Journal article
Acturarial bridges to dynamic hedging and option pricing
Insurance, mathematics & economics, Vol.18(3), p.183
11/01/1996
Abstract
The method of Esscher (1932) transforms is extended to changing probability measures in a certain class of stochastic processes that model security prices. According to the Fundamental Theorem of Asset Pricing, security prices are calculated as expected discounted values with respect to an equivalent martingale measure. If the measure is unique, it is obtained by the method of Esscher transforms; if not, the risk-neutral Esscher measure provides a unique and transparent answer, which can be justified if there is a representative investor maximizing his expected utility. Self-financing replicating portfolios are constructed in the (multidimensional) geometric shifted (compound) Poisson process model, in which the classical (multidimensional) geometric Brownian motion model is a limiting case. With the aid of Esscher transforms, changing numeraire is explained concisely. The way certain American type options on two stocks can be priced is shown. Applying the optional sampling theorem to certain martingales, several explicit pricing formulas without having to deal with differential equations are obtained.
Details
- Title: Subtitle
- Acturarial bridges to dynamic hedging and option pricing
- Creators
- Hans U GerberElias S W Shiu
- Resource Type
- Journal article
- Publication Details
- Insurance, mathematics & economics, Vol.18(3), p.183
- Publisher
- Elsevier Sequoia S.A
- ISSN
- 0167-6687
- eISSN
- 1873-5959
- Language
- English
- Date published
- 11/01/1996
- Academic Unit
- Statistics and Actuarial Science
- Record Identifier
- 9984257730502771
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