# 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?

• What is that ln(1+D/S) ? Shouldn't it be D/S-1 or ln(D/S) ? – onlyvix.blogspot.com Feb 22 '16 at 1:08

## 2 Answers

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.

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}

• Would be very helpful for the person who downvoted this answer to say why ... – phdstudent Feb 6 '16 at 14:37
• Implied volatility has a specific meaning, which is volatility such that plugged into B-S formula produces market price. Your "answer" did not answer the question that was asked. – onlyvix.blogspot.com Feb 22 '16 at 1:04
• Not true. The measure I posted above is called Moment Free Implied Volatility. So give the question is not very specific my answer actually fits. – phdstudent Feb 22 '16 at 9:26
• I understand the confusion as both have "implied volatility" in it, but the question was about strike specific implied volatility, i.e. B-S IV. If you look at the vollib link provided in the question, you will also see explicit reference to B-S. And in the option chain quotes yahoo finance also calculates strike specific IV. – onlyvix.blogspot.com Feb 23 '16 at 14:16