A dual-stochastic real options model for sports tourism investment: A case study in China

As the deep integration of sports and tourism continues, sports tourism projects are emerging as an important driver of regional economic transformation and consumption upgrading. However, these projects typically exhibit strong revenue seasonality, long construction cycles, and high market uncertainty, which makes traditional static evaluation methods inadequate for capturing investment feasibility and risk structures. Based on the theory of investment under uncertainty, this study develops a dual-stochastic real options model that couples an Ornstein-Uhlenbeck process with exogenous seasonality (ES-OU) for revenues and a Geometric Brownian Motion (GBM) for construction costs, to characterize the dynamic investment boundary and optimal entry timing under multiple risk constraints. The model is solved using a hybrid numerical framework that combines the Crank-Nicolson-ADI finite-difference scheme with Monte Carlo simulation, ensuring both accuracy and stability. Using the Fanjingshan Mountain Sports Experience Base in Guizhou as a comparable case, parameters are calibrated and simulations conducted with Guiyang's tourism income and the CSI 300 Building Materials Index. The results show an optimal investment boundary of approximately CNY 196 million per quarter, an investment trigger probability of 62.4%, and a median trigger time of about 3.75 years, indicating a pronounced "delay-and-time-the-entry" decision pattern. Further analysis identifies construction cost and the long-run mean of revenues as the key economic drivers of entry timing: higher costs significantly postpone investment triggers, whereas improved revenue expectations advance entry. These findings validate the feasibility and explanatory power of the real options model in the sports tourism context, reveal the dynamic mechanism of investment behavior under joint revenue-cost uncertainty, and provide quantitative guidance for investment timing, risk identification, and policy design in sports tourism projects.