Various indicators are commonly used to gauge relative value in the volatility market. Amongst those we can mention volatility cones and the spread between implied and historical volatility. In particular, these two indicators tend to be difficult to use in isolation: for instance, a volatility in the middle of its cone and far above realised levels will look relatively expensive while a volatility in the middle of its cone and far below realised levels will look relatively cheap. In other words, we need to look at a combination of indicators to try and identify value. In this article, we have studied extreme values of the volatility risk premium and found that large readings were symptomatic of large mis-pricings in the market. As such, our new indicator gives us an indication of the best currency pairs to look at to try and extract value.
Volatility Risk Premium
The volatility risk premium is generally defined as the difference between implied and realised volatility for a given maturity. These two quantities are intrinsically very different: realised volatility is backward looking (computed from past spot returns) while implied volatility is forward looking (an estimate of realised volatility for the days or months to come). This explains why implied volatility usually trades at a premium to realised: market makers need to charge a premium to account for the uncertainty related to their estimate of volatility. Conversely, hedgers are willing to pay an insurance premium to get protection against exchange rates uncertainty.
The volatility risk premium is a well documented characteristic of currency markets. Most studies rely on the fact that implied volatility usually trades at a premium to realised volatility and consequently, in the long run, short volatility positions will generate excess returns.
In this study, we have decided to look at the volatility risk premium from a different angle: we study extreme values and question their informative value.
High Volatility Risk Premia Are Symptomatic
Of Large Mis-Pricings
Using one-month implied and realised volatilities in the four major currency pairs--euro/dollar, dollar/yen, euro/yen and cable--over the past three years, we have computed and compared:
* The volatility risk premium at each date. For instance, on April 1, we compute the risk premium as the difference between the implied volatility prevailing on April 1 from the
realised volatility calculated from spot returns over March (these two values can be obtained simultaneously, but one is backward looking while the other is forward looking)
* The actual difference between implied volatility and realised volatility referring to the same term. For instance, we compare implied volatility prevailing on April 1 to the realised volatility calculated from spot returns over the month of April. This error term can only be measured ex post but has the advantage of comparing values referring
to the same period in time (April in this example). We will refer to the absolute value of this difference in terms of absolute error.
Figure 2 shows the relationship between the volatility risk premium (x-axis) and the absolute error (y-axis). While this chart does not show any strong pattern for average values of the volatility risk premium, it is interesting to note that very low volatility risk premia seem to coincide with small absolute errors while high volatility risk premia coincide with large absolute errors.
Figure 3 shows the absolute error committed while using the full sample compared with instances when the volatility risk premium was below or above two standard deviations from its average.
The pattern is common over all currencies and the message is quite clear: the smallest absolute errors do indeed occur when the volatility risk premium is low, while the largest absolute errors are systematically incurred when the volatility risk premium is high.
Table 1 provides us with some interesting additional statistics. It shows that for all currency pairs apart from cable, the increase in the absolute error using only the higher values of the risk premium is statistically different from the one obtained using the full sample. This leads us to the conclusion that high volatility risk premia are symptomatic of large mis-pricings in the market and therefore of more trading opportunities.
| Risk Premium Relative To Its Distribution | |||
| All Series | Below 1 St. Dev. | Above 2 St. Dev. | |
| EUR/USD | |||
| Average error | 1.73% | 9.80% | 3.59% |
| St. Dev. | 0.1 | 0.32 | 0.58 |
| t-value | 16.74 | -2.94 | 3.19 |
| USD/JPY | |||
| Average error | 2.30% | 1.15% | 4.35% |
| St. Dev. | 0.15 | 0.33 | 0.57 |
| t-value | 15.61 | -3.52 | 3.56 |
| EUR/JPY | |||
| Average error | 2.63% | 1.32% | 4.35% |
| St. Dev. | 0.19 | 0.24 | 0.75 |
| t-value | 13.56 | -5.42 | 2.31 |
| GBP/USD | |||
| Average error | 1.38% | 0.64% | 2.19% |
| St. Dev. | 0.09 | 0.08 | 0.59 |
| t-value | 15.38 | -8.71 | 1.36 |
| Newy-West heteroskedasticity and autosorrelation consistent stand errors |
Conclusion And Further Research
This study shows that high volatility risk premia usually coincide with large mis-pricings, whereas low volatility risk premia are far less informative. From this empirical regularity it is also possible to construct a barometer indicator, that will indicate when the option market is offering interesting trading opportunities.
This week's Learning Curve was written by Anne Sanciaumeand Giovanni Pillitteri, foreign exchange strategists at Lehman Brothers in London.
