Machine Learning Vasicek Model Calibration with Gaussian Processes

Sousa, J. Beleza; Esquível, Manuel L.; Gaspar, Raquel M.

doi:10.2139/ssrn.1724906

Cited by 5 publications

(7 citation statements)

References 2 publications

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“…Solutions for the mean and variance of a zero-coupon bond for affine models have been already known for a while (see, for example, [14]). Souza et al in [11] have also obtained similar formulae for Vasicek model. We choose to present here derivations for all the moments for completeness.…”

Section: Analytic Solutions For Affine Modelsmentioning

confidence: 54%

“…Can GPs be used in order to fit parameters of i nterest-rate models? Indeed, in [11] Sousa et al suggest using GPs for fitting parameters in Vasicek model. We will consider the calibration process in detail.…”

Section: Model Calibration/fittingmentioning

confidence: 99%

“…The authors of [11] note that using only one GP realization path as a training set for parameters fitting is unsatisfactory. They experiment with currently quoted prices and conclude that the confidence intervals resulting from parameter uncertainties are large.…”

Section: Model Calibration/fittingmentioning

confidence: 99%

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Consistent Yield Curves via Static Hedging

Rojek¹,

Wilmott²

2013

Wilmott

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Interpolating yield curves between observable points can be done in various ways. In this paper, we show that market making in tradeable instruments with static hedging can be considered as a consistent basis for such interpolation. This approach leads to solutions where parameters match the historical rates while currently quoted prices are also perfectly reconstructed. We also show that the interpolation solution derived from the minimum variance optimization for the static hedge ratios is equivalent to statistical inference with Gaussian Processes Regression (GPR). We offer closed-form solutions for affine interest-rate models for market making as well as for profit-seeking scenarios.

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Section: Analytic Solutions For Affine Modelsmentioning

confidence: 54%

Section: Model Calibration/fittingmentioning

confidence: 99%

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Consistent Yield Curves via Static Hedging

Rojek¹,

Wilmott²

2013

Wilmott

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“…Consider the model of financial market where a bond price is governed by a geometric Ornstein-Uhlenbeck process (1)…”

Section: The Objective Price Of a European Call Option Issued On A Bomentioning

confidence: 99%

European call option issued on a bond governed by a geometric or a fractional geometric Ornstein-Uhlenbeck process

Mishura¹,

Rizhniak²,

Zubchenko³

2014

Modern Stoch. Theory Appl.

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European call option issued on a bond governed by a modified geometric Ornstein-Uhlenbeck process, is investigated. Objective price of such option as a function of the mean and the variance of a geometric Ornstein-Uhlenbeck process is studied. It is proved that the "Ornstein-Uhlenbeck" market is arbitrage-free and complete. We obtain risk-neutral measure and calculate the fair price of a call option. We consider also the bond price, governed by a modified fractional geometric Ornstein-Uhlenbeck process with Hurst index ∈ (1/2, 1). Limit behaviour of the variance of the process as → 1/2 and → 1 is studied, the monotonicity of the variance and the objective price of the option as a function of Hurst index is established.

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“…Regarding pricing, the same tradition of relying on stochastic calculus techniques is followed (Brigo & Mercurio, ; Rebonato et al, ); in relation to trading strategies, we can mention the work of (Duarte et al, ) that sets the “gold‐standard” in fixed‐income arbitrage. Regarding potential alternatives using more data‐driven approaches as we saw with currency, indices and equities options, we can only mention the work of Souza et al (Sousa et al, ) which calibrates the Vasicek interest rate model under the risk neutral measure by learning the model parameters using Gaussian processes for regression. Considering trading strategies and return prediction, we can find even less academic research; perhaps most of the research are inside the counterparts that exchange such products (banks, hedge funds, etc.).…”

Section: Introductionmentioning

confidence: 99%

A derivatives trading recommendation system: The mid‐curve calendar spread case

Koshiyama

Firoozye

Treleaven

2019

Intell Sys Acc Fin Mgmt

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Summary Derivative traders are usually required to scan through hundreds, even thousands of possible trades on a daily basis. Up to now, not a single solution is available to aid in their job. Hence, this work is aimed to develop a trading recommendation system, and to apply this system to the so‐called Mid‐Curve Calendar Spread (MCCS) trade. To suggest that such approach is feasible, we used a list of 35 different types of MCCSs; a total of 11 predictive and 4 benchmark models. Our results suggest that linear regression with l1‐regularisation (Lasso) compared favourably to other approaches from a predictive and interpretability point of views.

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Machine Learning Vasicek Model Calibration with Gaussian Processes

Cited by 5 publications

References 2 publications

Consistent Yield Curves via Static Hedging

Consistent Yield Curves via Static Hedging

European call option issued on a bond governed by a geometric or a fractional geometric Ornstein-Uhlenbeck process

A derivatives trading recommendation system: The mid‐curve calendar spread case

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