Showing 1 - 10 of 17
We propose an accurate data-driven numerical scheme to solve stochastic differential equations (SDEs), by taking large time steps. The SDE discretization is built up by means of the polynomial chaos expansion method, on the basis of accurately determined stochastic collocation (SC) points. By...
Persistent link: https://www.econbiz.de/10013200937
We present in a Monte Carlo simulation framework a novel approach for the evaluation of hybrid local volatility (Dupire 1994, Derman and Kani 1998) models. In particular, we consider the stochastic local volatility model - see e.g. Lipton et al. (2014), Piterbarg (2007), Tataru and Fisher...
Persistent link: https://www.econbiz.de/10012969484
We present a framework for efficient calibration of the time-dependent SABR model in an FX context. In a similar fashion as in Piterbarg (2005) we derive effective parameters, which yield an accurate and efficient calibration. On top of the calibrated FX-SABR model we add a non-parametric local...
Persistent link: https://www.econbiz.de/10013032314
We model the joint dynamics of stock and interest rate by a hybrid SABR-Hull-White model, in which the asset price dynamics are modeled by the SABR model and the interest rate dynamics by the Hull-White short-rate model. We propose a projection formula, mapping the SABR-HW model parameters onto...
Persistent link: https://www.econbiz.de/10013068513
We construct multi-currency models with stochastic volatility and correlated stochastic interest rates with a full matrix of correlations. We first deal with a foreign exchange (FX) model of Heston-type, in which the domestic and foreign interest rates are generated by the short-rate process of...
Persistent link: https://www.econbiz.de/10013069789
We define an equity-interest rate hybrid model in which the equity part is driven by the Heston stochastic volatility [Hes93], and the interest rate (IR) is generated by the displaced-diffusion stochastic volatility Libor Market Model [AA02]. We assume a non-zero correlation between the main...
Persistent link: https://www.econbiz.de/10013070335
In this article we define a multi-factor equity-interest rate hybrid model with non-zero correlation between the stock and interest rate. The equity part is modeled by the Heston model [Heston-1993] and we use a Gaussian multi-factor short rate process [Brigo,Mercurio-2007; Hull-2006]. By...
Persistent link: https://www.econbiz.de/10013070982
We discuss a competitive alternative to stochastic local volatility models, namely the Collocating Volatility (CV) model, introduced in Grzelak (2016). The CV model consists of two elements, a 'kernel process' that can be efficiently evaluated and a local volatility function. The latter, based...
Persistent link: https://www.econbiz.de/10012851327
We discuss the Heston [Heston-1993] model with stochastic interest rates driven by Hull-White [Hull,White-1996] (HW) or Cox-Ingersoll-Ross [Cox, et al.-1985] (CIR) processes. Two projection techniques to derive affine approximations of the original hybrid models are presented. In these...
Persistent link: https://www.econbiz.de/10012750871
The focus of this paper is on finding a connection between the interest rate and equity asset classes. We propose an equity interest rate hybrid model which preserves market observable smiles: the equity from plain vanilla products via a local volatility framework and the interest rate from caps...
Persistent link: https://www.econbiz.de/10012715627