Research On Freight Options Pricing And Calibration

In the financial market,studies on modern freight derivatives with freight index being the underlying assets have gradually matured.Freight option is an emerging shipping derivative,and there have been many achievements in the researches on the pricing of this option.In the option pricing theory,the volatility is the factor of great importance affecting the pricing results,and the volatility was calibrated from the point view of stochastic volatility in most existing literature.In this thesis,the pricing of freight options was considered under the jump diffusion model and the regime-switching model.Numerical simulation procedure was established for the option pricing problem,and volatility calibration was realized through the equivalent inverse theory for parameters estimation.In chapter 2,the partial differential integral equations(PIDEs)that governs the freight option price derived from Feynman-Kac theorem,and the existence of solution of PIDE was strictly established by mathematical induction and the dominant control convergence theory.The PIDEs were solved by finite difference method,the implicit and explicit scheme for pricing were derived.In the numerical simulation,three widely used distributions describing the jumping process were carried out to compare and analyze the pricing results by proposed algorithm.In the chapter 3,volatility calibration was realized through solving related inverse problem.In the calibration,it is assumed that volatility is a function related to the price of the underlying asset.The related inverse problem was defined so that the difference of actual price and computed price for estimated parameters was minimized.The Tikhonov regularization was utilized to make the inverse problem well-posed,and the calculus of variation was applied to derive the governing equation for the volatility function.Finally,an iterative algorithm with satisfactory calibration accuracy was designed for the jump diffusion model and the regime-switching model.In chapter 4,numerical examples were carried out to test the validity and efficiency of proposed algorithms.The simulation results were discussed.Other parameters in the model also have an impact on the calibration result.The larger the parameter describing the jump amplitude,the more accurate the calibration result of the algorithm will be.This calibration algorithm can qualitatively analyze the implied volatility of the market and provide a reference for managing market risks.The conclusions and future works were considered in chapter 5.