Convexity of the optimal stopping boundary for the American put option
نویسندگان
چکیده
منابع مشابه
On the Optimal Exercise Boundary for an American Put Option
An American put option is a derivative financial instrument that gives its holder the right but not the obligation to sell an underlying security at a pre-determined price. American options may be exercised at any time prior to expiry at the discretion of the holder, and the decision as to whether or not to exercise leads to a free boundary problem. In this paper, we examine the behavior of the...
متن کاملOptimal exercise boundary for an American put option
The optimal exercise boundary near the expiration time is determined for an American put option. It is obtained by using Green's theorem to convert the boundary value problem for the price of the option into an integral equation for the optimal exercise boundary. This integral equation is solved asymptotically for small values of the time to expiration. The leading term in the asymptotic soluti...
متن کاملConvexity of the Exercise Boundary of the American Put Option on a Zero Dividend Asset
The Black–Scholes model is widely used to value options. An important advantage of the model is that European options can be valued analytically by the Black–Scholes formula (Merton 1992; Hull 1997). The situation is quite different, however, for American put options with optimal early exercise. While considerable progress has been made, no completely satisfactory analytic solution has been fou...
متن کاملCharacterization of the American Put Option Using Convexity
ABSTRACT Understanding the behaviour of the American put option is one of the classic problems in mathematical finance. Considerable efforts have been made to understand the asymptotic expansion of the optimal early exercise boundary for small time near expiry. Here we focus on the large-time expansion of the boundary. Based on a recent development of the convexity property, we are able to esta...
متن کاملOn the Early Exercise Boundary of the American Put Option
We study the short time behavior of the early exercise boundary for American style put options in the Black–Scholes theory. We develop an asymptotic expansion which shows that the simple lower bound of Barles et al. is a more accurate approximation to the actual boundary than the more complex upper bound. Our expansion is obtained through iteration using a boundary integral equation. This integ...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2004
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2004.06.018