Valuing the option to purchase an asset at a proportional discount: A correction

Gu [Gu, Y. A. (2002). Valuing the option to purchase an asset at a proportional discount. The Journal of Financial Research, 25 (1), 99-109] introduces proportional-strike options to study a residential real estate program in China. Under this program, a state employee can buy her house at a fraction of the market price. The employee can also qualify for a subsidized mortgage. Given that the homeowner has the option, but not the obligation, of taking the subsidy, we show that the solution of the housing problem derived by Gu can be wrong. We provide a numerical example to illustrate the point.