= 27d567bc2d48d9f40e9ccc20ea370b15)
Lumifer comments on When the uncertainty about the model is higher than the uncertainty in the model - LessWrong
You are viewing a comment permalink. View the original post to see all comments and the full post content.
= 783df68a0f980790206b9ea87794c5b6)
Loading…= b715d02e85f7b3b4ae65ca3d3e450868)
Subscribe to RSS Feed
Powered by Reddit
= f037147d6e6c911a85753b9abdedda8d)
You are viewing a comment permalink. View the original post to see all comments and the full post content.
Comments (78)
A stock closed at $100/share and opened at $80/share -- e.g. the company released bad earnings after the market closed.
There were no prices between $100 and $80, the stock gapped. Why is this relevant? For example, imagine that you had a position in this stock and had a standing order to sell it if the price drops to $90 (a stop-loss order). You thought that your downside is limited to selling at $90 which is true in the world of continuous prices. However the price gapped -- there was no $90 price, so you sold at $80. Your losses turned out to be worse than you expected (note that sometimes a financial asset gaps all the way to zero).
In the Black-Scholes context, the Black-Scholes option price works by arbitrage, but only in a world with continuous prices and costless transactions. If the prices gap, you cannot maintain the arbitrage and the Black-Scholes price does not hold.
Right, good explanation. Just to make it clearer in an alternate way, I would reword the last sentence:
Well, that's not quite what I mean.
There are many ways to derive the Black-Scholes option price. One of them is to show that that in the Black-Scholes world, the BS price is the arbitrage-free price (see e.g. here). The price being arbitrage-free depends on the ability to constantly be updating a hedge and that ability depends on prices being continuous.
If you change the Black-Scholes world by dropping the requirement for continuous asset prices, the whole construction falls apart. Essentially, the Black-Scholes formula is a solution to a particular stochastic differential equation and if the underlying process is not continuous, the math breaks down.
The real world, however, is not the Black-Scholes world and there ain't no such thing as a "Black-Scholes based strategy which was making you steady money".
If your function isn't continous you can't use Calculus and therefore you lose your standard tools. That means a lot of what's proven in econophysics simply can't be used.