illustrated by several examples.

Analysis of Option Butterfly Portfolio Models Based on Nonparametric Estimation Deep Learning Method

“…For example, the idea of Yatchew and Hardle [18] is to use nonparametric least squares method and Bootstrap method to consider tail constraints under the condition of the call option price to find better the effect of getting the tail constraint. Hardle and Hlavka [19] and Birke and Pilz [20] have further studied the nonparametric estimation method under call option pricing no-arbitrage constraints but only for the different estimation method. Monteiro and Santos [21] have established a nonparametric regression model with both call and put option data, which has been transformed into a quadratic programming model to solve it.…”

Editorial to the special issue on Applicable semiparametrics of computational statistics

“…However, over the last decades, Wolfgang Karl Härdle has made many seminal contributions to applicable semiparametrics, both from theoretical and applied perspectives. These contributions range from robust nonparametric regression (Härdle 1984a, b;Marron 1985a, b, 1990a, b;Härdle and Gasser 1985;Härdle and Kelly 1987;Härdle et al , 1992aHärdle and Bowman 1988;Härdle and Tsybakov 1988;Härdle and Vieu 1992;Härdle and Mammen 1993), over single index models Horowitz and Härdle 1996), real steps into computational statistics (Müller et al 1997;Klinke et al 1997;Härdle et al 2001), true applicable semiparametrics (Liang et al 1999;Hall et al 2000;Wang et al 2004) to the development of dynamic semiparametric factor models (Fengler et al 2007;Brüggemann et al 2008;Park et al 2009;Härdle and Hlavka 2009). The conducted work has not only a strong theoretical background, but also solid empirical justification, which makes the methods developed by Wolfgang Karl Härdle highly valuable.…”

Nonparametric Estimation of Risk-Neutral Densities

“…Instead of an integrated criterion also an averaged criterion like the mean average squared error (MASE) can be used which replaces integration with summation in (16). When using a second order kernel straightforward calculations yield…”

“…Li (1987) showed that each of the above three criteria leads to an optimally selected L in the sense that they all minimize the asymptotic weighted integrated squared error (see (16)). In this sense the obtained L are asymptotically equivalent.…”