Call up and out down and out 

where 




, 


where 
w = The European option value S = The spot price of the underlying asset X = Strike price L = Lower Boundary U = Upper Boundary = Lower boundary curvature = Upper boundary curvature = Volatility of underlying asset b = Cost of carry r = Risk free rate t1 = End of monitoring period T2 = Expiry date M = The Cumulative bivariate normal density function N = The Cumulative normal density function 

Put up and out down and out 
where 





where 
w = The European option value S = The spot price of the underlying asset X = Strike price L = Lower Boundary U = Upper Boundary = Lower boundary curvature = Upper boundary curvature = Volatility of underlying asset b = Cost of carry r = Risk free rate t1 = End of monitoring period T2 = Expiry date M = The Cumulative bivariate normal density function N = The Cumulative normal density function 

See Also 
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