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Binary Barrier Options

Down and in cash (at hit) or nothing (S>H):

Value: A5 η=1

Up and in cash (at hit) or nothing (S<H):

Value: A5 η=-1

Down and in asset (at hit) or nothing (S>H):

Value: (K=H) : A5 η=1

Up and in asset (at hit) or nothing (S<H):

Value: (K=H) : A5 η=-1

Down and in cash (at expiry) or nothing (S>H):

Value: B2+B4 η=1, =-1

Down and in cash (at expiry) or nothing (S<H):

Value: B2+B4 η=-1, =1

Up and in asset (at expiry) or nothing (S>H):

Value: A2+A4 η=1, =-1

Down and in asset (at expiry) or nothing (S<H):

Value: A2+A4 η=-1, =1

Up and out cash or nothing (S>H):

Value: B2-B4 η=1, =1

Down and out cash or nothing (S<H):

Value: B2-B4 η=-1, =-1

Up and out cash or nothing (S>H):

Value: A2-A4 η=1, =1

Down and out cash or nothing (S<H):

Value: A2-A4 η=-1, =-1

Down and in cash or nothing call (S>H):

Value: (X>H) : B3 η=-1

Value: (X<H) : B1-B2+B4 η=1, =1

Up and in cash or nothing call (S<H):

Value: (X>H) : B1 =1

Value: (X<H) : B2-B3+B4 η=-1, =1

Down and in cash or nothing call (S>H):

Value: (X>H) : A3 η=1

Value: (X<H) : A1-A1+A4 η=-1, =1

Up and in asset or nothing call (S<H):

Value: (X>H) : A1 =1

Value: (X<H) : A2-A3+A4 η=-1, =1

Down and in asset or nothing put (S>H):

Value: (X>H) : B2-B3+B4 η=1, =-1

Value: (X<H) : B1 =-1

Down and in cash or nothing put (S<H):

Value: (X>H) : B1-B2+B4 η=1, =-1

Value: (X<H) : B3 =-1

Down and in asset or nothing put (S>H):

Value: (X>H) : A2-A3+A4 η=1, =-1

Value: (X<H) : A1 =-1

Up and in asset or nothing put (S<H):

Value: (X>H) : A1-A2+A3 η=-1, =-1

Value: (X<H) : A3 =-1

Down and out cash or nothing call (S>H):

Value: (X>H) : B1-B3 η=1, =1

Value: (X<H) : B2-B4 η=1, =1

Up and out cash or nothing call (S<H):

Value: (X>H) : 0

Value: (X<H) : B1-B2+B3-B4 η=-1, =1

Down and out asset or nothing call (S>H):

Value: (X>H) : A1-A3 η=1, =1

Value: (X<H) : A2-A4 η=1, =1

Up and out asset or nothing call (S<H):

Value: (X>H) : 0

Value: (X<H) : A1-A2+A3-A4 η=-1, =1

Down and out cash or nothing put (S>H):

Value: (X>H) : B1-B2+B3-B4 η=1, =-1

Value: (X<H) : 0

Up and out cash or nothing put (S<H):

Value: (X>H) : B2-B4 η=-1, =-1

Value: (X<H) : B1-B3 η=-1, =-1

Down and out asset or nothing put (S>H):

Value: (X>H) : A1-A2+A3-A4 η=1, =-1

Value: (X<H) : 0

Up and out asset or nothing put (S<H):

Value: (X>H) : A2-A4 η=-1, =-1

Value: (X<H) : A1-A3 η=-1, =-1

where

where

,

,

, ,

where

S = Spot price of underling asset

X = Strike price

b = cost of carry

T = Time to maturity

= Volatility of underling asset

M = The Cumulative bivariate normal density function

N = The Cumulative normal density function

H = Barrier

 

See Also

oX_BinaryBarrier( ) Function

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