Pricings and Hedgings of the Perpetual Russian Options

19 Pages Posted: 21 Oct 2011

See all articles by Weiping Li

Weiping Li

Civil Aviation Flight University of China ; Oklahoma State University

Su

Oklahoma State University

Date Written: October 19, 2011

Abstract

In this paper, we study the optimal stopping time and the optimal stopping boundary for the perpetual Russian option under the diffusion process. The general continuation region is characterized by a function b(p; t) depending on both variables t and the maximum value of the stock and initial starting value P0. Previous studies assume that the continuation region is given by a function depending upon the time t only. This is unreal hypothesis for the diffusion to achieve. Our result shows that the Russian option can be described by a Black-Scholes equation over the continuation region and smooth boundary conditions on the optimal stopping boundary. Furthermore, we develop an evaluation method from the lookback option on the stopping time, and establish the Greek letters for the perpetual Russian option. We obtain the exact upper bound for the prices of the perpetual Russian options and demonstrate that both the payoff and the optimal stopping time are path-dependent by Monte Carlo simulations.

Keywords: Perpetual Russian Option, Optimal Stopping Time, Hedge, Geometric Brownian Motion

JEL Classification: G13

Suggested Citation

Li, Weiping and Chen, Su, Pricings and Hedgings of the Perpetual Russian Options (October 19, 2011). Available at SSRN: https://ssrn.com/abstract=1946545 or http://dx.doi.org/10.2139/ssrn.1946545

Weiping Li (Contact Author)

Civil Aviation Flight University of China ( email )

46 Nanchang road
Guanghan, Sichuan 618307
China

Oklahoma State University ( email )

Stillwater, OK
United States

Su Chen

Oklahoma State University ( email )

Stillwater, OK 74078-0555
United States
4053853832 (Phone)

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