[Guest]

Find a closed formula to price this fixed odds bet. I want to win N if over the next M days, the P has a high-low range (exceeding/not exceeding) Q points. For example: I get $50 if over the next 5 days the FTSE100 has a high-low range exceeding 2 points. For example, if the FTSE100 has a range of low=5,251.41 and high=5,253.94 over the next 5 days, I get $50 (because high – low = 2.53 > 2).

[Guest]

your example makes little sense, so it's hard to judge exactly what it is you want.

what i think your asking for is this.

you want the odds of P high - P low being more than Q over a given number of days, M.

well the first question would be, is P high - P low dependant on M, or not?

if not, then the P values will act like a coin toss. getting P high - P low on the 4th day,

compared to on the 5th day, would be no different. here then, you would most likely want it such that if

P high -P low > Q on any of the M days, you win the bet.

this would be the 1- (probability of P high -P low > Q on any particular day to the power of m).

if however P high - P low is dependant on M, then you want it such that P high - P low > Q exactly on the Mth day.

if this is the case then i'll need more info. (does the probability increase or decrease with M? by how much?)

Edited November 22, 2009 by phillip1882