Deep Learning for seasonality modelling in Inflation-Indexed Swap pricing

Abstract

An Inflation-Indexed Swap (IIS) is a derivative in which, at every payment date, the counterparties swap an inflation rate with a fixed rate. For the calculation of the Inflation Leg cash flows it is necessary to build a mathematical model suitable for the Consumer Price Index (CPI) projection. For this purpose, quants typically start by using market quotes for the Zero-Coupon swaps in order to derive the future trend of the inflation index, together with a seasonality model for capturing the typical periodical effects. In this study, we propose a forecasting model for inflation seasonality based on a Long Short Term Memory (LSTM) network: a deep learning methodology particularly useful for forecasting purposes. The CPI predictions are conducted using a FinTech paradigm, but in respect of the traditional quantitative finance theory developed in this research field. The paper is structured according to the following sections: the first two parts illustrate the pricing methodologies for the most popular IIS: the Zero Coupon Inflation-Indexed Swap (ZCIIS) and the Year-on-Year Inflation-Indexed Swap (YYIIS); section 3 deals with the traditional standard method for the forecast of CPI values (trend + seasonality), while section 4 describes the LSTM architecture, and section 5 focuses on CPI projections, also called inflation bootstrap. Then section 6 describes a robust check, implementing a traditional SARIMA model in order to improve the interpretation of the LSTM outputs; finally, section 7 concludes with a real market case, where the two methodologies are used for computing the fair-value for a YYIIS and the model risk is quantified.