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 Actualization: a basic principle
Issued on July 11 2011 par Strategies Options
Actualization is a mathematical process which makes possible to relativize financial flows.
I – The facts:
Financial industry, like every industry, makes payments and cashings of various amounts and over various periods. In order to appreciate these withdrawals and these cashings, one thus needs to price today how much these flows are worth. #A4229F II - Basic element for arbitrage: interest rate a - And if interest rates were zero… If interest rates are nil, then the value of a financial flow on an unspecified date would have the same value as it has today. The fact that the rates are not zero modifies the rules. b - The fact that interest rates are not zero implies… An amount X today does not have the same value as this same amount paid in 1 year for example. Indeed, to have to withdraw X today requires to have X on its account. To withdraw in 1 year requires to have today only one X' amount such as X' = X / ( 1 + r ) where r is the 1 year risk-free rate for example. To grab it, it is enough to think that having today X', one can invest them at the rate r during 1 year and to own finally in 1 year: [ X / ( 1 + r ) ] . ( 1 + r ) = X the expected amount. Thus the value of X in 1 year knowing risk-free rate r is today worth X' . Example : Using rate= 5%, $ 1000 in 1 year are worth today 1000 / ( 1 + 5% ) = 1000 / ( 1.05 ) = $ 952.381 If one does invest $ 952.381 with a annualized rate set at 5%, in 1 year it will be : 952.381 . ( 1 + 0.05 ) = 952.381 . ( 1.05) = $ 1000. Next : Actualization: A Basic Principle #2 Previous : Glossary OPTIONS 101 - INDEX OPTIONS 101 - CHAPTER I OPTIONS 101 - CHAPTER II OPTIONS 101 - CHAPTER III OPTIONS 101 - CHAPTER IV OPTIONS 101 - CHAPTER V OPTIONS 101 - CHAPTER VI Strategies Options |
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