American Options in the HobsonRogers Model
Abstract
In this article, we consider a risky asset $X$ for which evolution follows a model proposed by D.G. Hobson and L.C.G. Rogers\cite{HR98}. We assume that the volatility of $X$ depends on the ratio of the present value and the exponentially weighted average of the past value. Using the Markovian modelling of the enlarged twodimensional process, we show that, for the American put option with $X$ as the underlying asset, the continuation region and the stopped region are separated a striking curve . This striking curve lies between the two striking curves from the basic BSM model, yet is {\em not} monotone.
 Publication:

arXiv eprints
 Pub Date:
 February 2018
 arXiv:
 arXiv:1802.04990
 Bibcode:
 2018arXiv180204990S
 Keywords:

 Mathematics  Probability
 EPrint:
 This version is mainly to revise the statement and the proof of Proposition 3.4 on the monotonicity