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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. Copyright 2002 Blackwell Publishers.

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  • Masaaki Kijima, 2002. "Monotonicity And Convexity Of Option Prices Revisited," Mathematical Finance, Wiley Blackwell, vol. 12(4), pages 411-425.
  • Handle: RePEc:bla:mathfi:v:12:y:2002:i:4:p:411-425
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    File URL: http://www.blackwell-synergy.com/doi/abs/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," LSE Research Online Documents on Economics 24701, London School of Economics and Political Science, LSE Library.
    4. Juho Kanniainen & Robert Pich'e, 2012. "Stock Price Dynamics and Option Valuations under Volatility Feedback Effect," Papers 1209.4718, arXiv.org.
    5. Eric Rasmusen, 2004. "When Does Extra Risk Strictly Increase the Value of Options?," Finance 0409004, EconWPA.
    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.

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