Machine learning has been widely applied to solve intricate problems in finance. Yet in options theory, machine learning methods are less visited due to the structural complexity of the derivatives market. This dissertation focuses on using machine learning algorithms to obtain optimal decisions for three distinct option-related problems. In the first chapter, we apply a reinforcement learning technique – approximate dynamic programming to model a real option of an investment in the renewable energy sector. The second chapter combines Q-learning and progressive hedging to attain optimal decisions for an option portfolio. In the third chapter, we model the implied volatility surface that exists in option markets by an online adaptive support vector regression algorithm. Each of the three chapters presents detailed case studies and numerical experiments that prove the effectiveness of our proposed models and algorithms. Chapter 1 solves a real option problem of the investment timing of solar panels. Solar energy is rapidly emerging thanks to the decreasing installation cost of solar panels and the renewable portfolio standard imposed by state governments. Recently, third-party financing has become a common practice in solar panel investments. In this chapter, we discuss optimal timing for the host to potentially buy back the solar panels after being installed for a period of time and how to incorporate the optimal timing into a power purchase agreement between the host and the third-party developer. By a modified real option structure, we model the buyback contract as a real option and solve it with an approximate dynamic program based Monte Carlo simulation method. Chapter 2 focuses on financial options, in particular, a portfolio of American options. American options allow early exercise, which yields an additional challenge when optimizing a portfolio of American options, besides the weights of each option. We propose a reinforcement learning (Q-learning) algorithm for an American option portfolio, combining an iterative progressive hedging method and a quadratic approximation to Q-values by regression. By means of Monte Carlo simulation and empirical experiments we evaluate the quality of the algorithms proposed. In Chapter 3, we design a machine learning based method – online adaptive primal support vector regression (SVR) – to model the implied volatility surface (IVS). The algorithm proposed is the first derivation and implementation of an online primal kernel SVR. It features enhancements that allow online adaptive learning by embedding the idea of local fitness and budget maintenance. To accelerate our algorithm, we implement its most computationally intensive parts in a Field Programmable Gate Arrays hardware. Using intraday tick data from the E-mini S&P 500 options market, we show that our algorithm outperforms two competing methods and the Gaussian kernel is a better choice than the linear kernel. Sensitivity analysis is also presented to demonstrate how hyper parameters affect the error rates and the number of support vectors in our models.

Last modified

• 10/09/2018

Creator

• Yaxiong Zeng

DOI

• https://doi.org/10.21985/N2RJ17

Subject

• Industrial Engineering and Management Sciences

Keyword

• Financial application
• Support vector regression
• Reinforcement learning
• Option market
• Machine learning

Date created

• 2017-01-01

Resource type

• Dissertation

Rights statement

• In Copyright