Options probability...

[Rossini]

Hello all.

Firstly, I want to say that I know absolutely nothing about options (and because of this I wouldn't even contemplate trading them ;-).

But what I do want to know how to do is to be able to convert an option price into a %. In other words I want to be able work out what the market perceives the probability is of the option expiring in the money (or not). My goal is to be able to see what the market perceives the probability is of X happening; and use this additional information to help make trading decisions.

I know there are things called digital options (which I think is something similar?) but I want to be able to work this out on a variety of smaller stocks most of which I don't think there would be a digital option for anyway....

Can anyone help? ;-)

Ross

 

[Martinghoul]

You can obtain the risk-neutral PDF (probability density function) by differentiating the Price(strike) function twice. There's other methods, but this one is probably the most comprehensive.

 

[Jerry Westerby]

you might find this interesting (the pdf's at the bottom). Or you might not.

Bank of England | Statistics | Financial Market Data | Option-Implied Probability Density Functions for Short-term Sterling Interest Rates and the FTSE 100

 

[daveyc]

to get a quick look at probability of an option expiring in the money is to just simply look at the delta. so if you have a +-.10, the market is saying there is a 10% chance of your stock expiring in the money.

 

[Martinghoul]

to get a quick look at probability of an option expiring in the money is to just simply look at the delta. so if you have a +-.10, the market is saying there is a 10% chance of your stock expiring in the money.

That's actually not quite right...

 

[daveyc]

That's actually not quite right...

its close enough, no?

 

[Martinghoul]

its close enough, no?

Yeah, I think for vanilla stuff should be OK, but I always make sure that I remember that it's a shortcut that occasionally fails most spectacularly. So just use w/caution, is all...

 

[daveyc]

also, tos also has a 'probability of expiring' column which pretty much lines up with the deltas. but we all know the market moves and that 10 delta you sold could easily fall in the money or the volatility increase could take you out of that trade with big losses.

 

[Hoggums]

Some simple stats for you

Look at At the money options.. e.g.

If the FTSE is at 5500 and the Jan options cost 150 points to buy both sell and put at strike 5500. Then there is a (calculated) risk of 50% that the index will fall between 5200-5800 and a 50% chance that the index will be outside this range at expiry. (Jan 20th)

Formula is Strike +/- (put premium + call premium) = 5200-5800

This probably is related to the index at expiry only.

Statistically there is a 75% chance that the index will wonder outside the 5200-5800 range during the lifetime of the options.

Obviously these are all estimates which take into account current volatility. the greater the volatility then the more expensive the options and the wider the range.

 

[Jerry Westerby]

HCv2.0 ?

 

[slik]

I would disagree that the example given indicates a 50% of the index being outside this range. Surely the straddle is a tick interpretation of the standard deviation priced into a given period => at should indicate 65% probability of remaining in this range at expiration no?

Beyond that, delta is the widely accepted approximation of an option expiring ITM....... another can of worms is how you calculate delta; I can tell you black scholes partials is not the hedged deltas for pros...

 

[Petrescu]

It's easy. Just look at the current price of the underlying (not the option). The options market perceives the current price is the most likely price of the underlying at any time in the future. next look at the implied volatility. If it is .4 or 4 it means there is a 2 in 3 chance (1 standard deviation) the underlying will be somewhere between -40% lower or +40% higher than current price in 1 years time. next, ask yourself if you strongly disagree. If you do than make a trade.

Hello all.

Firstly, I want to say that I know absolutely nothing about options (and because of this I wouldn't even contemplate trading them ;-).

But what I do want to know how to do is to be able to convert an option price into a %. In other words I want to be able work out what the market perceives the probability is of the option expiring in the money (or not). My goal is to be able to see what the market perceives the probability is of X happening; and use this additional information to help make trading decisions.

I know there are things called digital options (which I think is something similar?) but I want to be able to work this out on a variety of smaller stocks most of which I don't think there would be a digital option for anyway....

Can anyone help? ;-)

Ross

 

[Petrescu]

I should have said "within" 1 years time not "in" 1 years time.

 

[vergis92]

Delta itself is a direct probability metric of how market makers perceive whether the Option will expire in the money, a Delta of 10 reflects a 10% probability, a Delta of 70 reflects a 70% probability etc.

it's only statisics based on the total number of stocks and past data, similar to the way that car insurance companies use statistics to assess the risk a client driver poses to them, and price his premums accordingly, I don't think Delta as a probability metric is useful at alll when trading a single stock, it cannot predict anything, much like car insurance premiums cannot predict who will crash next

 

[toomuch]

Option trades are like a teeter totter. IF you have a high win/loss % probability that means your risk/reward sucks. IF you have a great risk/reward possibility, that means your win/loss % probability sucks. Finding the middle ground is where you want to be.