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<p>In this paper, we introduce a comprehensive framework for pricing forwards and options within the freight derivatives market. The empirical distribution characteristics of freight rate data, coupled with discernible non-zero autocorrelation structures, compel us to explore stochastic models beyond mere geometric Brownian motion (GBM). To this end, we propose employing an exponential Lévy model featuring normal inverse Gaussian distributed increments, alongside the Barndorff-Nielsen and Shephard stochastic volatility model, to better elucidate the dynamics of freight rates. Our findings unequivocally demonstrate the inadequacy of the GBM in capturing freight dynamics, underscoring the superiority of our proposed models. These models effectively encapsulate both the market price of risk and volatility, thus refining the pricing formula. Leveraging forward contracts as a foundation, we derive pricing formulas for freight options based on the arithmetic average of the underlying. Through meticulous Monte Carlo simulations, we validate the accuracy of our explicit pricing formula, affirming its reliability in reflecting market realities. This study significantly contributes to the comprehension of shipping market dynamics by furnishing a robust framework rooted in stochastic processes. By amalgamating advanced methodologies with empirical data, we furnish stakeholders in the maritime industry with invaluable insights for navigating its intricate landscape.</p>

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Valuation of freight derivatives based on continuous-time stochastic models

  • 期刊论文

  • 发表日期：

    2025年1月6日

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  • Zul Izwan Mohtar,
  • Che Mohd Imran Che Taib

摘要

In this paper, we introduce a comprehensive framework for pricing forwards and options within the freight derivatives market. The empirical distribution characteristics of freight rate data, coupled with discernible non-zero autocorrelation structures, compel us to explore stochastic models beyond mere geometric Brownian motion (GBM). To this end, we propose employing an exponential Lévy model featuring normal inverse Gaussian distributed increments, alongside the Barndorff-Nielsen and Shephard stochastic volatility model, to better elucidate the dynamics of freight rates. Our findings unequivocally demonstrate the inadequacy of the GBM in capturing freight dynamics, underscoring the superiority of our proposed models. These models effectively encapsulate both the market price of risk and volatility, thus refining the pricing formula. Leveraging forward contracts as a foundation, we derive pricing formulas for freight options based on the arithmetic average of the underlying. Through meticulous Monte Carlo simulations, we validate the accuracy of our explicit pricing formula, affirming its reliability in reflecting market realities. This study significantly contributes to the comprehension of shipping market dynamics by furnishing a robust framework rooted in stochastic processes. By amalgamating advanced methodologies with empirical data, we furnish stakeholders in the maritime industry with invaluable insights for navigating its intricate landscape.