Essays in public economics and mathematical finance

Chapter 1Why do some economies remain technologically backward even when technologies on the frontier are available for adoption, virtually freely? If institutions are fragile and property rights insecure, potential adopters of frontier technologies may be dissuaded if adoption leads to increased expost conflict over rightful shares to the higher returns. In such a setting, publicly-funded protection of private property rights may successfully support the adoption of best-available technologies as a Nash equilibrium. The movement to more-secure property rights may or may not be welfare-enhancing.Abstract: Chapter 2In this chapter, valuation of a financial derivative, known as Stock Loan, is addressed when the underlying asset is subject to risk of bankruptcy. A stock loan is a financial derivative where the owner of an asset (a share of a stock) can obtain a loan from a lender (usually, a bank) using that asset as a collateral. The movements of the asset price is modeled to follow a geometric Brownian motion, with constant drift and volatility. Following the credit risk literature, risk of bankruptcy is introduced according to both structural and reduced form approaches. In the structural form modeling, default is introduced following the Black and Cox (1976) formulation, where the asset is declared as bankrupt as soon as the asset price falls below a pre-determined lower boundary. Modeling the lower boundary as a deterministic function of time, a closed form expression for the valuation of the financial derivative is obtained in terms of the probability distribution of the first passage time of Brownian motion and the valuation of the Down-and-out barrier option. The pricing formula in the structural form modeling is based on the celebrated Black and Scholes (1973) framework and therefore, is easy to implement. As a salient feature of structural form modeling, default time turns out to be a predictable stopping time. In the reduced form approach, bankruptcy is modeled to occur through a default intensity which is assumed to be a decreasing function of discounted stock price. The event of bankruptcy is modeled as a non-predictable phenomenon. In this formulation, the existence of an optimal exercise boundary is proved, which is of threshold type. This optimal decision threshold is crucially contingent on the policy variables that are treated as parameters of the system. We proceed further to use numerical methods to address the sensitivity analysis of the optimal exercise boundary. The results of our numerical simulation provide further insights into the linkage between optimal exercise boundary and the policy variables. We find that optimal exercise boundary is crucially contingent on the effective rate of return (defined as the difference between interest and lending rate) and exhibits a non-monotone relationship. We also find an interval where optimal exercise boundary shows a monotone increasing relationship with an increase in volatility. The sensitivity analysis in the reduced form modeling can be useful in recommending policy prescriptions in the valuation of mortgage backed securities.