Access the full text.
Sign up today, get DeepDyve free for 14 days.
Hyer Hyer, Lipton‐Lifschitz Lipton‐Lifschitz, Pugachevsky Pugachevsky (1997)
Passport to successRISK, 10
El Karoui El Karoui, Quenez Quenez (1995)
Dynamic programming and pricing of contingent claims in an incomplete marketSIAM Journal of Control and Optimization, 33
Andersen Andersen, Andreasen Andreasen, Brotherton‐Ratcliffe Brotherton‐Ratcliffe (1998)
The passport optionJournal of Computational Finance, 1
Hajek Hajek (1985)
Mean stochastic comparison of diffusionsZeitschrift fuer Wahrschein‐lichkeitstheorie verw Gebiete, 68
El Karoui El Karoui, Jeanblanc Picque Jeanblanc Picque, Shreve Shreve (1998)
Robustness of the Black and Scholes formulaMathematical Finance, 8
Rubinstein Rubinstein (1983)
Displaced diffusion option pricingJournal of Finance, 38
Bensoussan Bensoussan, Crouhy Crouhy, Galai Galai (1994)
Stochastic equity volatility and the capital structure of the firmPhilosophical Transactions of the Royal Society of London, Series A, 347
Henderson Henderson, Hobson Hobson (2000)
Local time, coupling and the passport optionFinance and Stochastics, 4
Cox Cox, Ross Ross (1976)
The valuation of options for alternative stochastic processesJournal of Financial Economics, 3
Hobson Hobson (1998)
Volatility mis‐specification, option pricing and super‐replication via couplingAnnals of Applied Probability, 8
Bergman Bergman, Grundy Grundy, Wiener Wiener (1996)
General Properties of options pricesJournal of Finance, 51
In this paper, we provide a new proof of the result that option prices are increasing in volatility when the underlying is a diffusion process. This has been shown to hold for convex payoff, path‐independent options by El Karoui et al. and Hobson amongst others. The advantage of the new proof is that it can be extended to establish monotonicity results for path‐dependent payoffs where the payoff depends on the maximum (or minimum) of the asset price process. The techniques used to prove each of these results are mean comparison theorems of Hajek and coupling of stochastic processes. Using these results, and the connection between passport and look back options, we prove that the price of a passport option is increasing in volatility for general diffusion models for the asset price. It is shown that the seller of a passport option can super‐replicate if the volatility is overestimated, regardless of the strategy followed by the holder. Copyright © 2000 John Wiley & Sons, Ltd.
Applied Stochastic Models in Business and Industry – Wiley
Published: Oct 1, 2000
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.