Changes of numéraire, changes of probability measure and option pricing
Geman, Hélyette (1995) Changes of numéraire, changes of probability measure and option pricing. Journal of Applied Probablity 32 (2), pp. 443-458. ISSN 0021-9002.
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 numéraire changes, this feature, besides providing a financial interpretation, permits efficient selection of the numéraire 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 numéraire change is illustrated by many examples, among which the extension to a stochastic interest rates framework of the Margrabe formula, Geske formula, etc.
Metadata
| Item Type: | Article |
|---|---|
| School: | Birkbeck Faculties and Schools > Faculty of Science > School of Computing and Mathematical Sciences |
| Depositing User: | Sarah Hall |
| Date Deposited: | 23 Jun 2020 08:20 |
| Last Modified: | 09 Aug 2023 12:48 |
| URI: | https://eprints.bbk.ac.uk/id/eprint/32347 |
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