Three Essays in Finance
- Author(s): Fabisiak, Alex John
- Advisor(s): Bernardo, Antonio E
- et al.
In the first chapter, I apply machine learning techniques to numerically solve high-dimensional continuous time models in finance. Traditional methods rely on finite difference schemes for solutions to partial differential equations. By approximating the solution with a deep neural network, I am able to leverage the computational efficiency of neural networks and batch gradient descent to accurately compute solutions involving many state variables. I demonstrate the accuracy and efficiency of this method for Black-Scholes options pricing problems and dynamic programming problems in up to 50 spatial dimensions, far beyond the capability of grid methods. I also develop a solution method to mean field game type problems, where both a value function and a distribution function must solve a system of differential equations, utilizing mixture density networks.
In the second chapter (with Ivo Welch), we develop a model where buyers prefer local over lower-cost vendors even in the absence of direct preferences, taxes, subsidies, contracts, sanctions, information asymmetries, audits, etc. Instead, they prefer locals because they internalize the fact that local agents will in turn be more likely to buy from them in the future. Local sellers understand that buyers' preferences give them limited local market power, and therefore raise their prices and earn surplus in equilibrium. Our model can explain how voluntary reciprocity among subsets of identical agents can sustain itself, and how ex-ante identical goods from ex-ante identical sellers can acquire and maintain sustainably differentiated prices.
In the third chapter (with Antonio Bernardo and Ivo Welch), we develop a model where firms with lower leverage are not only less likely to experience financial distress but are also better positioned to acquire assets from other distressed firms. With endogenous asset sales and values, each firm's debt choice then depends on the choices of its industry peers. With indivisible assets, otherwise identical firms may adopt different debt policies---some choosing highly levered operations (to take advantage of ongoing debt benefits), others choosing more conservative policies to wait for acquisition opportunities. Our key empirical implication is that the acquisition channel can induce firms to reduce debt when assets become more redeployable. This article has been accepted for publication and is forthcoming in the Journal of Financial and Quantitative Analysis.