Why Implied Volatility Estimates Differ Across Data Sources

# Difference in implied volatility calculation


# Difference in implied volatility calculation












I've been using vollib to calculate IV, but my answers have been different by tenths from other sources like NASDAQ and Yahoo. The answers range +- 0.5, sometimes even more. The inputs are: $S$ (float) – underlying asset price $K$ (float) – strike price $t$ (float) – time to expiration in years $r$ (float) – risk-free interest rate $q$ (float) – annualized continuous dividend rate

For $q$ I use $r=ln(1+\frac{D}{S})$, $D$ = annual dividend $S$ = spot price.

Any idea why this may happen?

## Answer by Neeraj (score 2)

https://quant.stackexchange.com/a/23131

A possible reason may be your computation of maturity period. Exchange compute the maturity in minute till expiry and then divide it by total trading minute in a year to arrive at maturity.

An another possible reason may be your choice of risk free interest rate. There are various proxy for risk free interest rate like Treasury rate and LIBOR of different maturities. Make sure your choice of risk free interest rate match by what is being used by NASDAQ.

## Answer by phdstudent (score 0)

https://quant.stackexchange.com/a/23132

Probably because volib assumes that the Black-Scholes holds which as we not is not true. A better way to compute implied volatility is to use a Moment-Free-Implied-Measure.

One possibility is to closely following the model-free estimate proposed by Demeter et al. (1999) and Carr and Madan (1998) who show that if one owns a portfolio of options across all strikes inversely weighted by the squared strike then one gets a variance exposure that does not depend on the price. The variance swap rate or implied volatility is approximated by: \begin{equation} \sigma_{i,t,\tau}^2=\int_{S_i(t)}^{\infty}\frac{2\Big(1-\log[\frac{K}{S_i(t)}]\Big)}{K^2}C_i(t,\tau,K)dK+\int_{0}^{S_i(t)}\frac{2\Big(1-\log[\frac{K}{S_i(t)}]\Big)}{K^2}P_i(t,\tau,K)dK \end{equation}