Optimal Control in Pricing Financial Derivatives

Student: Shveikin Evgenii

Supervisor: Vladimir R. Evstigneev

Faculty: Faculty of World Economy and International Affairs

Educational Programme: World Economy (Master)

Final Grade: 8

Year of Graduation: 2016

In this paper, the optimal control problem for option prising was formulated as a problem of calculus of variations. As a result, the form of the utility function and its first derivative in conjunction with the probability density function, which we consider as functions of contol, was found. Based on Jackwerth's formalism we were able to replace the risk-neutral probability density function with these functions in the formula for finding the expected value of future payments discounted at the risk-free rate, and get the option pricing model. It can be used to evaluate the parameters of the distribution function of the underlying asset, and thus to study the nature of the expectations of market participants, i.e. to get the information about the investors' expectations about the price of the underlying asset directly from the option's premium.

Full text (added May 16, 2016)

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