Choosing the Lognormal Mean for Black Scholes

[guru]

For me valuing an option is valuing implieds

And to value implides someone may use BS to obtain implides from the current option prices, then approximate IV for different options (whether on the option chain or not), and then use BS again to value those different options. In fact, thousands of people use BS every day to display P&L charts of options that use BS to value those options, so how do you dare to tell them that they didn’t use BS?
(I’m using it little differently programmatically but also as utility to estimate option pricing with input being the IV, though also an output in other cases).

You could argue technically that approximating an option’s IV from other IVs (or using any pricing model) requires some method unrelated to BS, but that could lead to overengineered math geek speak that’s only good for arguing that BS isn’t used for one technical task among others that use BS to estimate an option’s price. I may even agree, but I bet you that most people won’t have a clue why you’re making contradictory statements about not being able to use BS to value options but using BS to translate IV to option prices, or “valuing inplieds”, and other fluff, so you stating that “it should not be misunderstood” is a bit ironic when you don’t put an effort into making someone understand it

 

[newwurldmn]

One thing I don't understand about Black Scholes is why the mean (drift) of the stock return lognormal distribution is set to the risk-free interest rate minus the dividend rate. Wouldn't it be more accurate to use historical mean return, if the history is sufficiently long?

According to https://www.investopedia.com/ask/answers/042415/what-average-annual-return-sp-500.asp, the average annualized return for S&P 500 is 10% within a ~100-year period. But if I use that as the lognormal mean, the option pricing for SPY will be quite different from the market (more expensive calls and cheaper puts), which is based on near-zero interest rate.

Does this mean the market doesn't really think S&P 500 will continue to yield 10% per year on average, even though it has performed like that reliably for almost 100 years?

Because of the no arbitrage principle.

black scholes isn’t predicting where the stock will trade but rather what price the forward of the stock should be. Anything other than the risk free rate - dividends is arbitragible.

 

[SunTrader]

You would have thought LTCM would have put an end to BS but then again much of Wall Street has the same herd mentality.

 

[DiceAreCast]

Actually for vanilla options most pros hardly ever talk about price. They price the implieds, they even negotiate the price in terms of implieds. Also the hedge that is often exchanged with the options trade is based on the implieds. That's at least how it works in the otc space. And for exchange traded options the only time where price matters is the payment phase. Supply and demand is often expressed in implieds as well. Speaking of plain vanilla options here...

And to value implides someone may use BS to obtain implides from the current option prices, then approximate IV for different options (whether on the option chain or not), and then use BS again to value those different options. In fact, thousands of people use BS every day to display P&L charts of options that use BS to value those options, so how do you dare to tell them that they didn’t use BS?
(I’m using it little differently programmatically but also as utility to estimate option pricing with input being the IV, though also an output in other cases).

You could argue technically that approximating an option’s IV from other IVs (or using any pricing model) requires some method unrelated to BS, but that could lead to overengineered math geek speak that’s only good for arguing that BS isn’t used for one technical task among others that use BS to estimate an option’s price. I may even agree, but I bet you that most people won’t have a clue why you’re making contradictory statements about not being able to use BS to value options but using BS to translate IV to option prices, or “valuing inplieds”, and other fluff, so you stating that “it should not be misunderstood” is a bit ironic when you don’t put an effort into making someone understand it

 

[newwurldmn]

You would have thought LTCM would have put an end to BS but then again much of Wall Street has the same herd mentality.

can you explain what losing on a bond basis that's levered 30:1 has to do with the black scholes framework?

 

[SunTrader]

can you explain what losing on a bond basis that's levered 30:1 has to do with the black scholes framework?

Myron Scholes was one of the founders but besides which there are limitations of the model such as the many assumptions as to a) price following the random walk theory ignoring black swans and "semi-black swans" and that RWT is only just that a theory, never proven. b) no allowances for volatility, arbitrage, taxes, dividends etc etc.

 

[DiceAreCast]

That is bullshit. Not only is that false but what point are you even trying to make?

Everything you said is missing is actually well accounted for in models that all derive from the foundational BS model

Myron Scholes was one of the founders but besides which there are limitations of the model such as the many assumptions as to a) price following the random walk theory ignoring black swans and "semi-black swans" and that RWT is only just that a theory, never proven. b) no allowances for volatility, arbitrage, taxes, dividends etc etc.

 

[newwurldmn]

Myron Scholes was one of the founders but besides which there are limitations of the model such as the many assumptions as to a) price following the random walk theory ignoring black swans and "semi-black swans" and that RWT is only just that a theory, never proven. b) no allowances for volatility, arbitrage, taxes, dividends etc etc.

all those limitiations were well understood before LTCM.

Why would LTCM's blow up (on bonds) invalidate the framework. Just because one of the founders of the firm was part of it when it blew up?

That's a weird way of looking at the world.

 

[DiceAreCast]

Exactly, BS and LTCM are utterly unrelated.

all those limitiations were well understood before LTCM. Why would LTCM's blow up (on bonds) invalidate the framework.

Is it just because of Myron Scholes? Does that mean that Obama was a terrible president because he had one mic slip with a Russian ambassador?

 

[newwurldmn]

Myron Scholes was one of the founders but besides which there are limitations of the model such as the many assumptions as to a) price following the random walk theory ignoring black swans and "semi-black swans" and that RWT is only just that a theory, never proven. b) no allowances for volatility, arbitrage, taxes, dividends etc etc.

there are models that account for all of these issues - including the situation where options aren't tradeable (like ESO's). They are variants of the fundamental model.