SIAM Digital Library
 
 
 

You are not logged in Logged Out Log In

Theory of Probability and its Applications / Volume 39 / Issue 1

Theory Probab. Appl. 39, pp. 61-102 (42 pages)

Toward the Theory of Pricing of Options of Both European and American Types. II. Continuous Time

A. N. Shiryaev, Yu. M. Kabanov, D. O. Kramkov, and A. V. Mel’nikov

Full Text: Download PDF | Buy PDF (US$25) | View Cart
In the first part of the paper [29] the options pricing theory was developed under the assumption that a $(B,S)$-market is discrete (in space and in time). It is assumed in the present text that a $(B,S)$-market is operating continuously in time. The riskless bank account$B = (B_t )_{t \geqq 0} $ is evolving according to the “compound interests” formula (1.1), and a risky stock price $S = (S_t )_{t \geqq 0} $ is governed by geometric Brownian motion (1.4).
The “martingale” pricing theory is presented for fair (rational) option price, hedging strategies, and rational expiration times. The Black-Scholes formula for a standard European call option is derived. The paper considers a number of other particular examples of European as well as American options.

KEYWORDS

PUBLICATION DATA

ISSN

0040-585X (print)  
1095-7219 (online)

Publisher

$abstract.society.value is a Member of CrossRef Society for Industrial and Applied Mathematics

ARTICLE DATA

History
Received July 05, 1993
Digital Object Identifier
http://dx.doi.org/10.1137/1139003

For access to fully linked references, you need to log in.

Close

Your Recent History Recent History Help

Recently Viewed

  1. Toward the Theory of Pricing of Options of Both European and American Types. II. Continuous Time
  2. Models for Option Prices
  3. A New Look at Pricing of the ”Russian Option“
  4. SISC Redefined
  5. Reactive Molecular Dynamics: Numerical Methods and Algorithmic Techniques
© SIAM By using SIAM Publications Online you agree to abide by the Terms and Conditions of Use. Banner art adapted from a figure by Hinke M. Osinga and Bernd Krauskopf (University of Bristol, UK).
close