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on Econometric Time Series |
| By: | Igor Halperin; Andrey Itkin |
| Abstract: | We propose a new framework for modeling stochastic local volatility, with potential applications to modeling derivatives on interest rates, commodities, credit, equity, FX etc., as well as hybrid derivatives. Our model extends the linearity-generating unspanned volatility term structure model by Carr et al. (2011) by adding a local volatility layer to it. We outline efficient numerical schemes for pricing derivatives in this framework for a particular four-factor specification (two "curve" factors plus two "volatility" factors). We show that the dynamics of such a system can be approximated by a Markov chain on a two-dimensional space (Z_t,Y_t), where coordinates Z_t and Y_t are given by direct (Kroneker) products of values of pairs of curve and volatility factors, respectively. The resulting Markov chain dynamics on such partly "folded" state space enables fast pricing by the standard backward induction. Using a nonparametric specification of the Markov chain generator, one can accurately match arbitrary sets of vanilla option quotes with different strikes and maturities. Furthermore, we consider an alternative formulation of the model in terms of an implied time change process. The latter is specified nonparametrically, again enabling accurate calibration to arbitrary sets of vanilla option quotes. |
| Date: | 2013–01 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1301.4442&r=ets |
| By: | Audrone Virbickaite; M. Concepci\'on Aus\'in; Pedro Galeano |
| Abstract: | A Bayesian non-parametric approach for efficient risk management is proposed. A dynamic model is considered where optimal portfolio weights and hedging ratios are adjusted at each period. The covariance matrix of the returns is described using an asymmetric MGARCH model. Restrictive parametric assumptions for the errors are avoided by relying on Bayesian non-parametric methods, which allow for a better evaluation of the uncertainty in financial decisions. Illustrative risk management problems using real data are solved. Significant differences in posterior distributions of the optimal weights and ratios are obtained arising from different assumptions for the errors in the time series model. |
| Date: | 2013–01 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1301.5129&r=ets |
| By: | Tschernig, Rolf; Weber, Enzo; Weigand, Roland |
| Abstract: | Fractionally integrated vector autoregressive models allow to capture persistence in time series data in a very flexible way. Additional flexibility for the short memory properties of the model can be attained by using the fractional lag perator of Johansen (2008) in the vector autoregressive polynomial. However, it also makes maximum likelihood estimation more diffcult. In this paper we first identify parameter settings for univariate and bivariate models that suffer from poor identification in finite samples and may therefore lead to estimation problems. Second, we propose to investigate the extent of poor identification by using expected log-likelihoods and variations thereof which are faster to simulate than multivariate finite sample distributions of parameter estimates. Third, we provide a line of reasoning that explains the finding from several univariate and bivariate simulation examples that the two-step estimator suggested by Tschernig, Weber, and Weigand (2010) can be more robust with respect to estimating the deterministic components than the maximum likelihood estimator. |
| Keywords: | fractional integration; long memory; maximum likelihood estimation; fractional lag operator |
| JEL: | C32 C51 |
| Date: | 2013 |
| URL: | http://d.repec.org/n?u=RePEc:bay:rdwiwi:27269&r=ets |
| By: | René Garcia; Daniel Mantilla-Garcia; Lionel Martellini |
| Abstract: | In this paper, we formally show that the cross-sectional variance of stock returns is a consistent and asymptotically efficient estimator for aggregate idiosyncratic volatility. This measure has two key advantages: it is model-free and observable at any frequency. Previous approaches have used monthly model based measures constructed from time series of daily returns. The newly proposed cross-sectional volatility measure is a strong predictor for future returns on the aggregate stock market at the daily frequency. Using the cross-section of size and book-to-market portfolios, we show that the portfolios’ exposures to the aggregate idiosyncratic volatility risk predict the cross-section of expected returns. <P> |
| Keywords: | Aggregate idiosyncratic volatility, cross-sectional dispersion, prediction of market returns, |
| Date: | 2013–01–01 |
| URL: | http://d.repec.org/n?u=RePEc:cir:cirwor:2013s-01&r=ets |