Reduced Order Models for Pricing European and American Options under Stochastic Volatility and Jump-Diffusion Models

European options can be priced by solving parabolic partial(-integro) differential equations under stochastic volatility and jump-diffusion models like Heston, Merton, and Bates models. American option prices can be obtained by solving linear complementary problems (LCPs) with the same operators. A finite difference discretization leads to a so-called full order model (FOM). Reduced order models (ROMs) are derived employing proper orthogonal decomposition (POD). The early exercise constraint of American options is enforced by a penalty on subset of grid points. The presented numerical experiments demonstrate that pricing with ROMs can be orders of magnitude faster within a given model parameter variation range

Investment in carbon dioxide capture and storage combined with enhanced water recovery

Carbon dioxide capture and storage combined with enhanced deep saline water recovery (CCS-EWR) is a potential approach to mitigate climate change. However, its investment has been a dilemma due to high costs and various uncertainties. In this study, a trinomial tree modelling-based real options approach is constructed to assess the investment in CCS-EWR retrofitting for direct coal liquefaction in China from the investor perspective. In this approach, the uncertainties in CO2 prices, capital subsidies, water resource fees, the residual lifetime of direct coal liquefaction plants, electricity prices, CO2 and freshwater transport distance, and the amount of certified emission reductions (CERs) are considered. The results show that the critical CER price for CCS-EWR retrofits is 7.15 Chinese yuan per ton (CNY/ton) higher than that (141.95 CNY/ton) for CCS retrofits. However, the exemption from water resource fees for freshwater recovered from saline water and a subsidy of 26% of the capital cost are sufficient to eliminate the negative impact of enhanced deep saline water recovery (EWR) on the investment economy of CCS-EWR. In addition, when the residual lifetime is less than 14 years, CCS-EWR projects are still unable to achieve profitability, even with flexible management and decision making; therefore, investors should abandon CCS-EWR investments. On the whole, the investment feasibility for CCS-EWR technology is not optimistic despite access to preferential policies from the government. It is necessary to establish a carbon market with a high and stable CER price