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Monotonicity And Convexity Of Option Prices Revisited

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  • Masaaki Kijima

Abstract

The Black‐Scholes option price is increasing and convex with respect to the initial stock price. increasing with respect to volatility and instantaneous interest rate, and decreasing and convex with respect to the strike price. These results have been extended in various directions. In particular, when the underlying stock price follows a one‐dimensional diffusion and interest rates are deterministic, it is well known that a European contingent claim's price written on the stock with a convex (concave. respectively) payoff function is also convex (concave) with respect to the initial stock price. This paper discusses extensions of such results under more general settings by simple arguments.

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  • Masaaki Kijima, 2002. "Monotonicity And Convexity Of Option Prices Revisited," Mathematical Finance, Wiley Blackwell, vol. 12(4), pages 411-425, October.
    • Handle: RePEc:bla:mathfi:v:12:y:2002:i:4:p:411-425
    DOI: 10.1111/j.1467-9965.2002.tb00131.x
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    Cited by:

    1. Kanniainen, Juho & Piché, Robert, 2013. "Stock price dynamics and option valuations under volatility feedback effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(4), pages 722-740.
    2. Erik Ekstrom & Johan Tysk, 2006. "Convexity preserving jump-diffusion models for option pricing," Papers math/0601526, arXiv.org.
    3. Mele, Antonio, 2004. "General Properties of Rational Stock-Market Fluctuations," Economics Series 153, Institute for Advanced Studies.
    4. Eric Rasmusen, 2004. "When Does Extra Risk Strictly Increase the Value of Options?," Finance 0409004, University Library of Munich, Germany.
    5. Jonas Al-Hadad & Zbigniew Palmowski, 2020. "Perpetual American options with asset-dependent discounting," Papers 2007.09419, arXiv.org, revised Jan 2021.
    6. Курочкин С.В., 2016. "Выпуклость Множества Цен Опционов Как Необходимое И Достаточное Условие Отсутствия Арбитража," Журнал Экономика и математические методы (ЭММ), Центральный Экономико-Математический Институт (ЦЭМИ), vol. 52(2), pages 103-111, апрель.
    7. Martin Keller-Ressel, 2019. "The classification of term structure shapes in the two-factor Vasicek model -- a total positivity approach," Papers 1908.04667, arXiv.org, revised Jun 2021.
    8. Juho Kanniainen & Robert Pich'e, 2012. "Stock Price Dynamics and Option Valuations under Volatility Feedback Effect," Papers 1209.4718, arXiv.org.

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