Nicholas Vause
In a recent post, my co-author and I showed some charts suggesting that investors have been accepting less compensation for bearing credit risk. This type of risk can be very costly when it materialises, but the probability of that happening is typically very low. A similar risk is inherent in deeply out-of-the-money options. Here too, investors seem to be accepting less compensation for risk.
To assess this, I compare premiums of options that insure against sharp falls in the FTSE 100 equity index with model-based forecasts of the volatility – and hence scope for sharp falls – of that index. As it happens, option premiums are quoted in terms of volatility (with the Black-Scholes formula providing the mapping from premium to volatility), which makes the comparison straightforward. The volatility forecast was derived by modelling and extrapolating historical data on the FTSE 100 using a GARCH model.
The results are shown in the chart. On average, the option-implied volatility was around eight percentage points higher than the forecast volatility in the five years following the global financial crisis. That gap (known as the ‘volatility premium’) fell to around three percentage points on average in the subsequent five years, and it is now close to zero. While the precise values of the volatility premium plotted in the chart are sensitive to alternative specifications of the GARCH model, its downward trend is not.
Premium on equity options
Nicholas Vause work in the Bank’s Capital Markets Division.
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I thought the Black-Scholes formula had been recognised as seriously wrong, using an incorrect distribution of risk