In this article, we present the analytical approximation of zero-coupon bonds and swaption prices for general short rate models. The approximation is based on regular and singular expansions with respect to the small volatility and contains a low-dimensional integration. The model in hand...

We develop the algorithmic approach for Counterparty exposure calculation and automate its application to arbitrary complicated instruments. Assuming that the portfolio is priced by the backward (American) Monte-Carlo method, our approach allows calculating the credit exposure as a pricing...

In this article we present an efficient optimization for calculating the exposure and CVA for large portfolios of vanilla swaps. It is based on a "thin-out" procedure applied to fixed payment streams, which reduces a very frequent stream of payments to a much less frequent one. The procedure...

In this paper, we present advanced analytical formulas for SABR model option pricing. The first technical result consists of a new exact formula for the zero correlation case. This closed form is a simple 2D integration of elementary functions, particularly attractive for numerical...

We develop a technique of parameter averaging and Markovian projection on a quadratic volatility model based on a term-by-term matching of the asymptotic expansions of option prices in volatilities. In doing so, we revisit the procedure of asymptotic expansion and show that the use of the...

Markovian Projection is an optimal approximation of a complex underlying process with a simpler one, keeping essential properties of the initial process. The Heston process, as the Markovian Projection target, is an example.In this article, we generalize the results of Markovian Projection onto...

We develop a systematic approach to the reduction of dimensionality of smile-enabled models by projecting them onto a displaced version of the two-dimensional Heston process. The projection is the key for deriving efficient, analytical approximations to European option prices in such models....

Servicing clients can require posting Initial Margin (IM) for client trades, and for their hedges. IM should be forecast for both and reflected in MVA. For non-vanillas with dynamic hedges, forecasting hedge-trade IM is challenging as future hedge ratios are necessary, and future sensitivities...

A model/hedging performance is relatively poorly covered in the literature. This is particularly valid for general portfolios including both vanilla and exotic instruments. Practitioners generally use so called \pnl explain which measures whether portfolio price movements can be explained by...

In the first part of this paper (Antonov-Bianchetti, 2013) we developed the theoretical framework for pricing financial instruments under multiple sources of funding, leading to a non-linear pricing PDE and to Funding Value Adjustment (FVA).In this second part we develop the numerical framework...