[PairTheBoard]

[ QUOTE ]
[ QUOTE ]
I'm suspicious of Black-Scholes. It concludes that the value of an option is independent of any Trend in the stock, and as I see it does so by assuming an infinite bankroll that allows infinite hedging if the Trend goes against you. Since the Planet's entire options market is based on this Theorum you can actually get bets down if you want to gamble on a flaw.

PairTheBoard

[/ QUOTE ]

BS is not an empirical theory, even though it sounds like it means to be. Essentially BS says that a stock's "volatility" determines the value of its options. But in practice, there is no meaningful empirical definition of "volatility". Traders use "implied volatilities". What this means is that instead of trying to observe some kind of empirical volatility (eg actual standard deviation of underlying's returns over some period), they pick their price and work backwards to _derive_ the (implied) volatility. It's like saying I have a theory that the "M" characteristic determines how fast a person runs. But the only way for me to determine people's "M"s is to have them run and see how fast they are. You'll find this kind of analysis is very typical in economics (eg revealed preference theory), and yet they're still allowed in universities. BS actually is very useful (unlike most econ), because it allows you to compare related options and control complex hedging strategies with a single parameter. But if you go look up some options prices in the market, you'll see that every option on a single stock trades at a different implied volatility, and they bounce around constantly. So there is no sense in which you might "beat" BS--BS in practice takes market price as in input, it doesn't determine it.

Also, BS does not assume an infinite bank roll.

[/ QUOTE ]

Here's the thing that I don't get. If there is a trend in the stock - just like volatility, something you couldn't know until after the fact - it would theoretically not affect the value of the option, other than by how it affects the volatility. For example, it the trend has the stock doubling in a month then the option is worth more because a doubling stock has more volatilty than a flat one. But the high volatility due to the doubling trend is equally high volatilty for both puts and calls. The theory seems to imply that a put in such a stock is worth just as much as a call. Makes no sense.

PairTheBoard