Journal Article10.2307/3215299
Changes of numéraire, changes of probability measure and option pricing
TL;DR: In this paper, the authors show that many other probability measures can be defined in the same way to solve different asset-pricing problems, in particular option pricing, and this feature, besides providing a financial interpretation, permits efficient selection of the numeraire appropriate for the pricing of a given contingent claim and also permits exhibition of the hedging portfolio, which is in many respects more important than the valuation itself.
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Abstract: The use of the risk-neutral probability measure has proved to be very powerful for computing the prices of contingent claims in the context of complete markets, or the prices of redundant securities when the assumption of complete markets is relaxed. We show here that many other probability measures can be defined in the same way to solve different asset-pricing problems, in particular option pricing. Moreover, these probability measure changes are in fact associated with numeraire changes, this feature, besides providing a financial interpretation, permits efficient selection of the numeraire appropriate for the pricing of a given contingent claim and also permits exhibition of the hedging portfolio, which is in many respects more important than the valuation itself. The key theorem of general numeraire change is illustrated by many examples, among which the extension to a stochastic interest rates framework of the Margrabe formula, Geske formula, etc.
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Option pricing: A simplified approach☆
TL;DR: In this paper, a simple discrete-time model for valuing options is presented, which is based on the Black-Scholes model, which has previously been derived only by much more difficult methods.
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