Numerical example: How can I calculate the probability of the complex event below to occur within a particular duration of time. If the event does not occur it is classed a failure. The current price of a stock called XYZ is $100 (i.e delta of +-0.5 for an $100 strike call/put) First Condition: I need the stock to touch $90. Before touching the $90 any price may be touched that is less than $110. If $110 or higher is touched before the $90 that is a failure. NOTE: When XYZ at the start was $100; A $90 put strike had a delta of -0.27 and A $110 call strike had a delta of +0.27. Second Condition: If the first Condition is satisfied(i.e $90 had just been touched without touching $110 first), then now XYZ can touch any price, even $110 or above but the new restriction is that it can not touch $80. NOTE: Because price just touched $90 deltas have changed. However at the start when XYZ was at $100 the $80 put strike would have a delta of -0.21. Delta is approximately twice the probability of touch. I need an approximate answer to what the probability of the stock to follow the complex part is going to be? Thanks for your contributions.
Tricky question. Assuming the stock is moving at random, it has a 50% chance of touching $90 and a 50% chance of touching $110, a 10% move in both cases (from its initial $100 price). Of course if the stock is already in a downtrend (below some moving average for instance), it will probably touch $90 first. Keep in mind that financial markets are not random (they "trend"), so it is almost impossible to calculate the probability of the events you are describing.
I plot the distribution of daily price changes in % for about 5000 stocks. It looks normal with center at 0. I plot frequency distribution of how long a stock can stay above a moving average. As you can see, about 90% can't stay about 50MA within 10 days. I have tried 30 and 40 MA and they show similar trend. Patient! Look at the industry trend. They tend to trend together. This just an example and not a recommendation. When charts show nice trend be weary... VIAC and DISCA.
The option markets ,I.e skew and all that fun stuff would disagree with your assessment.. Are you familiar with basic option theory and probability of touch??
You forgot to mention that while the distributions of daily and even monthly stock returns are more or less symmetric about their means, the tails are fatter than would be expected with normal distributions. And this has been observed in every freely-traded financial market, including (but not limited to) the Futures and the Forex markets. This explains why simple trend-following techniques work.
Yes, but here we are simply talking about the probability of a stock moving 10% up or down. Can you calculate it?
this is all wrong. it’s possible to price the implied probability of this using the vol surface but someone with more knowledge than I about exotics would have to chime in.