Valuation of European Two-Asset Rainbow Options under the Merton Jump-Diffusion Model
Keywords:
Merton Jump-Diffusion Model, Valuation of European Two-Asset RainbowAbstract
This research investigates the valuation of European two-asset rainbow options within the framework of the Merton jump-diffusion model. Given the complexity and uncertainties inherent in smart city projects and the necessity for financial instruments to manage risks, this study employs the Merton jump-diffusion model to account for sudden price jumps and structural shocks, addressing the limitations of classical continuous models. Semi-closed-form formulas for options on the minimum and maximum of two correlated assets were derived. For numerical analysis and the calculation of sensitivity parameters (the Greeks), finite difference methods (FDM) and Monte Carlo simulations were employed. The numerical results demonstrate the satisfactory convergence of the proposed formulas and their high accuracy compared to more complex numerical approaches. The analysis reveals that volatility, asset correlation, and jump intensity play decisive roles in option pricing. These findings, while enriching the literature on derivative pricing, provide a practical framework for managers and policymakers in smart urban governance to quantify and manage the multidimensional risks of infrastructure projects with greater precision.
Keywords: Rainbow Option, Merton Jump-Diffusion Model, Smart City Governance, Finite Difference Method, Risk Management, Multi-Asset Derivatives.
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