donaldduke said:
Robertral,
You been quoting these formulas for some time now.. Its
a bit hard for us mere mortals (although i did get an A in maths
at Olevel) to grasp..
What would be more usefull would be a real worked example:
Lets say the the Dow is trading up 20 points from the open and
IG offer a binary bet for Dow to close up more than 50 points.
They quote a market 25(bid)-30(offer). Its two hours before the
close.
I buy at 30 offer expecting the Dow to close above 50 points from the open, i will make 70 if it does lose 30 if doesnt.
How would IG hedge this specific bet using options...
Or if its easier to explain a range bet like 50-60 points
that would be fine too.
To start with the formula I quoted before replicates a tight bull spread.
Think about a bull spread. If the strikes are close together then this will give you a binary?!?!?!?
My equation Binary = (1/k) * [Call(X+k) - Call(X)] is exactly the same. k is just the min difference between strikes for a given market.
[As an aside you can take the limit of k to 0 and incorporate the vol smile in there.....]
Lets say that the binary is for a market F an we want to price the binary with a strike of 105 using the following formula
Binary = (1/k) * [Call(X+k) - Call(X)]
where X = 100 (the binary strike, depending on how you derive the binary)
k is the difference in strike prices....
the 1/k multiplier is to normalise the payoff to 1 if S>X...just draw a payoff diagram for Call(X+k) - Call(X) and you will see you have to divide by the strike difference to get you 1 payoff.
I.e the options market has strikes of 95 100 105...I can replicate a binary by buying a 100 call and selling a 105 call....
Thing is with the above if the market is between 100 and 105 I have pin risk as I'm not gonna get my 0 or 1 pay off....I'm gonna get something in between…...this is where the lottery comes into play for the MM.....i.e sell something for 100 when it costs you 95....
It all depends on how volatile your market is
I can't give you exact numers for the sheaaaat you have quotes as I dont know the other parameters but I hope the following helps...
With the range binaries you have to use a truncated lognormal integral to price, using the lower and upper bounds (i,.e your range binary limits)...if you know stoch calc this will ring a bell...it's quite hard to write this stuff in this format...
exp(-rT)*E[a>S_T>b | S_t<T ] = ????
If it's pure pricing you want I can write you up a word document how price binaries and sheaaaat
For MM hedging on this sheaaaatt it all depends on the flow….you might get roughly equal amounts of punters buying options on each range within the package, thus it’s easy to hedge the books with a simply tight bull spread. It depends on the flow. Otherwise the MM would take a global view of the book.
Please give me a PM or whatever if this doesn’t make any sense, as I’m very happy to write a word doc to explain this stuff