A quick math type question here. Is it possible to get the price of a ‘No Touch and One Touch ‘ option, using the delta of vanilla options? Assuming the binary options(i.e No Touch/ One Touch) are priced between 0$ and 100$. So an event with 50% probability would cost 50$. It is also said that 2*delta=prob. of Touch approximately, not sure how accurate it is. The example below is a complex combination of One Touch and No Touch options. Ex: A stock current price is at 100$(delta 0.5). What is the probability that the stock price would never touch 115$(delta 0.27), but must touch 85$(delta 0.27) but after 85$ is touched it never return back to or above 100$ throughout the life of the option?
I don’t expect exact answers, or complex derivations. I just want to know if there simple explanations using basic mathematical and statistical concepts. For example, using the basic blue and black balls in a bag probability concept in math/statistics. Simply put approximations to perhaps the right answer.