SSRN Author: Jerome DetempleJerome Detemple SSRN Content
http://www.ssrn.com/author=57354
http://www.ssrn.com/rss/en-usWed, 01 Nov 2017 04:48:37 GMTeditor@ssrn.com (Editor)Wed, 01 Nov 2017 04:48:37 GMTwebmaster@ssrn.com (WebMaster)SSRN RSS Generator 1.0REVISION: American Options with Discontinuous Two-Level CapsThis paper examines the valuation of American capped call options with two-level caps. The structure of the immediate exercise region is significantly more complex than in the classical case with constant cap. When the cap grows over time, making extensive use of probabilistic arguments and local time, we show that the exercise region can be the union of two disconnected set. Alternatively, it can consist of two sets connected by a line. The problem then reduces to the characterization of the upper boundary of the first set, which is shown to satisfy a recursive integral equation. When the cap decreases over time, the boundary of the exercise region has piecewise constant segments alternating with non-increasing segments. General representation formulas for the option price, involving the exercise boundaries and the local time of the underlying price process, are derived. An efficient algorithm is developed and numerical results are provided.
http://www.ssrn.com/abstract=3005451
http://www.ssrn.com/1638342.htmlTue, 31 Oct 2017 04:36:44 GMTREVISION: American Options with Discontinuous Two-Level CapsThis paper examines the valuation of American capped call options with two-level caps. The structure of the immediate exercise region is significantly more complex than in the classical case with constant cap. When the cap grows over time, making extensive use of probabilistic arguments and local time, we show that the exercise region can be the union of two disconnected set. Alternatively, it can consist of two sets connected by a line. The problem then reduces to the characterization of the upper boundary of the first set, which is shown to satisfy a recursive integral equation. When the cap decreases over time, the boundary of the exercise region has piecewise constant segments alternating with non-increasing segments. General representation formulas for the option price, involving the exercise boundaries and the local time of the underlying price process, are derived. An efficient algorithm is developed and numerical results are provided.
http://www.ssrn.com/abstract=3005451
http://www.ssrn.com/1611188.htmlMon, 24 Jul 2017 03:42:56 GMTREVISION: On American VIX Options under the Generalized 3/2 and 1/2 ModelsIn this paper, we extend the 3/2-model for VIX studied by Goard and Mazur (2013) and introduce the generalized 3/2 and 1/2 classes of volatility processes. Under these models, we study the pricing of European and American VIX options and, for the latter, we obtain an early exercise premium representation using a free-boundary approach and local time-space calculus. The optimal exercise boundary for the volatility is obtained as the unique solution to an integral equation of Volterra type.
We also consider a model mixing these two classes and formulate the corresponding optimal stopping problem in terms of the observed factor process. The price of an American VIX call is then represented by an early exercise premium formula. We show the existence of a pair of optimal exercise boundaries for the factor process and characterize them as the unique solution to a system of integral equations.
http://www.ssrn.com/abstract=2909938
http://www.ssrn.com/1579866.htmlTue, 04 Apr 2017 09:01:26 GMTREVISION: On American VIX Options under the Generalized 3/2 and 1/2 ModelsIn this paper, we extend the 3/2-model for VIX studied by Goard and Mazur (2013) and introduce the generalized 3/2 and 1/2 classes of volatility processes. Under these models, we study the pricing of European and American VIX options and, for the latter, we obtain an early exercise premium representation using a free-boundary approach and local time-space calculus. The optimal exercise boundary for the volatility is obtained as the unique solution to an integral equation of Volterra type.
We also consider a model mixing these two classes and formulate the corresponding optimal stopping problem in terms of the observed factor process. The price of an American VIX call is then represented by an early exercise premium formula. We show the existence of a pair of optimal exercise boundaries for the factor process and characterize them as the unique solution to a system of integral equations.
http://www.ssrn.com/abstract=2909938
http://www.ssrn.com/1564696.htmlWed, 08 Feb 2017 08:09:48 GMT