Extrapolating Implied Volatility to Short Expiries
Summary
The document addresses how to estimate implied volatility for expiries shorter than the first available maturity on a volatility surface, with very short dated binary options as the motivating use case. One proposed method is to hold volatility flat at the same forward moneyness: map the target strike to the corresponding strike at the first listed maturity and use that volatility. The answer claims this is calendar arbitrage free under Black-Scholes dynamics.
A second response points to research that combines implied volatility and trading volume to forecast next day volatility, using volume to switch between an ARCH forecast and the option-implied expectation. It does not establish that this approach works for minute-scale horizons. The suggestions are limited: the flat-moneyness rule relies on its stated model assumptions, and the forecasting reference concerns daily forecasts rather than a demonstrated short-expiry calibration. No empirical comparison or validated method for pricing five-minute binaries is provided.
Key ideas
- Flat volatility at matched forward moneyness is proposed for maturities shorter than the first surface pillar.
- The proposed extrapolation is described as calendar arbitrage free under Black-Scholes dynamics.
- A cited forecasting approach uses trading volume to switch between ARCH and implied volatility signals.
- Daily volatility forecasts do not establish accuracy for minute-scale option expiries.
- The discussion offers suggestions but no empirical validation for very short dated binary pricing.
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Full text
# Extrapolating implied volatilities to small time
# Extrapolating implied volatilities to small time
Could anyone please direct me to literature or methods for extrapolating the implied volatility surface towards small expiry? I'm looking to price very short time to expiry binary options (e.g. 5 minutes).
Looking at the implied vol surface derived from the market, the shortest available being 1 month, what are suitable interpolation/extrapolation methods for modeling the surface at maturities < 1 month?
I've seen suggestions that at small time there are closed or near-closed asymptotic expansions for IV, would it be possible to use this as a point and some form of spline interpolation?
Thanks in advance!
## Answer by FKaria (score 4)
https://quant.stackexchange.com/a/10037
A really simple and arbitrage free solution is to extrapolate flat volatility on the same moneyness. Let's say that you want an implied volatility for strike $K$ at time $t<t_1$, and $t_1$ is the first pillar on the surface.
You look at the moneyness level $k=K/F_t$, then look for $K'$ to get the volatility at the same moneyness level of the first pillar $k=K'/F_{t_1}$. This is $K'=\frac{K}{F_t}F_{t_1}$. Then, you take the volatility $$ \sigma\left(t_1,\frac{K}{F_t}F_{t_1}\right)\ . $$ It is easy to show that this method is calendar arbitrage free assuming the Black-Scholes dynamics.
## Answer by aajajim (score 3)
https://quant.stackexchange.com/a/9513
5 minutes is a very short time period!
If you have access to real time data of Implied Volatility and transaction Volume of the underlying of your option than you can take a look to the following article:
Volatility Forecasts, Trading Volume, and the ARCH versus Option-Implied Volatility Trade-off
In this article, the authors use the information from daily volume and implied volatility to forecast next day volatility. The Volume is used here as a Dummy variable to switch between the ARCH and the Expectation from IV. I'm not saying that it would work for your needs, but you can take a look to it, and I would be interested on your results!Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.