# How implied volatility affect options pricing?

TSLA between 23 and 24 October 2019 had their earnings report. TSLA mark price on 23 October was 252\$. On 24 October, half an hour after market open reached 297\$. as we saw around 44\$ push.

if average delta/gamma is 0.73\$ how much will that be for the 44\$ increase in price and the 10% decrease in volatility.

Is there any calculation i can do.

Please can anyone check on their platform and elaborate.

• I don't claim to understand "the Greeks", but from Using the "Greeks" to Understand Options on Investopedia, they are an attempt to explain/predict changes in an option's price, not the driver of the change in price. In this case, presumably, lots of people wanted the options so the price rose. – TripeHound Oct 29 '19 at 10:34
• Thank you TripeHound i really appreciate the article. – David Oct 29 '19 at 13:06
• What do you mean by "average delta/gamma"? gamma in a non-linear change so the change from gamma may have been much higher than what you calculate. – D Stanley Oct 29 '19 at 13:08
• @TripeHound - Because implied volatility contracts after an earnings announcement, the time premium component due to implied volatility actually shrank. The call's price rose because the stock's price rose \$44, not because lots of people wanted the options. – Bob Baerker Oct 29 '19 at 14:07

It's hard to tell exactly without full quotes before and after, but one thing I see is that Vega is change in price per absolute change in implied vol, not relative change in implied vol. I see that the implied vol went from about 43% to 40%, for a vol change of -3%. So the change due to volatility change would be `(0.3)*(-3) = -0.9`, not `-4`.

You should also use the delta and gamma from 10/23, not the average delta and gamma.

i would appreciate if you can elaborate more on your previous answer (absolute change in implied vol, not relative change in implied vol), and if i should look for the imp. volatility somewhere else as i am looking on the underlying stock(TSLA) daily 1 year chart.

Implied volatility is not calculated from the historical change in stock price. It is back-calculated from market prices of various options. Each strike and expiry will have a different implied volatility, which results in a volatility surface. To price an option, you find the implied volatility from that surface that matches the strike and tenor of your option.

I have an excel sheet that calculates implied volatility from option price and other inputs (you can find sheets online that will do this). By my calculations, IV for that option went from about 43% to 40%, or a 3% drop when using it to estimate price change due to vega.

• What was gamma on 10/23? With that large a move you're going to get some increase due to gamma. Also, re-read my answer - the change from IV would be about -\$1, not -\$4. – D Stanley Oct 29 '19 at 13:48
• what i mean by average delta/gamma is that on 23 October delta was 0.08, on 24 October it is 0.12 – David Oct 29 '19 at 13:49
• i can see on my DAILY 1 year STOCK chart(not options chart), it is around -10% to -13%. – David Oct 29 '19 at 13:51
• Again, re-read the answer. The change from vol change should be about -\$1, not -\$4. That explains most of it. I also suspect you've underestimated the change due to gamma. – D Stanley Oct 29 '19 at 13:51
• The overnight change for a 3% decrease in implied volatility would be 81 cents. Any option pricing formula (or web site calculator) would provide the implied volatility – Bob Baerker Oct 29 '19 at 13:56

Looking at you original post before editing, you asked why the call's price increase wasn't \$1.72 instead of \$5? I came up with an overnight delta change of .097. Multiply that by the price change of \$44 and you get \$4.27. Add that to \$2.60 and the new premium should be at least \$6.87. A price change of \$1.72 is way off.

I know what the Greeks are but the only one that I have any knowledge of and use for is delta so I can't tell you what's wrong with your method of price change calculation. What I do know is that projecting price change via an average of Greeks is inaccurate because delta is non linear as it changes incrementally as price changes. So let's try something more accurate, namely an option pricing model for the Jun \$420 call.

10/23

\$242

\$420 call = \$2.60

IV = .418

Delta = .176

10/24

\$297

\$420 call = \$7.60

IV = .384

Delta = .079

Note that I have backfitted delta and IV based on the market prices that you provided. In line with your observations, IV dropped about 10%. So what I can tell you is that based on the data you provided, there is no there there. IOW, the pricing is as expected.

EDIT

There are many calculators available online. The option pricing formula used can vary so there are often minor discrepancies between the calculations each one generates. Here are two:

Calculator 1

Calculator 2

You might have to register to access the IVolatility calculator. It's free.