Can asset price dynamics be accurately modeled using lognormal mixtures? This paper introduces a new class of analytically tractable models for asset price dynamics, based on the assumption that asset price density is a mixture of known basic densities. Focusing on the lognormal-mixture model as a fundamental example, the authors derive explicit dynamics, closed-form formulas for option prices, and analytical approximations for the implied volatility function. Explicit dynamics, closed form formulas for option prices and analytical approximations for the implied volatility function were derivied. The study introduces the asset-price model obtained by shifting the lognormal-mixture dynamics and investigates its analytical tractability. This approach captures the dynamics of an asset price based on the assumption that the asset-price density is given by the mixture of known basic densities. Ultimately, the research provides insights into asset pricing and volatility modeling. By providing tractable analytical solutions and demonstrating calibration to real market data, the models presented in this work offer valuable tools for financial analysts, risk managers, and academics studying financial markets. It presents a specific example of calibration to real market option data.
International Journal of Theoretical and Applied Finance publishes research in financial economics. This paper fits the journal’s scope by introducing a new model for asset price dynamics, focusing on options pricing and volatility. It offers analytical tractability and empirical calibration to market data, relevant to finance professionals.