Probability of a stock to follow a specific pathway

[taowave]

Judging by the responces in this thread,Good luck finding an offer

I want to buy a lookback put on T-Rex's career.

 

[taowave]

What's the HV of the stock??

Present a historical price return distribution of the stock,and pray the past is an indicator of the future

Or simply hire a quant well versed in Tradex-physics

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?

 

[newwurldmn]

suppose it’s 200bc. How do you explain an apple falling from a tree.

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?

 

[taowave]

Lol.... Without bouncing off the ground back to the top branch

suppose it’s 200bc. How do you explain an apple falling from a tree.

 

[Tradex]

I would use a Monte Carlo Simulation using a GARCH time series with bootstrap for the distribution of daily changes.

In other words you are using brute force to predict the possible behavior of a semi-random event (the up and down movements of a stock).

Have you tried a similar approach in the past?

 

[newwurldmn]

I would use a Monte Carlo Simulation using a GARCH time series with bootstrap for the distribution of daily changes.

I would use a binomial or trinomial tree with local vols implied by the surface and run montecarlo on that.

 

[destriero]

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.

There are people on this board would could price it for you, but you're known, so as a buyer of the structure you're fucked bc the mkt would be skewed against you.

There is no utility in pricing it the way you're asking. The complexity would make the market stupid wide.

You buy a $90 touch.

You buy a $110 no touch (sell a touch).

**** Barrier is touched ****

You buy an $80 no touch (sell a touch).

 

[JamesJ]

In other words you are using brute force to predict the possible behavior of a semi-random event (the up and down movements of a stock).

Have you tried a similar approach in the past?

Did my BSc thesis in applied mathematics on something like that.
Up/Downs are random and not iid.

With computational power cheap and fast, brute force looks fine to me, especially given the complexity with possible intraday barrier breaks, for which one imho has to interpolate or use smaller time steps than daily with more sophisticated distributions (ie. a 5min change in first half hour will be more than around noon).

 

[destriero]

And you can do this Monday on binary.com. You're $100MM away from having an ISDA or $10MM from trading on a PB's ISDA, so what exactly is the point?

 

[destriero]

Did my BSc thesis in applied mathematics on something like that.
Up/Downs are random and not iid.

With computational power cheap and fast, brute force looks fine to me, especially given the complexity with possible intraday barrier breaks, for which one imho has to interpolate or use smaller time steps than daily with more sophisticated distributions (ie. a 5min change in first half hour will be more than around noon).

Intraday barrier breaks would kill it. These are PD exotics.