Machine Learning Vasicek Model Calibration with Gaussian Processes

Abstract

In this article, we calibrate the Vasicek interest rate model under the risk neutral measure by learning the model parameters using Gaussian processes for machine learning regression. The calibration is done by maximizing the likelihood of zero coupon bond log prices, using mean and covariance functions computed analytically, as well as likelihood derivatives with respect to the parameters. The maximization method used is the conjugate gradients. The only prices needed for calibration are zero coupon bond prices and the parameters are directly obtained in the arbitrage free risk neutral measure.Keywords Arbitrage free risk neutral measure; Calibration; Gaussian processes for machine learning; Vasicek interest rate model; Zero coupon bond prices.

Machine Learning for Multiple Yield Curve Markets: Fast Calibration in the Gaussian Affine Framework

“…Calibration of log-bond prices in the simple Vasiček model framework via Gaussian processes for machine learning has already been applied in Beleza Sousa et al (2012) for a single maturity and in Beleza Sousa et al (2014) for several maturities. They both rely on the theory of Gaussian processes presented in Rasmussen and Williams (2006).…”

“…They both rely on the theory of Gaussian processes presented in Rasmussen and Williams (2006). While in Section 3 we extend Beleza Sousa et al (2012) by presenting an additional optimization method, Beleza Sousa et al (2014) and Section 4 constitute a different access to the calibration of interest rate markets with several maturities. While Beleza Sousa et al (2014) calibrated solely zero-coupon log-bond prices, from which one is not able to construct a post-crisis multi-curve interest rate market, we calibrate zero-coupon log-bond prices and log-δ-bond prices on top in order to encompass forward rate agreements and to be conform with the multi-curve framework (cf.…”

“…As a first step, we calibrate the single-curve Vasiček interest rate model following Beleza Sousa et al (2012). To begin with, we want to mention the important difference in mathematical finance between the objective measure P and the risk-neutral measure Q.…”

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

“…Regarding pricing, the same tradition of relying on stochastic calculus techniques is followed (Brigo & Mercurio, 2007;Rebonato et al, 2011); in relation to trading strategies, we can mention the work of (Duarte et al, 2006) 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, 2012) 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.).…”

A Derivatives Trading Recommendation System: the Mid-Curve Calendar Spread Case

“…Regarding pricing, the same tradition of relying on stochastic calculus techniques is followed (Brigo & Mercurio, 2007;Rebonato, McKay, & White, 2011). 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, Esquível, & Gaspar, 2012) 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, being perhaps most of the research residing inside the counterparts that exchange such products (banks, hedge funds, etc.).…”