Indicators

Monday, June 29th 2020

# Forecasting The Options Volatility Surface

Forecasting the implied volatility surface requires observations of statistical volatility, slope, derivative and earnings effects and can help assess market prices of options.

Summary

Forecasting the options volatility surface requires observations of statistical volatility, slope, derivative, and earnings effects. ORATS breaks the volatility surface into several parameters, including a 20-day forecast of future statistical volatility, infinite forecast of implied volatility, earnings forecast, strike slope forecast, and curvature or derivative forecast. These observations are used in volatility forecasting models to compare implied volatility surface parameters and market values to forecasted parameters and theoretical values computed using these parameters. ORATS also produces metrics on the accuracy of these forecasts.

Making a forecast for each option can provide a guide on what to trade: What is overvalued and what is undervalued.

Before creating forecast, historical observations of skew parameters should be produced. ORATS has chosen to break the volatility surface into the following parameters:

- 20 business day (~1 month calendar) forecast of future statistical volatility - orFcst20d. This forecast is based on observations often back to 2007 of historical volatility using a modified Parkinson method.

- Infinite forecast of implied volatility - orFcstInf. This forecast is based on observations of summarized implied volatility.

- Earnings forecast - fcstErnEffct. ORATS forecasted earnings effect considers day of and day after earnings, seasonality, recentness, median and average of move divided by expected move.

- Strike slope forecast and infinite slope forecast, slopeFcst, slopeFcstInf. Observations of slope forecasted.

- Curvature or derivative forecast - derivFcst, derivFcstInf. Observations of derivative forecasted.

These sophisticated methods of summarizing and manipulating the implied volatility surface allow us to compare summary characteristics across related equities and over time. These observations are then used in volatility forecasting models. In options trading, to find an edge, it is useful to compare implied volatility surface parameters and market values to forecasted parameters and to theoretical values computed using these parameters.

We produce metrics on the accuracy of these forecasts:

- fcstR2 – is the R2 for our statistical forecast orFcst20d

- fcstR2Imp is for implied forecast orIvFcst20d

- impliedR2 is R2 for the market’s IV prediction of future HV.

Given the at-the-money implied volatility, the slope and the derivative, an implied volatility can be calculated for each strike. First, a call delta is calculated for the strike using a standard option pricing model (not provided). Second, the slope and derivative for the expiration is calculated given the interpolated slope and derivative for that expiration. Third, the implied volatility formula is used to determine the strike implied.

Formula: Atmiv*(1+(slope/1000+(deriv/1000*(delta*100-50)/2))*(delta*100-50))

For example, assume the following:

- atmIvM1: 30

- slope: 1

- deriv: 0.1

- delta: 0.75

- dte: 30

Since we are finding the month 1 volatility the 30 day slope and derivative can be used. 30*(1+(1/1000+(0.1/1000*(0.75*100-50)/2))*(0.75*100-50)) = 31.688

Example 2, assume:

- 30dayatmiv: 32

- infiniteATMIV: 28

- slope: 1

- deriv: 0.08

- slopeInf: 2

- derivInf: 0.1

- delta: 0.25

- dte: 90

In this example we first need to interpolate the IV, slope and derivative between the 30 day and in the infinite. This is done by weighting the 30day * 81% and the infinite 19% (see below).

IV = 0.81 * 32 + 0.19 * 28 = 31.26

Slope = 0.81 * 1 + 0.19 * 2 = 1.19

Derivative = 0.81 * 0.1 + 0.19 * 0.08 = 0.084

Implied volatility at 25 delta:

31.26*(1+(1.19/1000+(0.084/1000*(0.25*100-50)/2))*(0.25*100-50))=31.15

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