Smoothing Options Implied Volatilities Using ORATS SMV System

Options quotes are cleaned, normalized and smoothed. The resulting option Greeks and theoretical values give our clients an edge in the market.

Summary

ORATS SMV System smooths market volatilities derived from options quotes, producing theoretical values and accurate option Greeks. The system cleans and normalizes quotes, solves for a residual yield rate, and fits a non-arbitrageable smooth curve through strike implied volatilities. The resulting data is critical for risk management and trading, and is available from 2007 to present.

Smooth market volatilities (SMV) derived from the options market helps traders make sense of a plethora of exchange quotes. Options quotes are cleaned, normalized and smoothed in the SMV system. By smoothing the IVs, call and put theoretical values can be compared to market bid-ask quotes to see if the options are under or overpriced. The smoothed IVs produce more consistent greeks by which to manage risk too. By parameterizing the smoothed curve, the shape can be evaluated comparing to other tickers or to history of the skew parameter.

The first step in the SMV System is cleaning the quotes and applying good inputs to our modified binomial pricing engine. Using ORATS popular dividend feed and option pricing methodologies, a residual yield is solved for based on the put-call parity formula. Applying the residual yield rate process helps with summarizing hard-to-borrow stocks or stocks with differing dividend assumptions. The effect is to line up the call and put implied volatilities.

Next, using the call and put mid-price IVs, a non-arbitrageable smooth curve is fit through the strike implied volatilities. This smoothing system produces powerful theoretical values and accurate option Greeks. The Strikes Report shows each option's bid-asks, greeks and theoretical values. Delta, Vega, Theta, Rho, Phi and theoretical values are critical for risk management and trading.

ORATS SMV also differentiates itself is by producing meaningful analytics on thinly traded securities. The SMV incorporates historical information when the current confidence in the market summarization is low.

Moreover, the SMV treatment of the wings, the small delta out of the money calls and puts, produces more realistic implied volatilities than unadjusted IVs based on bid-ask prices with little premium.

Let's look at an example of American Air Lines (AAL).

Here, we plot the call and put ask implied volatilities in green and blue against the SMV line in red. See how the call IVs go way up to 90%, and the puts IV in the 80% range when the at the money IVs are under 40%.

The process ORATS uses is to continue the rational slope of the volatility skew when there is little premium left and the IVs start to lose their meaning.

Theses SMV market datasets are available from 2007 to present.

The SMV system descriptions for data in the Strikes reports are below. Notice there is an External Volatility section in the SMV and those values are fed by the ORATS forecasts of volatility.

Strikes Report Headers:

Parameter Description

ticker Underlying symbol.

stkPx Stock Price at the time of the options prices observation. For indexes such as SPX, the stock price is the solved price using put-call parity at each expiration.

expirDate Expiration Date.

yte Years to expiration.

strike Option strike.

cVolu Call volume today.

cOi Call open interest from the day before calculation.

pVolu Put volume.

pOi Put open interest from the day before calculation.

cBidPx Call Bid Price.

cValue Call theoretical value based on smooth volatility.

cAskPx Call Ask Price.

pBidPx Put Bid Price.

pValue Put theoretical value based on smooth volatility.

pAskPx Put Ask Price.

cBidIv Call Bid Implied Volatility.

cMidIv Call Mid Market Implied Volatility.

cAskIv Call Ask Implied Volatility.

smoothSmvVol ORATS smoothed implied volatility applied to the strike.

pBidIv Put Bid Implied Volatility.

pMidIv Put Mid Implied Volatility.

pAskIv Put Ask Implied Volatility.

iRate Continuous interest (risk-free) rate.

divRate The continuous dividend yield of discrete dividend’s NPV.

residualRateData Implied Interest Rate Data.

smoothedResidualRate Smoothed Implied Rate Used in Calculations.

delta Delta

gamma Gamma

theta Theta

vega Vega

rho Rho

phi Phi

Ext Vol ORATS forecast of volatility for the strike

Ext Call Theo The theoretical value of the call based on the Ext Vol.

Ext Put Theo The theoretical value of the put based on the Ext Vol.

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