Journal article
Martingale Approach to Pricing Perpetual American Options
ASTIN bulletin, Vol.24(2), pp.195-220
11/1994
DOI: 10.2143/AST.24.2.2005065
Abstract
The method of Esscher transforms is a tool for valuing options on a stock, if the logarithm of the stock price is governed by a stochastic process with stationary and independent increments. The price of a derivative security is calculated as the expectation, with respect to the risk-neutral Esscher measure, of the discounted payoffs. Applying the optional sampling theorem we derive a simple, yet general formula for the price of a perpetual American put option on a stock whose downward movements are skip-free. Similarly, we obtain a formula for the price of a perpetual American call option on a stock whose upward movements are skip-free. Under the classical assumption that the stock price is a geometric Brownian motion, the general perpetual American contingent claim is analysed, and formulas for the perpetual down-and-out call option and Russian option are obtained. The martingale approach avoids the use of differential equations and provides additional insight. We also explain the relationship between Samuelson's high contact condition and the first order condition for optimality.
Details
- Title: Subtitle
- Martingale Approach to Pricing Perpetual American Options
- Creators
- Hans U Gerber - Université de Lausanne, SwitzerlandElias S.W Shiu - The University of Iowa, U.S.A
- Resource Type
- Journal article
- Publication Details
- ASTIN bulletin, Vol.24(2), pp.195-220
- Publisher
- Cambridge University Press; Cambridge, UK
- DOI
- 10.2143/AST.24.2.2005065
- ISSN
- 0515-0361
- eISSN
- 1783-1350
- Number of pages
- 26
- Language
- English
- Date published
- 11/1994
- Academic Unit
- Statistics and Actuarial Science
- Record Identifier
- 9983985839502771
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