Nonparametric and bootstrap techniques applied to financial risk modeling

Abstract

For the purpose of quantifying financial risks, risk managers need to model the behavior of financial variables. However, the construction of such mathematical models is a difficult task that requires careful statistical approaches. Among the important choices that must be addressed,we can list the error distribution, the structure of the variance process, the relationship between parameters of interest and explanatory variables. In particular, one may avoid procedures that rely either on too rigid parametric assumptions or on inefficient estimation procedures. In this thesis, we develop statistical procedures that tackle some of these issues, in the context of three financial risk modelling applications. In the first application, we are interested in selecting the error distribution in a multiplicative heteroscedastic model without relying on a parametric volatility assumption. To avoid this uncertainty, we develop a set of model estimation and selection tests relying on nonparametric volatility estimators and focusing on the tails of the distribution. We illustrate this technique on UBS, BOVESPA and EUR/USD daily stock returns. In the second application, we are concerned by modeling the tail of the operational losses severity distribution, conditionally to several covariates. We develop a flexible conditional GPD model, where the shape parameter is an unspecified link function (nonparametric part) of a linear combination of covariates (single index part), avoiding the curse of dimensionality. We apply successfully this technique on two original databases, using macroeconomic and firm-specific variables as covariates. In the last application, we provide an efficient way to estimate the predictive ability of trading algorithms. Instead of relying on subjective and noisy sample splitting techniques, we propose an adaptation of the .632 bootstrap technique to the time series context. We apply these techniques on stock prices to compare 12,000 trading rules parametrizations and show that none can beat a simple buy-and-hold strategy