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Standard Barrier Pricing

Mertons (1973) and Reiner and Rubinstein (1991) formulae for pricing Standard barrier options:

where

,

 

,

 

,

 

"In" Barriers

Down and in call S >H

Cdown&in(X>H) = C+E =1, =1

Cdown&in(X<H) = A-B+D+E =1, =1

Up and in Call S<H

Cup&in(X>H) = A+E =-1, =1

Cup&in(X<H) = B-C+D+E =-1, =1

Down and in put S>H

Pdown&in(X>H) = B-C+D+E =1, =-1

Pdown&in(X>H) = A+E =1, =-1

Up and in put S>H

Pup&in(X>H) = A-B+D+E =-1, =-1

Pup&in(X>H) = C+E =-1, =-1

"Out" Barriers

Down and out call S >H

Cdown&out(X>H) = A-C+F =1, =1

Cdown&out(X<H) = B-D+F =1, =1

Up and out Call S<H

Cup&out(X>H) = F =-1, =1

Cup&out(X<H) = A-B+C-D+F =-1, =1

Down and out put S>H

Pdown&out(X>H) = A-B+C-D+F =1, =-1

Pdown&out(X>H) = F =1, =-1

Up and out put S>H

Pup&out(X>H) = B-D+F =-1, =-1

Pup&out(X>H) = A-C+F =-1, =-1

where

X = Strike price

T = Time to maturity

r = risk free rate

N = The cumulative normal distribution function

S = Sport price

H = Barrier

K = Predetermined cash payoff

 

See Also

oX_Barrier( ) Function

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