Arbitrage free volatility surface and negative implied dividend yield

[stepandfetchit]

Cheers! I've attached the data I obtained from yfinance eod on the 11th when the market was closed. I used the bid/ask mid for calls and puts (the numbers read last Price, bid, ask). I can see how you arrived at your forward here from the pictures you've attached using the bid/ask mid for the calls and puts. Is that the bid/ask from the 11th eod?

How do you determine the risk-free rate? I've utilised a term structure model to fit the zero coupon bonds data from the Treasury to the time left to expiry.

What is value U in your picture and how is it calculated?

Your implied dividend + borrow cost seems to have come out to ~3.06% here, in order for you to arrive at the forward using S*exp^(rfr-borrow-dividend).

It seems the issue is you are using BID and ASK after the market closed, so they are not relevant after market has closed (need to be captured at the close while they are still valid). -- I use simple process for interest rates adjusted to the term duration from the daily values from ivolatility (s/b about the same as the LIBOR rates). The U derivation is based on techniques from a Chain Boostrap white paper published by Steve Speer back in 2016. This method, IMO, is ideal for index products with continuous dividends. "U" = Ndx-PVDiv where "Ndx" is the implied index value for this chain at the chain timestamp and “PVDiv” is the present value of dividends for this index, on this date, for this DTE. U is derived from the option chain (unique per expiry) by fitting best estimate from Call/Put parity. U derived from Exp(-RT) * X + (C-P) Where care is taken to discard errant BIDs and ASKs and remove strikes with excess error contribution. Note: This method negates the need to individually address dividends as U value includes the impact of dividends allowing the dividend input of your model to be zero.
The "Forward" in my post is simply "F = Exp(RT) *U"
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Hopefully this gives a better idea of one approach.

 

[newwurldmn]

continuous div is a good assumption but for a four day option over a weekend you probably need to figure out the actual divs (or use the implied div+borrow or assume the borrow is zero).

The sample size is so small that you may not be running the average annual dividend rate. I dont know. It’s interesting that in your calculation the implied borrow was equal to the dividend.

It’s hard to say what’s going on with the info you presented because the vol changed so much. Was this calculation done eod Thursday or eod Wednesday. The vol is too low for eod Wednesday I think.

strike iv delta gamma rho theta vega
3975 0.2352 0.5067 0.0033 0.3228 -4.6071 2.0301
3970 0.2361 0.5233 0.0033 0.3332 -4.6244 2.0269

Fascinating fact about the arbitrageurs, I am utilizing FactSet's method for volatility surface modelling as a guide and found it quite surprising that they employ continuous implied dividends for the index and discrete for equities (https://insight.factset.com/hubfs/White Papers/Implied_Volatility_Surface_WP.pdf)

What would be the most suitable approach for obtaining the dividend and borrow that fits the market implied?

 

[brownianpotion]

continuous div is a good assumption but for a four day option over a weekend you probably need to figure out the actual divs (or use the implied div+borrow or assume the borrow is zero).

The sample size is so small that you may not be running the average annual dividend rate. I dont know. It’s interesting that in your calculation the implied borrow was equal to the dividend.

It’s hard to say what’s going on with the info you presented because the vol changed so much. Was this calculation done eod Thursday or eod Wednesday. The vol is too low for eod Wednesday I think.

Wednesday eod, it seems the difference came from me taking the bid/ask vs last price. The last price was recorded ~1h before the close so I went with the bid/ask mid.

Regarding the IV being to low: tough for me to say. I'm just starting to put my uni theory knowledge into practice, but stepandfetchit seems to get roughly the same iv 23.59 vs mine 23.61 for the 3700 strike.

The vega might throw you off, I just discovered a flaw in py_vollibs codebase for the vega calculation.

 

[newwurldmn]

Wednesday eod, it seems the difference came from me taking the bid/ask vs last price. The last price was recorded ~1h before the close so I went with the bid/ask mid.

Regarding the IV being to low: tough for me to say. I'm just starting to put my uni theory knowledge into practice, but stepandfetchit seems to get roughly the same iv 23.59 vs mine 23.61 for the 3700 strike.

The vega might throw you off, I just discovered a flaw in py_vollibs codebase.

Use mid price for your calculations.

 

[newwurldmn]

For what it’s worth: on Friday afternoon around 2pm, I traded a jan 13, jan 20 jelly roll and the market was -2.5 at -1.7. I filled at -2. That is I bought forward delta 2 points less than I sold spot delta.

 

[newwurldmn]

For what it’s worth: on Friday afternoon around 2pm, I traded a jan 13, jan 20 jelly roll and the market was -2.5 at -1.7. I filled at -2. That is I bought forward delta 2 points less than I sold spot delta.

correction: I updated my trade blotter this morning and I sold forward delta 2 points higher than I bought spot delta.