arXiv subjects

Mariano Zeron

Publications and source records attributed to Mariano Zeron.

4 recordsLinked to original sources

arXiv2025

The FRTB-IMA computational challenge for Equity Autocallables

When the Orthogonal Chebyshev Sliding Technique was introduced it was applied to a portfolio of swaps and swaptions within the context of the FRTB-IMA capital calculation. The computational cost associated to the computation of the ES values - an essential component of the capital caluclation under FRTB-IMA - was reduced by more than $90\%$ while passing PLA tests. This paper extends the use of the Orthogonal Chebyshev Sliding Technique to portfolios of equity autocallables defined over a range of spot underlyings. Results are very positive as computational reductions are of about $90\%$ with passing PLA metrics. Since equity autocallables are a commonly traded exotic trade type, with significant FRTB-IMA computational costs, the extension presented in this paper constitutes an imporant step forward in tackling the computational challenges associated to an efficient FRTB-IMA implementation.

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arXiv2020

Tensoring volatility calibration

Inspired by a series of remarkable papers in recent years that use Deep Neural Nets to substantially speed up the calibration of pricing models, we investigate the use of Chebyshev Tensors instead of Deep Neural Nets. Given that Chebyshev Tensors can be, under certain circumstances, more efficient than Deep Neural Nets at exploring the input space of the function to be approximated, due to their exponential convergence, the problem of calibration of pricing models seems, a priori, a good case where Chebyshev Tensors can excel. In this piece of research, we built Chebyshev Tensors, either directly or with the help of the Tensor Extension Algorithms, to tackle the computational bottleneck associated with the calibration of the rough Bergomi volatility model. Results are encouraging as the accuracy of model calibration via Chebyshev Tensors is similar to that when using Deep Neural Nets, but with building efforts that range between 5 and 100 times more efficient in the experiments run. Our tests indicate that when using Chebyshev Tensors, the calibration of the rough Bergomi volatility model is around 40,000 times more efficient than if calibrated via brute-force (using the pricing function).

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arXiv2020

Dynamic sensitivities and Initial Margin via Chebyshev Tensors

This paper presents how to use Chebyshev Tensors to compute dynamic sensitivities of financial instruments within a Monte Carlo simulation. Dynamic sensitivities are then used to compute Dynamic Initial Margin as defined by ISDA (SIMM). The technique is benchmarked against the computation of dynamic sensitivities obtained by using pricing functions like the ones found in risk engines. We obtain high accuracy and computational gains for FX swaps and Spread Options.

q-fin.RM↗

arXiv2020

Dynamic Initial Margin via Chebyshev Tensors

We present two methods, based on Chebyshev tensors, to compute dynamic sensitivities of financial instruments within a Monte Carlo simulation. These methods are implemented and run in a Monte Carlo engine to compute Dynamic Initial Margin as defined by ISDA (SIMM). We show that the levels of accuracy, speed and implementation efforts obtained, compared to the benchmark (DIM obtained calling pricing functions such as are found in risk engines), are better than those obtained by alternative methods presented in the literature, such as regressions (\cite{Zhu Chan}) and Deep Neural Nets (\cite{DNNs IM}).

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