/biz/ - Business & Finance

>>54313564
>>54313472
The Black-Scholes formula is used extensively for options pricing. Funds may use their own proprietary method for pricing options as well, but this is the gold standard. Note that forex traders use Vanna-Volga pricing for their models, which is a modified BS model to take into account interest rate differentials between countries.

Anyways, the BS model takes the time to expiry, the strike price, and the implied volatility (IV) to price out the fair market value of a contract (it also factors in dividends and the risk-free rate). It's entirely possible for the price to be above or below the FMV depending on liquidity and supply/demand (try buying a deep OTM call on MSFT 2 years in the future vs an ATM SPY call with 10 days to expiry). The bid/ask spread on options can be enormous, so liquidity matters.

The formula looks scary, but it isn't. The takeaway here is that you can isolate each of those variables and see how it changes w.r.t. each of the other inputs. These are the Greeks.
>Delta: Price change as underlying price changes
>Theta: Price change as time passes
>Gamma: Delta change(!) as underlying price changes
>Vega: Price change as IV changes
>Rho: Price change as interest rate changes. Nobody cares about this because you aren't a hedge fund manager
One delta is one share. Remember this.

Volatility is the main driver with for option pricing. Some people prefer to quote options in terms of IV or in terms of delta (eg 25, 50 delta for puts or calls). Volatility is the "risk premium" and the way I rationalize it is as "How much IV does the contract have to have to math out the price, since the other inputs are fixed and known?". Really IV is the only variable on pricing. You can model how underlying prices affect things, but IV just depends on market demand.