gaussian process – SITMO Machine Learning

Long Memory in Financial Time Series

In finance, it is common to model asset prices and volatility using stochastic processes that assume independent increments, such as geometric Brownian motion. However, empirical observations suggest that many financial time series exhibit long memory or persistence. For example, volatility shocks can persist over extended periods, and high-frequency order flow often displays non-negligible autocorrelation. To capture such behavior, fractional Brownian motion (fBm) introduces a flexible framework where the memory of the process is governed by a single parameter: the Hurst exponent.

Here we present a yield curve interpolation method, one that’s based on conditioning a stochastic model on a set of market yields. The concept is closely related to a Brownian bridge where you generate scenario according to an SDE, but with the extra condition that the start and end of the scenario’s must have certain values. In this paper we use Gaussian process regression to generalization the Brownian bridge and allows for more complicated conditions. As an example, we condition the Vasicek spot interest rate model on a set of yield constraints and provide an analytical solution.

The resulting model can be applied in several areas:

Monte Carlo scenario generation
Yield curve interpolation
Estimating optimal hedges, and the associated risk for non tradable products

Tag: gaussian process

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Long Memory in Financial Time Series

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