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> Call-Put Parity : american style issue
 Call-Put Parity : american style issue
Issued on August 08 2010 par Strategies-options.com
Call-Put Parity is specifically set for european style options. What about american style ones ?
We saw that a long european style call added to a short european style put, same strike, same expiry was worth the spot funded by borrowing an amount corresponding to the strike.
I - Important case of american style option : early exercise The relationship above can be quite different with american style options. Early exercise make things to differ, because as long as an option is far from expiry, its value can't be zero. In case of early exercise for the long call or the short put, the value of that option is its payoff, that is S (spot) - K (strike). But the remainder is still worth something. II - Let's take a look at the call put parity delta Volatility is 30%, interest rate are set to 5% and the spot and strikes are $100. - a 1 year european style call is worth $14.23 - a 1 year european style put is worth $ 9.35 A portfolio set with a long call and a short put would be worth 14.23 - 9.35 = $4.88 that is Spot - K . exp( - rate * T ) = 100 - ( 100 * exp( - 0.05 * 1)). This portfolio has a delta that is always 1 or 100%   This same portfolio made of american style options would be worth: - a 1 year american style call is worth $14.23 - a 1 year american style put is worth $ 9.75 Portfolio=14.23 - 9.75 = $4.48. Equality doesn't hold anymore.  A remarkable aspect is the delta of this portfolio can be greater than 100% (117% at 69.83), because if one option is exercized, the second one still get a delta that is not zero, especially if the stock dropped down. Next : Call Put Symmetry Previous : Call-put Parity: A Typically European Relation Relationships Between Option Sensitivities - INDEXRelationships Between Option Sensitivities - CHAPTER I Relationships Between Option Sensitivities - CHAPTER II Relationships Between Option Sensitivities - CHAPTER III Strategies-options.com |
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