Calculating options prices

[Magnus Knight]

Hi,

I'm trying to understand the behavior of an options price, I feel it should have moved more than it has.

I'm new here, and I have been trying to find the answer on my own, but all of the calculations I've done are coming out different than what is actually happening, so I'm a bit stuck. I will appreciate any help that can be offered.

In this example, yesterday I purchased some VXX 18 puts with an expiration date of January 15, 2021. I purchased these options for 1.61. At the time, I think Delta was around -0.60, Implied Volatility was 1.0793, Vega at about 0.01, and Theta about -0.055.

VXX closed yesterday at 17.55 and at the time of this writing it is 16.52.

Today, my option is trading at 1.89. This seems a bit low to me if I do what I think is the correct math.

Currently, Delta is -0.703, Implied Volatility is 96.6, Vega is still about 0.01, and Theta -0.051.

The math I did is:
17.55 - 16.52 = 1.03 (difference in VXX price)
107.93 - 96.6 = 11.33 (Implied Volatility difference)
11.33 * 0.01 (Vega) = 0.1133
1.03 * 0.65 (Avg. Delta) = 0.6695 - 0.1133 = 0.5562 - 0.051 = 0.5052

So my approximation is the option should have moved roughly 0.50 on this 1.03 VXX move. Instead the option is currently trading at 1.89, which is only a 0.28 move, which is nearly half what I expected to see.

Any help is appreciated. I don't know what I'm missing here. I get that things can be bit up or sold down, but I think this is too big of a difference to be that.

 

[caroy]

Normal skew is flipped in options on vxx, sqqq, uvxy, and the like that usually move contrary to the indexes. Vol falls as these move down so that decreases the value of the option. Plenty of sharper minds on these boards than mine who probably have better input.

 

[Magnus Knight]

Thanks for the reply.

I expect vol to move down as the underlying equity moves down in these, however, I thought I accounted for that with the difference in Imp Vol, but my numbers still don't seem to be coming out right for me.

 

[stepandfetchit]

Thanks for the reply.

I expect vol to move down as the underlying equity moves down in these, however, I thought I accounted for that with the difference in Imp Vol, but my numbers still don't seem to be coming out right for me.

I have not verified the accuracy of your numbers, but just a note or two. If you are using the broker's IV numbers, they are not known for being very accurate. Also noted your precision for Vega seems truncated, which is not helping you. Deriving IV may be best served by "reverse engineering" it from the price to keep from falling into some of the many of the pitfalls. [Note that the individual option Implied Volatility is the Volatility value needed to reflect the observed option price] However, I suspect you may be chasing the wrong problem. Note that if you are "predicting" an option value, you are predicting both the underlying AND the IV, which may move independent from time to time.

If you will post the points in time for the entry to the nearest minute as well as the time of your "test sample", someone may be able to provide more detail. -- It is possible the only flaw in your eval is the iv values between the two points in time.--

 

[matrik]

I have not verified the accuracy of your numbers, but just a note or two. If you are using the broker's IV numbers, they are not known for being very accurate. Also noted your precision for Vega seems truncated, which is not helping you. Deriving IV may be best served by "reverse engineering" it from the price to keep from falling into some of the many of the pitfalls. [Note that the individual option Implied Volatility is the Volatility value needed to reflect the observed option price] However, I suspect you may be chasing the wrong problem. Note that if you are "predicting" an option value, you are predicting both the underlying AND the IV, which may move independent from time to time.

If you will post the points in time for the entry to the nearest minute as well as the time of your "test sample", someone may be able to provide more detail. -- It is possible the only flaw in your eval is the iv values between the two points in time.--

I'm definitely no expert - just getting into options - but I agree with this guy. From what I understand, many of the calculations you can do yourself will be more accurate, and probably more current, than what many popular broker platforms will display. Either way, doing the math is a great way to ensure you understand how pricing and volatility works and, potentially, what outside factors might be affecting them.

 

[.sigma]

Maybe nobody truly knows the accurate way to price premium?

 

[Magnus Knight]

I have not verified the accuracy of your numbers, but just a note or two. If you are using the broker's IV numbers, they are not known for being very accurate. Also noted your precision for Vega seems truncated, which is not helping you. Deriving IV may be best served by "reverse engineering" it from the price to keep from falling into some of the many of the pitfalls. [Note that the individual option Implied Volatility is the Volatility value needed to reflect the observed option price] However, I suspect you may be chasing the wrong problem. Note that if you are "predicting" an option value, you are predicting both the underlying AND the IV, which may move independent from time to time.

If you will post the points in time for the entry to the nearest minute as well as the time of your "test sample", someone may be able to provide more detail. -- It is possible the only flaw in your eval is the iv values between the two points in time.--

Thanks stepandfetchit.

I'm using Interactive Brokers as my platform. I can't speak to any accuracy of their IV numbers, so I have no idea how accurate they are. I'll try to find an authoritative source like CBoE to compare against.

My Vega was not truncated at the time, it really was 0.01. Now it's 0.009, which is still really close. I definitely understand my numbers and math could be off a bit. If I would have came up close to the actual number, then I wouldn't be scratching my head so much, but 0.28 to 0.50 seems quite a difference to me.

Deriving the IV is something I haven't done or seen, or even thought about doing frankly, but I will look into this. Thanks for the suggesting and giving me a direction to go to look into this.

Your last comment, I think you are asking for the times I executed the trades? If so, I made the purchase on January 6 at 3:59:33 PM for 1.61. As of 9:52 Eastern Time this morning I'm still holding this position, but in my original post, I posted the numbers they were at that time, so my numbers at the time used January 7 at 3:50 PM. Sorry if I misunderstood your statement here.

 

[Magnus Knight]

Just a quick follow up...I started looking at deriving the IV and I came across the Black Scholes calculators online, and I found this one that allows me to set an expiration in days instead of years, so I used it. https://www.calkoo.com/en/black-scholes-option-pricing-model

When I entered in my numbers, it came up very close to what Interactive Brokers is reporting; not exactly the same, but really close. I also now see what you mean about the Vega being truncated. I wasn't intentionally doing it, but it is being done by IB in its reporting.

Also, comparing against the CBoE quotes (accounting for delay), I see that at least today, there seems to be about a 3 to 4 percent difference in IV, while IV is near 100%.

I'm still looking into this, but even with these small changes in numbers, I'm still not seeing a difference of almost half in the option price. I'll keep digging.

 

[stepandfetchit]

Just a quick follow up...I started looking at deriving the IV and I came across the Black Scholes calculators online, and I found this one that allows me to set an expiration in days instead of years, so I used it. https://www.calkoo.com/en/black-scholes-option-pricing-model

When I entered in my numbers, it came up very close to what Interactive Brokers is reporting; not exactly the same, but really close. I also now see what you mean about the Vega being truncated. I wasn't intentionally doing it, but it is being done by IB in its reporting.

Also, comparing against the CBoE quotes (accounting for delay), I see that at least today, there seems to be about a 3 to 4 percent difference in IV, while IV is near 100%.

I'm still looking into this, but even with these small changes in numbers, I'm still not seeing a difference of almost half in the option price. I'll keep digging.

I think the IV IB is providing is close enough. I did a calculation for the ATM IV about the time of entry and found my computed value very close to your IB value, so don't think the issue with the gross error is the IV. (so the sheet below is using your values, not calculated IV) As a test, I grabbed an Excel sheet from the web, which provided BSM and just plugged in your values for the following day (where you expected the value of the option to not match your expectations). I found the value to be within 1 penny. Let me know if I missed something! Note: you may not be accounting for time. -- I track time to nearest minuite, which may be the issue. Also, I use the nearest term LIBOR data for interest rates. Below is the excel sheet with the data for yesterday, but using the IV numbers IB provided you!

Link to this Excel sheet on the web: "https://excelatfinance.com/xlf/black_scholes.php"
For Stock (price) I entered 16.52,
for exercise 18
for Rate: 0.15459954422709% <-- you can round it (this was copy/paste)
Sigma: your number of 96.6%
Time: =8.14236111111111/365.25
The calculated Put price was 1.90, where you observed 1.89 which may be close enough for government work.

 

[stepandfetchit]

Here is using the link you provided: -- My interest rate is not intended for DTE < 30 days, and I use the 30 day rate so have some error there, but is close enough for most applications. I do not see any issues or unresolved mysteries. Thanks for posting as it seems fairly clear IB is indicating accurate IV numbers for the options you reference.