Jun, D. and Ku, H. (2013) Valuation of American Partial Barrier Options. Review of Derivatives Research, 16, 167-191. https://doi.org/10.1007/s11147-012-9081-1

has been cited by the following article:

• TITLE: The Barrier Binary Options

  AUTHORS: Min Gao, Zhenfeng Wei

  KEYWORDS: Binary Option, Barrier Option, Arbitrage-Free Price, Optimal Stopping, Geometric Brownian Motion, Parabolic Free Boundary Problem

  JOURNAL NAME: Journal of Mathematical Finance, Vol.10 No.1, February 26, 2020

  ABSTRACT: We extend the binary options into barrier binary options and discuss the application of the optimal structure without a smooth-fit condition in the option pricing. We first review the existing work for the knock-in options and present the main results from the literature. Then we show that the price function of a knock-in American binary option can be expressed in terms of the price functions of simple barrier options and American options. For the knock-out binary options, the smooth-fit property does not hold when we apply the local time-space formula on curves. By the properties of Brownian motion and convergence theorems, we show how to calculate the expectation of the local time. In the financial analysis, we briefly compare the values of the American and European barrier binary options.