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Binary-Vanilla relationships
Issued on July 01 2011 par Strategies-options.com

Binary options can be expressed with vanilla ones.
Binary options can be expressed with vanilla ones.



I - Using Black & Scholes we get

Call = S . N( d1 ) - ( exp( - r . T ) ) . K . N( d2 )
Put = - S . N( - d1 ) + ( exp( - r . T ) ) . K . N( - d2 )

We know that
ΔCall = N( d1 )
ΔPut = - N( - d1 )

If we call
CB the binary call
PB the binary put



II - Black & Scholes and the binary options

CB = ( exp( - r . T ) ) . K . N( d2 )
PB = ( exp( - r . T ) ) . K . N( - d2 )

Hence,
Call = ( ΔCall . S ) - ( K . CB)
Put = ( ΔPut . S ) + ( K .PB )

An easy way to find Binary options value using vanilla's ones is:

CB = ( ΔCall.S - Call ) / K
PB = ( -ΔPut.S + Put ) / K





Next : Binary Option : Delta
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Other Derivatives - INDEX
Other Derivatives - CHAPTER I
Other Derivatives - CHAPTER II
Other Derivatives - CHAPTER III
Other Derivatives - CHAPTER IV

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