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Joint high-low probability of geometric Brownian motion

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created by: Thijs van den Berg (http://www.sitmo.com)
Joint high-low probability of geometric Brownian motion equation

The probability that the high and the low of an underlying are within the range [L,H]. The underlying behavior is geometric Brownian motion with a yield (drift) \mu, volatility \sigma, and has an initial value of S_0

List of symbols

Probability of x
Start value of the geometric Brownian motion
T End of the interval of which the high and low are measured
H High
L Low
Y Yield of the geometric Brownian motion
Volatility of geometric Brownian motion

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