A Hybrid Approach to Valuing American Parisian Options

Pricing of American Parisian option as executive option based on the least‐squares Monte Carlo approach

“…Through the above study status analysis, it can also be observed that there are limits in the present research on the American Paris option, thus this study has made some modifications and additions. The important advances are as follows: Although there are relevant studies on the pricing of Parisian options, most of them are European Parisian single‐barrier options (Anderluh, 2008; Avellaneda & Wu, 1999; Bernard & Boyle, 2011; Chen et al, 2013; Chen & Suchanecki, 2007; Chesney et al, 1997; Chesney & Vasiljević, 2018; Dassios & Wu, 2010; Gauthier, 2002; Labart & Lelong, 2009b; Le et al, 2016; Lee & Kim, 2014; Zhu & Chen, 2013), European Parisian double‐barrier options (Anderluh & van der Weide, 2009; Dassios & Lim, 2018; Dassios & Wu, 2011a, 2011b; Gao, 2013; Labart & Lelong, 2009a; Liu et al, 2022), and American single‐barrier Parisian options (Chesney & Gauthier, 2006; Chu et al, 2014; Haber et al, 1999; Jetley & Gustafson, 2007; Le et al, 2018; Lu et al, 2018; Zhu et al, 2015), whereas there are few study resources on American double‐barrier Parisian options.Hemmer et al (1999) proved that when the utility function of the manager is a power function and the relative risk aversion is 0.5, the optimal incentive contract contains the fixed income part, the linear part related to the change of stock price, and the convex part related to the change of stock price. Directly granting equity is a linear incentive method where the value of holding equity is linearly proportional to the stock price.…”

“…Avellaneda and Wu (1999) priced the Parisian option by translating the issue into a PDE and employing the grid approach for numerical computation. Jetley and Gustafson (2007) proposed a hybrid mathematical approach, which combines the Monte Carlo simulation approach and the grid approach to determine American Parisian knock-in and knock-out options. The grid approach is utilized to establish the early exercise border of the option, and the Monte Carlo approach is used to produce the movement route of the underlying asset.…”