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2 results

  • Recovering a Piecewise Constant Volatility from Perpetual Put Option Prices

  • Part of
  • Bing Lu
  • Journal:
    Journal of Applied Probability / Volume 47 / Issue 3 / September 2010
    Published online by Cambridge University Press:
    14 July 2016, pp. 680-692
    Print publication:
    September 2010
    • Article
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  • In this paper we present a method to recover a time-homogeneous piecewise constant volatility from a finite set of perpetual put option prices. The whole calculation process of the volatility is decomposed into easy computations in many fixed disjoint intervals. In each interval, the volatility is obtained by solving a system of nonlinear equations.

  • Nonexponential asymptotics for the solutions of renewal equations, with applications

  • Part of
  • Chuancun Yin, Junsheng Zhao
  • Journal:
    Journal of Applied Probability / Volume 43 / Issue 3 / September 2006
    Published online by Cambridge University Press:
    14 July 2016, pp. 815-824
    Print publication:
    September 2006
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  • Nonexponential asymptotics for solutions of two specific defective renewal equations are obtained. These include the special cases of asymptotics for a compound geometric distribution and the convolution of a compound geometric distribution with a distribution function. As applications of these results, we study the asymptotic behavior of the demographic birth rate of females, the perpetual put option in mathematics of finance, and the renewal function for terminating renewal processes.