According to the theory proposed by Acerbi & Scandolo (2008), the value of a portfolio is defined in terms of public market data and idiosyncratic portfolio constraints imposed by an investor holding the portfolio. Depending on the constraints, one and the same portfolio could have different...

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...

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...

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...

In this article we propose an efficient Monte Carlo scheme for simulating the stochastic volatility model of Heston (1993) enhanced by a non-parametric local volatility component. This hybrid model combines the main advantages of the Heston model and the local volatility model introduced by...

Credit Valuation Adjustment (CVA) has become an important field as its calculation is required in Basel III, issued in 2010, in the wake of the credit crisis. Exposure, which is defined as the potential future loss on a financial contract due to a default event, is one of the key elements for...

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...

Three computational techniques for approximation of counterparty exposure for financial derivatives are presented. The exposure can be used to quantify so-called Credit Valuation Adjustment (CVA) and Potential Future Exposure (PFE), which are of utmost importance for modern risk management in...

We present an extension of stochastic volatility equity models by a stochastic Hull-White interest rate component while assuming non-zero correlations between the underlying processes. We place these systems of stochastic differential equations in the class of affine jump diffusion - linear...

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...