Exploring the Relation Between Risk Reversals and Spot FX Rate for USDTRY
(by Eren Ocakverdi and Mehmet Aras Orhan)
Introduction
Options market professionals often refer to an implied volatility surface via its prevailing shape at a specific horizon. Moreover, volatility surface from OTC markets are often quoted in discrete points using a measure of level (ATM volatility), skewness (Risk Reversals) and curvature (Butterflies). This empirically motivated method of specifying a volatility surface is called Vanna-Volga (VV) and is popular among FX market practitioners.
As options are considered advanced instruments by the public and the FX Options on particular trade mostly in OTC markets, the information content of the options prices is rarely understood.
In this short piece, we investigate the relationship between VV components of a FX volatility surface and spot FX prices. Inspired by an earlier study conducted in 2003, we use 25 Delta Risk Reversals (dRR25) and spot FX prices to see if the former can be used to forecast the latter.
Methodology and Data
In the time series context, causal relationships among variables are usually based on their predictive ability of one another and is referred to as Granger Causality (GC). If past values of a variable (X) significantly contribute to forecasting of another variable (Y) in the presence of its own past values, then the result is interpreted as “X Granger-causes Y”. If this statistical relationship is reciprocal, then it means these two variables are endogenous.
Stability of estimated parameters are a general concern in time series analysis and GC is no exception. One can suspect the occurrence of structural changes especially when the data covers a long period. Shi, Phillips and Hurn (2018) and Shi, Hurn and Phillips (2020) proposed alternative ways to test the stability of such causal relationships over time. Time Varying Granger Causality (TVGC) analysis allows for time variation through recursive estimation methods and use bootstrap techniques for proper inference.
Here we used Forward Expanding and Rolling window algorithms to generate the sequence of test statistics for the purpose. Former method starts with a minimum window length and increases the sample size by one observation until the end where entire sample is used. In latter method, however, the chosen window size is moved/rolled through sample by dropping the first observation and adding the next one.
Causality analysis for daily data can be tricky as it is quite difficult to control the noise component in high frequency. dRR25 is a forward-looking indicator and is assumed to carry information for the coming month (i.e. 22 business days). The impact, however, does not have to be fully reflected on the exact 22nd day of FX returns and may have spread over time.
Mixed Data Sampling (MIDAS) approach provides a plausible framework to investigate whether the impact of dRR25 on exchange rate returns is cumulative. The MIDAS method is proposed by Ghysels et al. (2006), which allows one to estimate a regression equation with variables at different frequencies, especially when the dependent variable is sampled at a lower frequency. The idea is to incorporate information from the high frequency data into the lower frequency regression in a parsimonious fashion. This enables one to obtain linear projections without explicitly specifying the dynamics of the explanatory variables.
Findings
We first employed TVGC analysis on both changes and levels. Daily data covers January 2010 to May 2024 period.
We don’t observe statistically significant relationship (i.e. test statistics above critical values), until the severe shock as of December 2021. Such a sudden and extreme volatility triggered a structural shift and has changed the connection between these indicators. However, moving statistics tell us that the relationship is getting weaker and fall below the significance threshold.
The main implication of this finding is that although dRR25 has gained some predictive power induced by an idiosyncratic event, it has been losing its value in forecasting USDTRY as more data pile up.
As for the MIDAS analysis, we converted daily exchange returns to monthly frequency by taking end-of-period values for each month, while keeping dRR25 at daily frequency. Our base model includes a constant and the first lag of returns to mimic the random walk behaviour.
Model selects 18 lags in addition to contemporaneous relationship, which suggests that the cumulative impact of changes in dRR25 last up to 18 days. Due to forward-looking nature of dRR25 and to polynomial structure imposed, weights are in ascending order as expected.
Our last exercise intends to demonstrate the contribution of daily information from dRR25 to explain the monthly depreciation of TRY, which is simply the accumulated change of daily returns.
Even by visual inspection, it is obvious that using daily dRR25 data increases the explanatory power, and this is verified by the improved goodness of fit measure (i.e. RMSE) between the two models. However, please note that the model is not useful for forecasting purposes, since all these happen within a month making the relationship contemporaneous in lower frequency.
Discussion
Option prices reflect the expectations of market professionals and therefore carry valuable information for future dynamics of a given asset. In this piece, we specifically focused on the dRR25 component and gave it a try to see if its current values can be used to forecast the future changes in USDTRY. Although there is a significant concurrent association between the variables of interest due to constant bilateral flow of information, it becomes less pronounced when we empirically try to verify that risk reversal is a solid leading indicator of FX spot rate behaviour. Absence/lack of a strong and stable lead-lag relationship makes it ineffective from the forecasting point of view.