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Dynamic functional time-series forecasts of foreign exchange implied volatility surfaces

Journal: International Journal of Forecasting

Date: 2022

Author: Han Lin Shang, Fearghal Kearney

Abstract:
This paper presents static and dynamic versions of univariate, multivariate, and multilevel functional time-series methods to forecast implied volatility surfaces in foreign exchange markets. We find that dynamic functional principal component analysis generally improves out-of-sample forecast accuracy. Specifically, the dynamic univariate functional time-series method shows the greatest improvement. Our models lead to multiple instances of statistically significant improvements in forecast accuracy for daily EUR-USD, EUR-GBP, and EUR-JPY implied volatility surfaces across various maturities, when benchmarked against established methods. A stylised trading strategy is also employed to demonstrate the potential economic benefits of our proposed approach.

Link: Google Scholar

Background and Context

Research Focus

This study develops new methods to forecast implied volatility surfaces in foreign exchange markets using dynamic functional time-series analysis.

Data Coverage

Analysis covers EUR-USD, EUR-GBP, and EUR-JPY currency pairs from January 2008 to December 2016, examining implied volatility across different option maturities.

Methodology

The research employs univariate, multivariate and multilevel functional time-series methods with both static and dynamic functional principal component analysis.

Superior Performance of Dynamic Functional Time Series Methods

  • Dynamic methods (DFTS, DMFTS, DMLFTS) consistently outperform their static counterparts
  • The dynamic univariate method (DFTS) shows significant improvement over the basic FTS approach
  • DMLFTS achieves the highest R² value of 0.9988, indicating superior model fit

Forecasting Accuracy Across Different Time Horizons

  • Forecasting accuracy decreases as the prediction horizon increases
  • DFTS maintains better accuracy than the Random Walk benchmark
  • One-day ahead forecasts show the highest accuracy across all methods

Trading Strategy Performance Across Currencies

  • EUR-GBP shows the highest trading strategy returns at 0.55%
  • EUR-USD demonstrates modest positive returns of 0.02%
  • EUR-JPY shows negative returns despite good forecasting accuracy

Model Performance Across Different Maturities

  • Forecasting accuracy improves for longer maturity options
  • 2-year maturity options show the lowest forecast errors
  • Short-term (1-month) options are the most challenging to forecast

Within-Cluster Variability Analysis

  • Within-cluster variability remains consistently high across maturities
  • 6-month maturity shows the highest within-cluster variability
  • Demonstrates strong common trend capture across different maturities

Contribution and Implications

  • Dynamic functional time-series methods significantly improve implied volatility forecasting accuracy
  • The methodology provides economically significant trading opportunities in EUR-GBP and EUR-USD markets
  • Results demonstrate practical value for options traders and risk managers in foreign exchange markets

Data Sources

  • Model Performance Comparison: Constructed using data from Table 1 showing R² values
  • Forecasting Accuracy: Based on MAFE values from Table 4
  • Trading Strategy Returns: Derived from Table 11 showing daily mean returns
  • Maturity Analysis: Constructed using MAFE values from Table 4
  • Within-Cluster Variability: Based on data from Table 2