Pricing Options using Black Scholes Merton

[@paperscissors8336]

Black Shoals does not consider volatility or assumes that it is constant but it is not the case. When trading, I often see options pricing vary from what my assumptions are.

[@nnadivictorc]

Did you consider transaction costs, dividends etc?

[@cole6167]

Correct. Part of opening the position might include comparing your expectations of _the change in implied volatility_ to the price/IV prevailing in the market at order entry. You could argue that this "oversimplification" in the pricing model must be compensated for somehow when trading (by either ignoring possible changes in IV, taking a speculative position on IV changes, preemptively hedging for changes in IV, etc). Like Patrick said, volatility over the life of the contract (which lay ahead in the future) is not known. So this is less about computation with the model and more about decision-making in one's trading practice while facing unknown factors.

[@santiagoheier5961]

Hey Patrick, great video! That being said, I am still a little confused about why we are using implied volatility. The whole point of pricing an option is to substantiate what the derivative is worth on an intrinsic level and then compare that to what the market is pricing these options at. If we back inputs out of current option prices, how is this not counterintuitive to the whole point of valuing the option? What if the market as a whole is wrong about the perceived volatility? We would have to assume efficient market theory is correct (which I refuse to believe lol) ... anyways, pardon the lengthy question, just trying to better understand practical application of this model

[@cole6167]

Good question! 1. We "back out" the volatility input for the contract since it can only be determined in the future. Also, the computed IV can be compared across contracts/series/underlyings, so that computation result is valuable even if it isn't a theoretical price. 2. No need to believe efficient markets! You can use the pricing model to compute the IV for a contract and decide that the market has "mispriced" the contract from your perspective. The pricing model is not a trading decision engine -- it doesn't need to produce specific outputs, nobody must follow it, and it cannot decide whether a price is distorted. It's an optional (but widespread) tool that can build confidence while trading.

[@santiagoheier5961]

@@cole6167 ahhhh I see, so essentially we’re looking at priced volatility differentials and buying those we believe to be bargains based on comps?

[@cole6167]

@@santiagoheier5961 that's the idea! That one approach can prompt quite a variety of trading decisions like: - "IV is higher on QQQ than on SPY, so I will sell puts there" - "IV is strangely low 120 days to expiration, so I will buy those in a calendar instead of selling a vertical" - "IV tends to fall over time, so my next risk-on trade will bias toward selling premium rather than buying it" No wonder such a versatile tool is so widely used!

[@santiagoheier5961]

@@cole6167 Thanks Cole! I sincerely appreciate the response, I’ll have too look into learning more about these trading strategies so I can develop a couple of my own and apply them to large potential gain opportunities that are not heavily identified in the market (something that sounds easy but I’m sure will be very challenging to actually execute lol)

[@itooflemma]

Just search practitioners black Scholes model

[@nnadivictorc]

Awesome video sir. Please what parameter is "d"?

[@user-sg1qu8io6v]

Volatility a “bit” of a chicken egg problem 😂😂😂

[@ztrading16]

Is it possible to trade vix index by using quantitative approach?

[@cole6167]

why wouldn't it be? The VIX has tradable options and futures and relationships to highly liquid products (S&P500 options) -- may be a very good candidate for empirical-/model-driven trading...

[@nrpbrown]

Huh, this made a lot of things click. Thank you