# BS model without volatility

Maybe it is a naive question, I simply can't understand how the industry is using the BS model to price options, as the option pricing formula requires implied volatility as an input, which itself is derived from the option market prices.

I just don't get how it all ties together given that one of the inputs is dependent on the output.

EDIT

Example: Assume it is Sunday, and public trading will open on Monday on a brand new equity share priced at \$s of a new company Amazing Inc. (no dividends, 0% interest rate) and I want to issue a new call option, with strike kon it, expiring in a year, how can I price it in dollars without having any volatility figures at hand??

• Here is one way to think about it: Assume i ask for the price of a call option on Amazon. You said 250 quid. This process can take few seconds at least. By the time i respond to the quote, the underling price might have moved by 10 quid. So is the call option price still valid? Maybe not. As options are really bets on vol, quoting price in vol make more sense, and you don't have to worry about the underlying price moving. May 18 '20 at 18:11
• Thanks for your reply, it helps but prices are not quoted in volatility units, they are quoted in dollars.
– user24980
May 18 '20 at 18:31
• separately assume it is Sunday, and public trading will open on Monday on a brand new equity share of a new company Amazing Inc. and I want to issue a new call option on it expiring in a year, how can I price it in dollars without having any volatility figures at hand??
– user24980
May 18 '20 at 18:35
• thanks, soz don't follow. Could you clarify: when you say the industry is using BS to price options, where do you find that they do so - presumably this is confidential? May 18 '20 at 18:38
• afraid it is not - only for quotes in say OTC. May 18 '20 at 18:45

It's all about transposing prices into some space that changes more slowly, such that data you can garner from prices provided by someone else at some other point in time can be used to estimate value at some other point in time.

Its effectively an interpolation and extrapolation tool.

Say you have option prices at strikes of 10, 20, 30, 40, etc. And you want the price for a 35 strike option. You could interpolate in price space, or you could transpose the option prices into vols and then interpolate in vol space. The latter works better. Even more obvious, if you need to extrapolate to other prices, then you can take the volatility "smile" from the strikes you have, and attempt to extrapolate this, it will give you a potentially better answer.

Likewise, if you have the option prices from one day, and then you need to calculate them the next day, you can adjust the underlying stock price, expected dividend yield, discounting, and time to maturity while keeping the volatility the same as your previous data point, and it will give you an idea of the option price.

Black Scholes is a model that everybody knows does not work. This is evident by the fact that every option strike has a different implied volatility (despite one of the underlying assumptions of the model being that volatility is constant). What it is though is a very useful function for transforming option prices into another space which allows you to estimate the value of that option given changes to other underlying properties.

• thanks that's helpful. there is always the "if you know the price of the option", but what if I simply want to price an option without having any previous option price data, are there other models out there that I should use instead?
– user24980
May 19 '20 at 5:38
• @jbs There is nothing forcing you to use any model. BS in this context is useful as described by will to decompose the degrees of freedom of an option price in a non-linear fashion (say price and “volatility” here) with the outcome that the dynamics of those is fairly independent (price moves “faster”, vol moves “slower”). You could decide to use Bachelier or you could even attempt a purely statistical description of the option price with a linear time series model. However in this latter case you would find yourself in a difficult situation to fit anything stable ;)
– Ezy
May 19 '20 at 9:30