Choosing the Lognormal Mean for Black Scholes

[SunTrader]

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.

Yes models, other ones. Not the BS model.

 

[DiceAreCast]

They are based on the BS model. What is wrong with you? Is it your hobby to disagree with facts in every thread you participate?

Yes models, other ones. Not the BS model.

 

[newwurldmn]

Yes models, other ones. Not the BS model.

Black scholes isn’t just the n(d1) formula. That was just one form of it.

But the whole premise of no-arbitrage snd replicabilty has been disproven by an overlevered failed hedge fund 20 years ago.

 

[SunTrader]

Black Scholes is one model.

Black passed away a couple of years after it was developed.

Many have developed their own versions to account for it's shortcomings.

LTCM over-leveraged because of their confidence in the model - whichever version they were using.

 

[LM3886]

Thanks for the replies. I'll take the conclusion that the market thinks S&P 500's 10% average annual return is rather risky and uncertain in the future.

In addition to BS, the lognormal mean also has implications to historical volatility (HV) calculation. Still taking SPY as an example, would you use the risk-free interest rate or the 10% long-term average return as the mean to compute HV? I think it would be more accurate to use 10%, because if using risk-free interest rate the 10% drift leaks into volatility. But obviously that will mismatch the implieds from market prices.

 

[jnbadger]

I would love to hear your phone call to your broker while they’re liquidating your account and you’re trying to convince them that everything will be alright and your stock will recover and return 10% according to some data you’ve looked at. I also wonder how many people tried that trick last year when their accounts where being liquidated. Negative oil price must’ve been especially fun for brokers listening to their bankrupt customers/traders.

Ouch. I forgot about negative oil. That was brutal to watch.

 

[jnbadger]

Please excuse my ignorance, but why do people get so hung up on which options model to use, and the details of how they are calculated? What model, and what calculation would've helped you last March when Covid hit, and implied volatility went through the roof?

 

[LM3886]

Please excuse my ignorance, but why do people get so hung up on which options model to use, and the details of how they are calculated? What model, and what calculation would've helped you last March when Covid hit, and implied volatility went through the roof?

Sure, models can be off, sometime far off. But most of the time they can be used as an approximation. Are you using a model-free approach?

 

[newwurldmn]

Thanks for the replies. I'll take the conclusion that the market thinks S&P 500's 10% average annual return is rather risky and uncertain in the future.

In addition to BS, the lognormal mean also has implications to historical volatility (HV) calculation. Still taking SPY as an example, would you use the risk-free interest rate or the 10% long-term average return as the mean to compute HV? I think it would be more accurate to use 10%, because if using risk-free interest rate the 10% drift leaks into volatility. But obviously that will mismatch the implieds from market prices.

better description is that the market doesn’t care to predict what the spx has done in the past. It doesn’t need to because it can create synthetic portfolios to hedge out that risk and it can with certainty price those synthetic portfolios.

There are models which try to take into account a different drift. I played around with it a little bit but i didn’t get very far into it. It will develop your own valuations for options which will obviously differ from my valuation for the option.

 

[newwurldmn]

Black Scholes is one model.

Black passed away a couple of years after it was developed.

Many have developed their own versions to account for it's shortcomings.

LTCM over-leveraged because of their confidence in the model - whichever version they were using.

Ltcm was statistical arb of bond prices. It had nothing to do with black scholes.
So again, how does LTCM’s blowup invalidate
The black scholes model when they weren’t even using it.

spend some time understanding the black-scholes model. Not the snd(1)-knd(2) one but the theory behind it. It’s incredibly elegant and no matter what lens you look at it, it tells a consistent story.
whether you use the closed form or a trionomial tree with local vol and jump diffusion, its underpinning philosophy is robust.