Simple options questions about IV and expiration

[keroppi]

1. If I am long an option and it's IV goes up by 50% does the value of the option go up by 50% or is there some convexity involved? If it is not a linear relationship, is there a graph to show what would happen to the option value based on change in IV alone

2. If I have a 10k account (non-margin account with Interactive Brokers) and I was long SPY call options and they exercise in the money but the value of my SPY positions after they expire is say 20k (after each option converts to 100 shares of SPY), would the broker close out some of my SPY positions post expiration? From my understanding, I now have 20k SPY exposure and if the value of my SPY positions drops by over 10k I would be in negative balance

3. In terms of SPY expiration is it based on SPY price at 4pm ET or 4.15pm ET?

 

[thecoder]

1. If I am long an option and it's IV goes up by 50% does the value of the option go up by 50% or is there some convexity involved? If it is not a linear relationship, is there a graph to show what would happen to the option value based on change in IV alone

Here's the relation for an ATM option (K=S=100, t=1, r=q=0) starting with IV=20% and increasing IV by 50% for the two pricing models BSM and FPM:

s = 20%:
BSM: CALL=7.965567455406 PUT=7.965567455406
FPM: CALL=7.925970943910 PUT=7.925970943910

s = 30% (+50%):
BSM: CALL=11.923538474048 PUT=11.923538474048
FPM: CALL=11.791142218895 PUT=11.791142218895

s = 45% (+50%):
BSM: CALL=17.802072573746 PUT=17.802072573746
FPM: CALL=17.364477971208 PUT=17.364477971208

s = 67.5% (+50%):
BSM: CALL=26.425998785705 PUT=26.425998785705
FPM: CALL=25.016211752822 PUT=25.016211752822

s = 101.25% (+50%):
BSM: CALL=38.731884142995 PUT=38.731884142995
FPM: CALL=34.435047665323 PUT=34.435047665323

This kind of analysis is usually done in so called "Volatility Surface Analysis" (a 3D analysis);
cf. https://en.wikipedia.org/wiki/Volatility_smile#Implied_volatility_surface

Further analysis shows that the increase of +50% IV does not lead to a change of +50% in the option premium; ie. it's not linear:

BSM:
11.923538474048 / 7.965567455406 * 100 = +49.68850042134587244200%
17.802072573746 / 11.923538474048 * 100 = +49.30192587119029977600%
26.425998785705 / 17.802072573746 * 100 = +48.44338307370640535500%
38.731884142995 / 26.425998785705 * 100 = +46.56734247617842776400%

FPM:
11.791142218895 / 7.925970943910 * 100 = +48.76590265517997478500%
17.364477971208 / 11.791142218895 * 100 = +47.26714044193168846200%
25.016211752822 / 17.364477971208 * 100 = +44.06544092083460124700%
34.435047665323 / 25.016211752822 * 100 = +37.65092814837758481800%

And regarding your 2nd question just a hint: you can close an option position any time...

 

[keroppi]

Very interesting to see the results for IV. The increase is slightly under 50% and declines as IV increases. Also interesting to see that it differs based on the pricing model

Yes, I am aware that you can close an option any time and almost always close it out before it expires.

I let an option expire ITM yesterday and I am curious what would happen next...

 

[thecoder]

Very interesting to see the results for IV. The increase is slightly under 50% and declines as IV increases. Also interesting to see that it differs based on the pricing model

Yes, I am aware that you can close an option any time and almost always close it out before it expires.

I let an option expire ITM yesterday and I am curious what would happen next...

You will have saved a commission , and will see the result normally on the next trading day, ie. on monday.

Btw, in case you didn't know: you can calculate/verify BSM yourself for example here online:
https://www.optioncreator.com/options-calculator

 

[keroppi]

Yes, I will find out although I am just wondering could the broker close out some of my positions post expiration as per my example above? I am a bit anxious that they might close some out...

 

[TheGoonior2]

I let an option expire ITM yesterday and I am curious what would happen next...

You will be assigned unless it was a cash settled option. You mentioned SPY, so you will be long shares since you were long a call. IB will adjust your account soon after market open to bring your account inline with the requirements.

Also, you don't need those online calculators. IB (and platforms like TOS) have far better tools for visualizing options positions and pricing and the various effects of changes in IV/time/price, etc.

 

[TheGoonior2]

You will have saved a commission ,

How so? It doesn't sound like the OP wants/intends to take delivery. In this case, the broker will sell the required number of shares first thing Monday morning (check with IB, but I think it is within the first 10-15 minutes). They will charge a commission for this just as if you had placed an order, except now you are forced to sell (unless you do it yourself pre-market).
If you are fortunate to get a bounce on Monday, I'd say unwind what you need manually in the pre-market (SPY is very liquid, so spreads are still reasonable) rather than let them do it for you.

 

[keroppi]

Thanks. Based on what you say, if the value of my SPY shares exceeds value of my account balance, I will be forced to close some of my shares?

Regarding SPY, do you know what time are you able to open or close positions pre-market with IB?

How so? It doesn't sound like the OP wants/intends to take delivery. In this case, the broker will sell the required number of shares first thing Monday morning (check with IB, but I think it is within the first 10-15 minutes). They will charge a commission for this just as if you had placed an order, except now you are forced to sell (unless you do it yourself pre-market).
If you are fortunate to get a bounce on Monday, I'd say unwind what you need manually in the pre-market (SPY is very liquid, so spreads are still reasonable) rather than let them do it for you.

 

[TheGoonior2]

You'd be best to just check with IB directly as to the specifics for the cash account. I have a margin account, and that's how it operates. Premarket opens at 4am EST. Based on past experience, I have always had time in the pre-market to unwind a position. Specifically, this was always a short position due to assignment of short calls. Since you can't short shares in an IRA, IB would cover all the short shares soon after market open if I left things as they were. I believe they told me previously that they'd start to liquidate within 10-15 minutes after market open. Not sure if that's true or not as I never left it up to them.