Browsing by Author "Li, Michael"

Humans have a remarkable ability to generalize, utilizing limited experience to efficiently search over decision spaces. Surprisingly, humans can often outper-form state of the art machine learning algorithms across a variety of search tasks. One explanation for this is that humans learn a flexible model of the search space which they exploit to make good decisions. In this thesis, we investigate whether humans can learn the shared structure among a family of functions. We cast this problem through the lens of learning the kernel hyperparameters of a Gaussian Process. We begin with a thorough analysis of human search strategies in a cor-related multi-armed bandit task, with the aim of understanding the limitations of a model assuming humans fix their kernel hyperparameters. We find that these models systematically undervalue human search strategies. We then introduce a set of function learning tasks, in which we iteratively reveal function values and collect human predictions, using a kernel learning framework to determine if human participants adapt their predictions to the environmental structure and show evidence of learning the true kernel hyperparameters. We do not find compelling evidence in favor of hyperparameter adaptation. However, we do show that participants learn function-specific structure and can produce function predictions that align closely with Gaussian Processes predictions when supplied with ample data and when tasked with interpolation. We also find that human participants can learn the correct scale of the functions and that participants tend to overestimate smoothness when extrapolating with limited data.

The calibration of certain stochastic volatility models is an important daily routine for financiers, and balancing accuracy with speed has been an area of recent research in quantitative finance. In the environment of the Heston model, one of the most popular stochastic volatility models, traditional calibration methods are often reasonably accurate but lacking in speed. Building on the growing literature surrounding the implementation of neural network methods in the calibration process, this thesis improves upon previous models and examines the effectiveness of approximating the semi-closed Heston pricing function using neural networks. We show that in line with previous results, the neural network implementation is able to dramatically speed up calibration of the Heston model compared to more traditional global optimization routines, with very small losses in accuracy. We also show that the effectiveness of the neural network approach relies heavily on the characteristics of the training set and the beliefs of the parameter bounds. Finally, as a case study we examine the application of our neural network approach to calibration to the S&P 500 index (SPX) over a recent period of time.