In this paper, we develop a series of approximations for a fast analytical pricing of European constant maturity swap (CMS) products, such as CMS swaps, CMS caps/floors, and CMS spread options, for the LIBOR Market Model (LMM) with stochastic volatility. The derived formulas can also be used for...

We revisit the cross-currency LIBOR Market Model armed with the technique of Markovian projection. We derive an efficient approximation for FX options and show how the FX skew can be modeled consistently with the interest rate skew in a common multifactor model

To price mid-curve or spread options we need flexible joint distributions of two underlying rates with fixed marginals. A Copula approach is a standard method to produce such joint distributions.It has, however, several drawbacks, especially, a low number of free parameters. For example, the...

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...

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...

We develop a systematic approach to Markovian projection onto an effective displaced diffusion, and work out a set of computationally efficient formulas valid for a large class of non-Markovian underlying processes. The generic derivation is followed by applications, including the calculation of...

In the large context of valuation adjustments, collectively referred to as “XVA”, we treat replication strategies as a unique way to calculate fair price equations. We consider different replication strategies (Piterbarg, Burgard-Kjaer and our contribution) and identify the valuation...

In the current low-interest-rate environment, extending option models to negative rates has become an important issue. This paper describes one such extension of the widely used SABR model. We stress that our solution is more natural and attractive than the shifted SABR.An exact formula is...

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...

Computing Standardized Initial Margin Model Margin Valuation Adjustment (SIMM-MVA) requires the simulation of future sensitivities, but these are expensive to compute for callable products. This paper introduces a method which avoids nested calls to the pricing function, similar to the use of...