The purpose of this paper is introducing rigorous methods and formulas for bilateral counterparty risk credit valuation adjustments (CVA's) on interest-rate portfolios. In doing so, we summarize the general arbitrage-free valuation framework for counterparty risk adjustments in presence of...

We present an embarrassingly simple method for supervised learning of SABR model's European option price function based on lookup table or rote machine learning. Performance in time domain is comparable to generally used analytic approximations utilized in financial industry. However, unlike the...

The aim of this paper is to investigate the ability of the Dynamic Variance Gamma model, recently proposed by Bellini and Mercuri (2010), to evaluate option prices on the S&P500 index. We also provide a simple relation between the Dynamic Variance Gamma model and the Vix index. We use this...

The implied volatility surface (IVS) is a fundamental building block in computational finance. We provide a survey of methodologies for constructing such surfaces. We also discuss various topics which can influence the successful construction of IVS in practice: arbitrage-free conditions in both...

Local volatility models are widely used to manage many exotic options in a way consistent with available market prices of vanilla options. Once calibrated, a local volatility grid can be used in numerical methods such as PDE or Monte Carlo to price and hedge exotic options consistently with...

In this article, the Universal Approximation Theorem of Artificial Neural Networks (ANNs) is applied to the SABR stochastic volatility model in order to construct highly efficient representations. Initially, the SABR approximation of Hagan et al. [2002] is considered, then a more accurate...

According to IFRS 9, an Entity shall assess - by performing a quantitative assessment - the relevance of the modification of the time value of money element, i.e. the modification of the interest that can be observed, e.g. in all the instruments whose underlying interest rate tenors are...

The purpose of the paper is twofold. First, it aims at identifying when UK and European (France, Germany, Italy and Spain) Credit Default Swaps(CDSs) exhibit explosivity with respect to their past behaviors. Second, it seeks to quantify the dynamics of CDS volatility spillover effects...

First, we show that implied normal volatility is intimately linked with the incomplete Gamma function. Then, we deduce an expansion on implied normal volatility in terms of the time - value of a European call option. Then, we formulate an equivalence between the implied normal volatility and the...

We revisit well-known stochastic volatility models with constant coefficients for single asset driven by one factor stochastic volatility as homogeneous diffusion and demonstrate an alternative to the classifications provided in Albanese and Lawi, and Henry-Labord`ere, to deduce asset price...