Innovating and Pricing Carbon-Offset Options of Asian Styles on the Basis of Jump Diffusions and Fractal Brownian Motions

Yue Qi () and Yue Wang
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Yue Qi: China Academy of Corporate Governance & Department of Financial Management, Business School, Nankai University, 94 Weijin Road, Tianjin 300071, China
Yue Wang: Department of Financial Management, Business School, Nankai University, 94 Weijin Road, Tianjin 300071, China

Mathematics, 2023, vol. 11, issue 16, 1-22

Abstract: Due to CO 2 emissions, humans are encountering grave environmental crises (e.g., rising sea levels and the grim future of submerged cities). Governments have begun to offset emissions by constructing emission-trading schemes (carbon-offset markets). Investors naturally crave carbon-offset options to effectively control risk. However, the research and practice for these options are relatively limited. This paper contributes to the literature in this area. Specifically, according to carbon-emission allowances’ empirical distributions, we implement fractal Brownian motions and jump diffusions instead of traditional geometric Brownian motions. We contribute to extending the theoretical model based on carbon-offset option-pricing methods. We innovate the carbon-offset options of Asian styles. We authenticate the options’ stochastic differential equations and analytically price the options in the form of theorems. We verify the parameter sensitivity of pricing formulas by illustrations. We also elucidate the practical implications of an emission-trading scheme.

Keywords: carbon offset; emission-trading scheme; carbon-offset investments; carbon-offset options; jump diffusions; fractal Brownian motions; stochastic differential equations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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