Efficient computation of option price sensitivities for options of American style
Having this extra flexibility means the American options generally trade at a premium to European options. For this reason, traders who value options theoretically will need to ensure that they use the correct pricing model for American options.
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The most common type of model used for options that have early exercise is the Binomial Model. Options that have a European exercise style mean that the buyer can only exercise the option at the expiration date of the contract. While almost all stock options are American style, all index option contracts are European styled. This is due to the complexities that would arise as a result of early exercising a cash index product.
American Option (Definition, Examples) | Top 2 Types of American Options
At the time of "exercise", every component stock price as well as the weight of each compared to the number of options, would need to be recorded. These values would then be used to determine the split of stocks at each strike price, which would be the component price at the time of exercised.
Administratively this is just too difficult for brokers to consider, which is why these products do not allow for early exercise. European options, however, are easier to price theoretically and are able to be price using Analytical models.
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Binomial models for option valuation - examining and improving convergence Dietmar P. Leisen , Matthias Reimer.
Option pricing: A simplified approach John C. Cox , Stephen A. Ross , Mark Rubinstein. Efficient computation of option price sensitivities using homogeneity and other tricks Oliver Reiss , Uwe Wystup. Foreign Exchange Risk. Risk Publications, London. Hakala , U. Deriving derivatives of derivative securities Peter Carr.
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