Mortgage Contracts and Underwater Default

We analyze recently proposed mortgage contracts that aim to eliminate selective borrower default when the loan balance exceeds the house price (the ``underwater'' effect). We show contracts that automatically reduce the outstanding balance in the event of house price decline remove the default incentive, but may induce prepayment in low price states. However, low state prepayments vanish if the benefit from home ownership is sufficiently high. We also show that capital gain sharing features, such as prepayment penalties in high house price states, are ineffective as they virtually eliminate prepayment. For observed foreclosure costs, we find that contracts with automatic balance adjustments become preferable to the traditional fixed-rate contracts at mortgage rate spreads between 50-100 basis points. We obtain these results for perpetual versions of the contracts using American options pricing methodology, in a continuous-time model with diffusive home prices. The contracts' values and optimal decision rules are associated with free boundary problems, which admit semi-explicit solutions

On the optimal exercise boundaries of swing put options

We use probabilistic methods to characterise time-dependent optimal stopping boundaries in a problem of multiple optimal stopping on a finite time horizon. Motivated by financial applications, we consider a payoff of immediate stopping of “put” type, and the underlying dynamics follows a geometric Brownian motion. The optimal stopping region relative to each optimal stopping time is described in terms of two boundaries, which are continuous, monotonic functions of time and uniquely solve a system of coupled integral equations of Volterra-type. Finally, we provide a formula for the value function of the problem

Integral equations for Rost's reversed barriers: existence and uniqueness results

We establish that the boundaries of the so-called Rost’s reversed barrier are the unique couple of left-continuous monotonic functions solving a suitable system of nonlinear integral equations of Volterra type. Our result holds for atom-less target distributions μ of the related Skorokhod embedding problem. The integral equations we obtain here generalise the ones often arising in optimal stopping literature and our proof of the uniqueness of the solution goes beyond the existing results in the field

Optimal Power Investment and Pandemics: A Micro-Economic Analysis

This paper derives the optimal investment policy of an electricity producer during a pandemic. We consider three problems: (1) investing in a gas-fired plant, (2) investing in a wind plant, and (3) investing in the best of a gas plant and a wind plant. Optimal investment boundaries are characterized and valuation formulas derived. For single technology projects, a pandemic postpones wind investment, but can accelerate gas investment when the relative price of gas decreases. For choices between the two technologies, a substitution effect can reinforce the single technology effects, accelerating gas investment under certain conditions. The paper examines the impact of pandemic parameters, economic parameters and policy parameters on the investment boundaries, the values of projects and the premium for green energy

Optimal Power Investment and Pandemics: A Micro-Economic Analysis

This paper derives the optimal investment policy of an electricity producer during a pandemic. We consider three problems: (1) investing in a gas-fired plant, (2) investing in a wind plant, and (3) investing in the best of a gas plant and a wind plant. Optimal investment boundaries are characterized and valuation formulas derived. For single technology projects, a pandemic postpones wind investment, but can accelerate gas investment when the relative price of gas decreases. For choices between the two technologies, a substitution effect can reinforce the single technology effects, accelerating gas investment under certain conditions. The paper examines the impact of pandemic parameters, economic parameters and policy parameters on the investment boundaries, the values of projects and the premium for green energy