Controlled options: derivatives with added flexibility

TL;DR

This paper introduces controlled options, a new class of derivatives allowing dynamic adjustment of payment distribution over time, with applications in commodities and energy trading, solved via stochastic control and Bellman equations.

Contribution

It presents a novel framework for derivatives with dynamic control features, extending traditional options with added flexibility and providing existence results and pricing methods.

Findings

Established existence of solutions for controlled options

Derived pricing rules using modified Bellman equations

Demonstrated applications in commodities and energy trading

Abstract

The paper introduces a limit version of multiple stopping options such that the holder selects dynamically a weight function that control the distribution of the payments (benefits) over time. In applications for commodities and energy trading, a control process can represent the quantity that can be purchased by a fixed price at current time. In another example, the control represents the weight of the integral in a modification of the Asian option. The pricing for these options requires to solve a stochastic control problem. Some existence results and pricing rules are obtained via modifications of parabolic Bellman equations.