Thoughts on options

Black-Scholes is the most widely recognized options pricing formula.

Options pricing is derived by summing up all the payoffs and their likelihood of occurring by the difference between the stock price and the strike price at the time of options expiration, which is then discounted to present value.

The calculation of option price is based on the probability of option being called, modified by possible returns on the stock that give payoff weightings to each probability, using the normal curve.

Problem with black-scholes is that, it's an approximation of the real world. There must be an understanding as to what the Black-Scholes predicts, for it to be useful in the real world in real life trading. For example:

Assumptions of the Black-Scholes Formula:

* volatility and interest rates are fixed

* infinite number of hedging

* trade size can be infinitely small

* infinite number of trading and trading liquidity

* does not consider fees or commissions on purchasing or borrowing stocks

* does not consider bid/ask spreads on prices or on interest rates

* does not consider dividends

* only for european options - no early exercise

* It is based on log-normal probability distribution.

So it's clear that the basic equation does not account for many real world conditions. The result is that there are many different versions of Black-Scholes formulas that offset different assumptions but no single formula works in all cases.

Also, the equation used the log-normal distribution for stock price movements. Unfortinately, there are no known statistical distribution models that perfectly describe stock price movements. The log-normal is the closest. This means that there are errors in black-scholes, especially in the edges.

There are lot more quiet days in the real market than the log-normal curve would predict and more volatile days -

i.e. given 1000 days of stock price movements, 3-stardard deviations should cover 99.74% of all stock price movements, covering 997.4 days, leaving 2.6 days that can be expected to fall outside the range, with the market price movement truly going crazy.

But in the real market, these crazy price swings can be as much as four times higher than what the model predicts. These are the days when the options writer goes bankrupt. The result is that deep out of the money options will have higher implied volatility than at the money options.

There are no perfect hedges in options. The only perfect hedge is a position that is fully closed and out of the market. Any open position, so long as it remains open, has exposure to possibility of loss. Note: Delta neutral positions will lose money given enough time. Because in the real world, there are bid/ask spreads, slippage, commissions and higher interest rates etc., which all must be overcome before profit.

The real key to Black-Scholes is the edge* - because this is what Black-Scholes is based on.

* What Black-Scholes essentially does is to compute the fair value (fair meaning zero-sum game, no winners or losers on either side, buyer or seller) of an option based on volatility outlook.

With that said, here's a journey of a young grad student (at the time) who embarked on a trading journey using leverage through housing crisis, with everything hanging out, guts and all - a fascinating read.

Summary: Econ grad student applies Mortgage Your Retirement theory at the top of the last bull market, starting around 2x leverage, loses $210K of borrowed money, and is forced is to sell what's left of his portfolio at S&P 821 in November 2008. The complete wipeout results in a reflective period where he recollects the circumstances that led him to adopt this strategy, some of which will be included in a book. He spends five weeks in Asia and begins writing about how risk and progress can be framed. Returning to the US, he slashes his expenses, finds several ways to increase income, earns 914% on the IRBLTG Fund, and pays off all his high interest credit card debt. Net worth tracker continues to be updated.

https://www.bogleheads.org/forum/viewto ... =10&t=5934