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on Econometric Time Series |
| By: | Carole Bernard; Zhenyu Cui; Don McLeish |
| Abstract: | Lions and Musiela (2007) give sufficient conditions to verify when a stochastic exponential of a continuous local martingale is a martingale or a uniformly integrable martingale. Blei and Engelbert (2009) and Mijatovi\'c and Urusov (2012c) give necessary and sufficient conditions in the case of perfect correlation (\rho=1). For financial applications, such as checking the martingale property of the stock price process in correlated stochastic volatility models, we extend their work to the arbitrary correlation case (-1 |
| Date: | 2013–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1310.0092&r=ets |
| By: | Carole Bernard; Zhenyu Cui; Don McLeish |
| Abstract: | In stochastic volatility models based on time-homogeneous diffusions, we provide a simple necessary and sufficient condition for the discretely sampled fair strike of a variance swap to converge to the continuously sampled fair strike. It extends Theorem 3.8 of Jarrow, Kchia, Larsson and Protter (2013) and gives an affirmative answer to a problem posed in this paper in the case of 3/2 stochastic volatility model. We also give precise conditions (not based on asymptotics) when the discrete fair strike of the variance swap is higher than the continuous one and discuss the convex order conjecture proposed by Keller-Ressel and Griessler (2012) in this context. |
| Date: | 2013–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1310.0099&r=ets |
| By: | Stefano De Marco; Caroline Hillairet; Antoine Jacquier |
| Abstract: | We study the shapes of the implied volatility when the underlying distribution has an atom at zero. We show that the behaviour at small strikes is uniquely determined by the mass of the atom at least up to the third asymptotic order, regardless of the properties of the remaining (absolutely continuous, or singular) distribution on the positive real line. We investigate the structural difference with the no-mass-at-zero case, showing how one can-a priori-distinguish between mass at the origin and a heavy-left-tailed distribution. An atom at zero is found in stochastic models with absorption at the boundary, such as the CEV process, and can be used to model default events, as in the class of jump-to-default structural models of credit risk. We numerically test our model-free result in such examples. Note that while Lee's moment formula tells that implied variance is \emph{at most} asymptotically linear in log-strike, other celebrated results for exact smile asymptotics such as Benaim and Friz (09) or Gulisashvili (10) do not apply in this setting-essentially due to the breakdown of Put-Call symmetry-and we rely here on an alternative treatment of the problem. |
| Date: | 2013–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1310.1020&r=ets |
| By: | Line Elvstrøm Ekner (Department of Economics, Copenhagen University); Emil Nejstgaard (Department of Economics, Copenhagen University) |
| Abstract: | We propose a new and simple parametrization of the so-called speed of transition parameter of the logistic smooth transition autoregressive (LSTAR) model. The new parametrization highlights that a consequence of the well-known identification problem of the speed of transition parameter is that the threshold autoregression (TAR) is a limiting case of the LSTAR process. We demonstrate how this fact impedes numerical optimization of the original parametrization, whereas this is not the case for the new parametrization. Next, we show that information criteria provide a tool to choose between an LSTAR model and a TAR model; a choice previously basedsolely on economic theory. Reestimation of two published applications illustrate the usefulness of our findings.. |
| Date: | 2013–09–19 |
| URL: | http://d.repec.org/n?u=RePEc:kud:kuiedp:1307&r=ets |
| By: | Bensalma, Ahmed |
| Abstract: | This paper proposes a new testing procedure for the degree of fractional integration of a time series inspired on the unit root test of Dickey-Fuller (1979). The composite null hypothesis is that of d>=d0 against d =d0, using the generalization of Sowell's results (1990), we propose a test based on the least favorable case d=d0, to control type I error and when d |
| Keywords: | Fractional integration, Fractional unit root, Dickey Fuller Test |
| JEL: | C1 C12 C16 C2 C22 |
| Date: | 2013–07–24 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:50315&r=ets |