With no opinion on the stock,I would look to the option market to lay off the risk and exploit your bias. Perhaps 20 grand in premium gets me. a 40 k payout if the stock trades at 90... Why would i forget about the derivative market if I can pick you off?? It's market making 101...
Right, so your answer is simply: "I don't know any mathematical formula that will allow me to calculate the probability of a stock reaching a certain level by a certain date. Because if I had such a formula, I would be a billionaire by now".
there are formulas to calculate it. I said so earlier but I don’t know them. Exotics traders utilize them every say. You said there was no formula because option theories are biased to the short sellers and the market makers. I can tell you how our exotics traders did it but I couldn’t replicate it myself easily.
Surely you jest.... The correct answer is YOU don't know any formula..I have already spoon fed the answer to you.. It's options 101... You do realize you are in a thread on exotics,you don't know probability of touch,yet you keep on keeping on... Even worse you have no idea how market makers / bookmakers make money.. Listen to Clint in Dirty Harry.. "A man has got to know his limitations"... Last but not least,you should be the billionaire as you clearly have built a far superior mathematical framework than every quant known to man.. Which exotic structures do you favor,or should I say are mispriced???
In all seriousness I think you would benefit from reading some finance books. you aren’t a bad guy but your knowledge about forex and options will greatly improve. everyone knows that long term capital failed on a tail event. That doesn’t discount the black scholes model. Just like bill gates extra marital affairs don’t discount his success in business.
You want the formula,but you don't want it in a B.S. framework...OK,why dont you first tell us how you price double no touch utilising moving averages.. No disrespect,but why are you commenting on something clearly out if your comfort zone.. You are a directional trader, clueless to basic option theory,trying to prove a point on exotics... Things that make you go hmmmmm
I would use a Monte Carlo Simulation using a GARCH time series with bootstrap for the distribution of daily changes.
Will you give me a break with options? Options contracts in the US only exist since 1968 (and 1973 for black scholes). Suppose we are in 1955 and I ask you this question: What is the mathematical probability that this $100 stock will drop to $90 without touching $110 first, what would you answer?