black scholes model pricing vs real life pricing

[JackRab]

How do you gauge what is fair value for your option? the obvious answer is 'whatever the market can bear', but how do you know if the current value is above or below 'fair value'?

Fair value is mainly determined through put/call-parity. If the ATM put trades at 2.10, then according to P/C-parity the ATM call should trade (read fair value) at x.xx

There is no real fair value based on IV alone... because IV can (and does) change frequently, depending on supply/demand. If there is constant buying in the ATM call... MM's will raise the IV. Sometimes you don't see that buying, if it's done OTC for instance.

Also, if the bid ask spread is wide... and there's generally not much interest in these options, you would have to pay up to get executed... which means above midpoint. Fair value might still be midpoint, but somebody needs to get an incentive to trade against you... that would be you paying x.xx above fair value.

 

[Abundance Magnet]

Fair value is mainly determined through put/call-parity. If the ATM put trades at 2.10, then according to P/C-parity the ATM call should trade (read fair value) at x.xx

There is no real fair value based on IV alone... because IV can (and does) change frequently, depending on supply/demand. If there is constant buying in the ATM call... MM's will raise the IV. Sometimes you don't see that buying, if it's done OTC for instance.

Also, if the bid ask spread is wide... and there's generally not much interest in these options, you would have to pay up to get executed... which means above midpoint. Fair value might still be midpoint, but somebody needs to get an incentive to trade against you... that would be you paying x.xx above fair value.

Yeah, i've found the actual fill prices to be so variable ... MM gotta manage their book too. Sometimes I sell an option and get it closer to the ask (above the mid), other times not. Same for the buy to close for the bid... Other times I see the MM play a game of baiting by having really wide B-A for the option... Hard to tell what 'fair value' from a mathematical or formulaic perspective...

 

[JackRab]

Hard to tell what 'fair value' from a mathematical or formulaic perspective...

You need to look at past traded prices and determine the IV levels they traded at... put skew etc in it and then you have a fair value. Then MMs will take it depending on indeed their book, hedging possibilities, underlying bid/ask etc.

But if there hasn't been any trades in a while... your guess is as good as theirs.

 

[water7]

If there is constant buying in the ATM call... MM's will raise the IV. Sometimes you don't see that buying, if it's done OTC for instance.

just curious Jack, if it's done OTC on trading hour,
how fast they update the surface?
is it happening in real time (seconds) or more like EOD?

thanks :]

 

[JSOP]

What price would you see? Based on what IV?

You need to understand that midpoint does not necessarily mean the point where everything gets traded.

You could argue that the midpoint is a market makers theoretical fair value... but for them to take a trade, it should give them an incentive to trade it. So x.xx below fair value... otherwise, how would they make money?
The more liquid certain options series are, the tighter the spreads and the more likely it will be that you get traded at around the midpoint.

But you can always assess the price you trade, via say the BS-model, to give you the IV you've just traded.

IMO, the only time BS really screws up is when there are things like (multiple) dividends involved. But it depends on what you use it for...

That's WHY I said the price calculated by the Black & Scholes model may NOT be the price that the option would be traded at in the market. Read what I wrote, please.

 

[newwurldmn]

That's WHY I said the price calculated by the Black & Scholes model may NOT be the price that the option would be traded at in the market. Read what I wrote, please.

black scholes is just a framework. You can plug in any price and get an implied vol and vice versa. Black scholes says nothing about what the fair price/volatility is. It’s more like a Rosetta Stone that allows you to translate fast moving dollar prices to slower moving volatility prices.

 

[Lee-]

A market maker is not going to price options strictly on BSM. Here's an example, if you were highly sophisticated (ie you have a team who can analyze the data, write the code, etc), would you price options based on BSM? I sure wouldn't.

Here's some simple examples to wrap your head around even if you were to decide to use BSM as a starting point:

1) use spread of the underlying to determine what you need to increase your options spread
2) adjust based on trading patterns of related contracts
3) earnings report dates as an adjustment
4) adjust based on dividend announcements
5) analyze news to adjust model price

Point is, a market maker recognizes that in practice, BSM is insufficient to be profitable long term and will be using many other inputs as part of their models. On top of all of that, a market maker is only going to quote the best price that they need to, not the best price their model allows.

 

[newwurldmn]

A market maker is not going to price options strictly on BSM. Here's an example, if you were highly sophisticated (ie you have a team who can analyze the data, write the code, etc), would you price options based on BSM? I sure wouldn't.

Here's some simple examples to wrap your head around even if you were to decide to use BSM as a starting point:

1) use spread of the underlying to determine what you need to increase your options spread
2) adjust based on trading patterns of related contracts
3) earnings report dates as an adjustment
4) adjust based on dividend announcements
5) analyze news to adjust model price

Point is, a market maker recognizes that in practice, BSM is insufficient to be profitable long term and will be using many other inputs as part of their models. On top of all of that, a market maker is only going to quote the best price that they need to, not the best price their model allows.

You are specifically talking about the closed form solution to BSM which requires constant dividends, European exercise, and static vol.

No real market maker will use the closed form solution, but I can assure you that pretty much every volatility trader uses Black-Scholes framework for pricing. Everything you just mentioned comes in the form of inputs to tha model.

 

[JackRab]

That's WHY I said the price calculated by the Black & Scholes model may NOT be the price that the option would be traded at in the market. Read what I wrote, please.

I was trying to explain to OP that the fair value is not dependent on the model you use. The model doesn't matter. I could use any options pricing model... but the market price is always the market price.... you might need different implied vols to get to that market price though. Put/Call-parity dictates the fair value, based on what the market thinks the implied vol should be...

If I would use B&S with calendar days... I should use an IV of 19 to get to a premium of 2.50.
If I use business days, I need to use an IV of 16.
If I use another model... I might have to use 18.85...

Basically, the model doesn't matter. If the market agrees on a price/premium of $2.50... than you use whatever IV you need to price according to the market.

So while I get what you meant by saying: "That's WHY I said the price calculated by the Black & Scholes model may NOT be the price that the option would be traded at in the market"... you're wording it upside down. You should say that one needs to get to a market conform price... and you get x.xx as implied vol... whether you use B&S or another model.

 

[JackRab]

just curious Jack, if it's done OTC on trading hour,
how fast they update the surface?
is it happening in real time (seconds) or more like EOD?

thanks :]

Volume or size of the last trade will dictate a possible change in implied vol surface.
So, if an OTC trade is only for a small size... smaller than the quoted size on screen, it wouldn't affect much. If it's 10x or more... you will start to see a shift before it actually trades. That's because there will be a few market makers involved in taking the OTC trade and if they start to find out what the other side wants to do, sell/buy and at roughly what price, they will quote accordingly.

So definitely real-time.... otherwise you wouldn't be pricing at the correct/current market (fair) value.