Q: Find a Black-Scholes 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).
I thought about the Black-Scholes pricing for the barrier range. Appreciate advice.
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