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...

We study 30 vintages of FRB/US, the principal macro model used by the Federal Reserve Board staff for forecasting and policy analysis. To do this, we exploit archives of the model code, coefficients, baseline databases and stochastic shock sets stored after each FOMC meeting from the model's...

Near-the-money options experience a rapid decline in time value over the weeks leading up to the expiry date. A possible strategy to alleviate the impact of the time decay effect is to unwind the hedge prior to expiry. However, appreciable time value is present for a reason: it is an indication...

This article describes a machine learning based approach applied to acquiring empirical forecasting models. The approach makes use of the LAGRAMGE equation discovery tool to define a potentially very wide range of equations to be considered for the model. Importantly, the equations can vary in...

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...

This paper proposes a simple and crude way of approximating the XVA sensitivities. In short, the idea is simply to recycle the existing base simulated portfolio values for the bumped ones. This is done by re-simulating the risk factors for the bumped market and finding out which other base state...

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 econometrics, long memory models for variance modeling like FIGARCH or FIAPARCH are characterized by a Fractional Differencing term. In order to estimate and apply these models, the infinite MacLaurin expansion of the differencing term has to be truncated at a certain level. We transfer the...

Estimating volatility from recent high frequency data, we revisit the question of the smoothness of the volatility process. Our main result is that log-volatility behaves essentially as a fractional Brownian motion with Hurst exponent H of order 0.1, at any reasonable time scale. This leads us...

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...