Convergence of estimated option price in a regime switching market

Anindya Goswami () and Sanket Nandan ()
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Anindya Goswami: IISER
Sanket Nandan: IISER

Indian Journal of Pure and Applied Mathematics, 2016, vol. 47, issue 2, 169-182

Abstract: Abstract In an observed semi-Markov regime, estimation of transition rate of regime switching leads towards calculation of locally risk minimizing option price. Despite the uniform convergence of estimated step function of transition rate, to meet the existence of classical solution of the modified price equation, the estimator is approximated in the class of smooth functions and furthermore, the convergence is established. Later, the existence of the solution of the modified price equation is verified and the point-wise convergence of such approximation of option price is proved to answer the tractability of its application in Finance. To demonstrate the consistency in result a numerical experiment has been reported.

Keywords: Semi-Markov processes; Volterra integral equation; non-local parabolic PDE; locally risk minimizing pricing; optimal hedging (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s13226-016-0182-7

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