Binary bets and odds pricing

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binus

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Hello, I am new here and heard about binary bets only in the last few days.

Although I understand the way it works, I would like to know the maths used for pricing these bets. This may have been posted before, but I could not find any formula. Underlying price, time to expiry, volatility must come into play but I have yet to figure it out ... If someone had FTSE 100 cash price on a 10 mn basis together with say end of day FTSE up binary taken at the same time that should be fairly easy to correlate. Unfortunately , I can't get these as I am on evening Internet connection only :cry: I
 
binus said:
Hello, I am new here and heard about binary bets only in the last few days.

Although I understand the way it works, I would like to know the maths used for pricing these bets. This may have been posted before, but I could not find any formula. Underlying price, time to expiry, volatility must come into play but I have yet to figure it out ... If someone had FTSE 100 cash price on a 10 mn basis together with say end of day FTSE up binary taken at the same time that should be fairly easy to correlate. Unfortunately , I can't get these as I am on evening Internet connection only :cry: I
Click to expand...

too easy.....

Up Bin = N(d2)
down Bin = 1-N(d2)

where d2 is the standrad d2 used in BS, d2 = [log(S/K) - (vol^2)*t ] / [vol*sqrt(t)]

any other Q's????
 
I'd like to dig up this one again. OK I have resolved the BS equation to this Excel formula. The calculates the call option premium.

= S*NORMSDIST((LN(S/K)+(Rf+V^2/2)*T)/(V*SQRT(T))) - K*EXP(-Rf*T)*NORMSDIST((LN(S/K)+(Rf+V^2/2)*T)/(V*SQRT(T))-V*SQRT(T))

Where:-

S = current Stock price
K = strike price
Rf = Risk-free rate
V = Volatility
Expiry = Expiry date
T = Time to expiry (in years)

I have fiddled around with the forumula to try and replicate a binary. But none are replicating like I expected. Including the previous posting. Any body help. I am probably being a wally somewhere but can't see it.

Robertral said:
too easy.....

Up Bin = N(d2)
down Bin = 1-N(d2)

where d2 is the standrad d2 used in BS, d2 = [log(S/K) - (vol^2)*t ] / [vol*sqrt(t)]

any other Q's????
Click to expand...
 
Scripophilist said:
I'd like to dig up this one again. OK I have resolved the BS equation to this Excel formula. The calculates the call option premium.

= S*NORMSDIST((LN(S/K)+(Rf+V^2/2)*T)/(V*SQRT(T))) - K*EXP(-Rf*T)*NORMSDIST((LN(S/K)+(Rf+V^2/2)*T)/(V*SQRT(T))-V*SQRT(T))

Where:-

S = current Stock price
K = strike price
Rf = Risk-free rate
V = Volatility
Expiry = Expiry date
T = Time to expiry (in years)

I have fiddled around with the forumula to try and replicate a binary. But none are replicating like I expected. Including the previous posting. Any body help. I am probably being a wally somewhere but can't see it.
Click to expand...

Here you go

Bin Up = Normsdist( (LN(S/K) - (0.5*(vol^2)*tau)) / (vol*sqrt(tau)) )

where S is the stock price,
where K is ur strike price (or pivot point),
where vol is your volatility,
where tau = (T - t) / 365, i.e T-t is the number of days until expiry

I've assumed zero risk free rate

Is this any good????
 
The above computes the BS call price, which does not give you a binary price!!!!!!
If you want the binary derivation give me a shout. Here is the equation for a simple binary up bet:


Bin Up = Normsdist( (LN(S/K) - (0.5*(vol^2)*tau)) / (vol*sqrt(tau)) )

where S is the stock price,
where K is ur strike price (or pivot point),
where vol is your volatility,
where tau = (T - t) / 365, i.e T-t is the number of days until expiry

I've assumed zero risk free rate

Bin Down = 1- Bin Up

Is this any good????
 
Thanks, I was there but that confirms my thought process. I guess the real trick (As with the original BS) is to define volatility.
 
I suppose, mulling this over, probably the best way to approach the volatility question is to turn it on it's head and work out the implied volatility and then you can make a judgement on it.

I keep looking at this and wondering why I didn't spot it before. I feel a bit daft looking at it now.

I've resolved the PUT option as =K*EXP(-Rf*T)*NORMSDIST(-D2)-S*NORMSDIST(-D1)

And therefore this is obvious how to calculate the down Binary.
 
Last edited:
Scripophilist said:
I suppose, mulling this over, probably the best way to approach the volatility question is to turn it on it's head and work out the implied volatility and then you can make a judgement on it.

I keep looking at this and wondering why I didn't spot it before. I feel a bit daft looking at it now.

I've resolved the PUT option as =K*EXP(-Rf*T)*NORMSDIST(-D2)-S*NORMSDIST(-D1)

And therefore this is obvious how to calculate the down Binary.
Click to expand...

Errmmmm what are you trying to do here? The binary price or an option price?

Try a vol of 16% in yuor binary......your price should be bounded on [0,1] or [0,100] if u multiply by 100

There is no point backing out the vol for an option as it's going to be the wrong vol.....try historical vol and get a feel for where the vol shoudl be on a daily basis
 
Just thinking out loud really. I've worked out the binary after realising I was brain dead so thanks for you help.

I hadn't thought about the fact your couldn't invert the cum norm distribution and had been working on messing around with the numbers for the volatility.

At the moment I am just messing around with the equation nothing else. No specific goal.

Again thanks for the sounding board.
 
Hi

Been following the formula stuff and have it in Excel. I can't get any good looking values out of it. Any chance of an example with the values for the parameters you have used for say a daily up/down on the FTSE or Dow?

Thanks
 
From the posts on this forum you should be able to get the formula into Excel easy enough. They seem to work pretty well for me.
 
Scripophilist said:
From the posts on this forum you should be able to get the formula into Excel easy enough. They seem to work pretty well for me.
Click to expand...

Yes I have the formula in Excel, what value do I need for volatility on the daily up/down FTSE? How do I enter the time, should I use seconds to expiry?

Thanks
 
time is in days i think... anyone any idea about how to enter the time - i.e. during market hours is the time remaining = mins remaining/market mins per day ??? How do you deal with pre-market?
 
nebuchadnezzar said:
time is in days i think... anyone any idea about how to enter the time - i.e. during market hours is the time remaining = mins remaining/market mins per day ??? How do you deal with pre-market?
Click to expand...

time to expiry = expiry time - tiem now = T-t (this is annulised)

in excel use the following for time to expiry =("09/02/2005 16:30:00" - now())/365

Pre market?????? as the binaries are based on a market that opens at 0800hrs (FTSE) then any price that your binary model pumps out before that time won't mean anything........
 
nebuchadnezzar said:
time is in days i think... anyone any idea about how to enter the time - i.e. during market hours is the time remaining = mins remaining/market mins per day ??? How do you deal with pre-market?
Click to expand...

Well with FTSE strike at 4995.5 an current price 4985, Volatility 10%. The resultant goes down only if I increase the time left (tau). Any ideas?
 
binus said:
Hello, I am new here and heard about binary bets only in the last few days.

Although I understand the way it works, I would like to know the maths used for pricing these bets. This may have been posted before, but I could not find any formula. Underlying price, time to expiry, volatility must come into play but I have yet to figure it out ... If someone had FTSE 100 cash price on a 10 mn basis together with say end of day FTSE up binary taken at the same time that should be fairly easy to correlate. Unfortunately , I can't get these as I am on evening Internet connection only :cry: I
Click to expand...

the math is somewhat more complicated than you imagine with black scholes option pricing formula being utilised with a twist - that is to say reiner rubinstein adjustments. If you are a mathemetician, it works fair enough - the rest of us make do with trying to make money on our view!
 
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