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An Intuitive Explanation of Black–Scholes

gregorygundersen.com

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Re: An Intuitive Explanation of Black–Scholes

#61

Post by e-master »

ncclporterror wrote: post #21

In modern finance the Black-Scholes formula is not used to "price" options in any meaningful sense. The price of options is given by supply and demand. Black-Scholes is used in the opposite way: traders deduce the implied volatility from the observed option prices. This volatility is a representation of the risk-neutral probability distribution that the markets puts on the underlying returns. From that distribution w…

I’ve seen it used for OTC option pricing - there’s no liquid market, so you are more of a market maker than a market taker.

Re: An Intuitive Explanation of Black–Scholes

#62

Post by RayVR »

e-master wrote: post #61
ncclporterror wrote: post #21

In modern finance the Black-Scholes formula is not used to "price" options in any meaningful sense. The price of options is given by supply and demand. Black-Scholes is used in the opposite way: traders deduce the implied volatility from the observed option prices. This volatility is a representation of the risk-neutral probability distribution that the markets puts on the underlying returns. From that distribution w…

I’ve seen it used for OTC option pricing - there’s no liquid market, so you are more of a market maker than a market taker.

Black Scholes is not used for any otc option pricing, except perhaps to provide an instantaneous estimate to get in the ballpark, but no one would use it for the final price.

Re: An Intuitive Explanation of Black–Scholes

#63

Post by ncclporterror »

IAmGraydon wrote: post #59
ncclporterror wrote: post #21

In modern finance the Black-Scholes formula is not used to "price" options in any meaningful sense. The price of options is given by supply and demand. Black-Scholes is used in the opposite way: traders deduce the implied volatility from the observed option prices. This volatility is a representation of the risk-neutral probability distribution that the markets puts on the underlying returns. From that distribution w…

>In modern finance the Black-Scholes formula is not used to "price" options in any meaningful sense. The price of options is given by supply and demand. I'm not sure what your point is. Yes, actual market prices are determined by...the market. The Black-Scholes formula is widely used in modern finance to MODEL the price of an option given different sets of inputs in theoretical situations.

The way the article is written, it appears that the formula is used as: 1. Observe market parameters (volatility of the underlying and risk free rate) 2. Plug into formula 3. Deduce a price for the option.

My point is that it is used in the opposite way: observe prices to deduce market parameters. You claim my point is obvious, but I'm not sure it would be obvious to a reader unfamiliar with modern finance reading this article, which is the target audience.

Re: An Intuitive Explanation of Black–Scholes

#64

Post by RandomLensman »

ncclporterror wrote: post #21

In modern finance the Black-Scholes formula is not used to "price" options in any meaningful sense. The price of options is given by supply and demand. Black-Scholes is used in the opposite way: traders deduce the implied volatility from the observed option prices. This volatility is a representation of the risk-neutral probability distribution that the markets puts on the underlying returns. From that distribution w…

For valuing financial products with no directly observable price, BS or its descendants matter quite a lot. For actually pricing a transaction on those, it becomes more complex but model value is typically an important input.

Re: An Intuitive Explanation of Black–Scholes

#65

Post by dahfizz »

FabHK wrote: post #51
ndesaulniers wrote: post #49

Earlier quoted context omitted.

Also, isn't it only used for European style options, not American?

European and American calls cost the same on non-dividend paying stocks (on dividend paying stocks, it might make sense to exercise an American just before the ex-date). Either way, as was pointed out, in reality BS is used as a deterministic one-to-one mapping between option prices and BS vols. Then, from market quotes (either as prices or as BS vols) a vol-surface is fitted (as a function of strike and expiry time)…

> European and American calls cost the same on non-dividend paying stocks

All else being equal, I would prefer to buy an option contract I can exercise at any time vs one I can only exercise on a certain date. It doesn’t make intuitive sense they would be priced the same, can you please elaborate?

Re: An Intuitive Explanation of Black–Scholes

#66

Post by blitzar »

ncclporterror wrote: post #63
IAmGraydon wrote: post #59

Earlier quoted context omitted.

>In modern finance the Black-Scholes formula is not used to "price" options in any meaningful sense. The price of options is given by supply and demand. I'm not sure what your point is. Yes, actual market prices are determined by...the market. The Black-Scholes formula is widely used in modern finance to MODEL the price of an option given different sets of inputs in theoretical situations.

The way the article is written, it appears that the formula is used as: 1. Observe market parameters (volatility of the underlying and risk free rate) 2. Plug into formula 3. Deduce a price for the option. My point is that it is used in the opposite way: observe prices to deduce market parameters. You claim my point is obvious, but I'm not sure it would be obvious to a reader unfamiliar with modern finance reading th…

> 1. Observe market parameters (volatility of the underlying and risk free rate) 2. Plug into formula 3. Deduce a price for the option.

In the FX market (interbank), the quoted and "traded" number is Implied Vol - the price of the option then follows from there (via the Black–Scholes model).

Re: An Intuitive Explanation of Black–Scholes

#67

Post by [deleted] »

ncclporterror wrote: post #21

In modern finance the Black-Scholes formula is not used to "price" options in any meaningful sense. The price of options is given by supply and demand. Black-Scholes is used in the opposite way: traders deduce the implied volatility from the observed option prices. This volatility is a representation of the risk-neutral probability distribution that the markets puts on the underlying returns. From that distribution w…

[deleted]

Re: An Intuitive Explanation of Black–Scholes

#68

Post by immibis »

tehjoker wrote: post #28
bjornsing wrote: post #8

Earlier quoted context omitted.

Yes. That’s basically how the stock market works. If you buy and hold an S&P 500 index fund you can expect to make an infinite amount of money, in an infinite amount of time. But few have the patience for that.

We'll hit the limit in a few decades or at most a couple centuries due to ecological limits on growth though (unless a robust space economy develops).

Or just poor people hitting the zero bound.

Re: An Intuitive Explanation of Black–Scholes

#69

Post by sokoloff »

FabHK wrote: post #51
ndesaulniers wrote: post #49

Earlier quoted context omitted.

Also, isn't it only used for European style options, not American?

European and American calls cost the same on non-dividend paying stocks (on dividend paying stocks, it might make sense to exercise an American just before the ex-date). Either way, as was pointed out, in reality BS is used as a deterministic one-to-one mapping between option prices and BS vols. Then, from market quotes (either as prices or as BS vols) a vol-surface is fitted (as a function of strike and expiry time)…

American style options are inherently more valuable. Imagine you had options on a stock that experienced a sharp but possibly temporary move. As a holder of an American style option, you could benefit from that temporary move, making it more valuable.

Re: An Intuitive Explanation of Black–Scholes

#70

Post by sokoloff »

twoodfin wrote: post #47
tehjoker wrote: post #28

Earlier quoted context omitted.

We'll hit the limit in a few decades or at most a couple centuries due to ecological limits on growth though (unless a robust space economy develops).

Sorry, which limits? How do those apply to the increasing economic value of turning the same amount of sand into faster and faster GPUs, for example?

There are still finite people willing to buy whatever the intermediate or end product of that fancy sand is. And finite energy and space. And only 5 billion years until the sun goes red giant.

The limits may be very large, but they aren’t infinite.

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