On mortgage design: Eliminating negative feedback loops with Continuous and Automatic Workouts
Rafal Wojakowski (University of Surrey, UK)
Joint work with Robert Shiller, Shahid Ebrahim and Mark Shackleton

Thursday June 5, 16:30-17:00 | session 9.7 | Insurance | room I

We establish a framework to study innovative types of mortgages in an economic environment with refinancings and prepayments. Families of contracts we consider include Participating Mortgages (PMs) and Continuous Workout Mortgages (CWMs). We argue that by facilitating better risk sharing PMs offer a means to preserve and enhance the efficiency and resiliency of the financial architecture. Public policy implications include employing PMs as workout loans ex post facto the sub-prime crisis. CWMs are home loans whose payments and balance are linked to a market-observable house price index and adjusted on regular basis. In essence, they are a two-in-one product: a home loan coupled with negative equity insurance. Our results help understanding the mechanics of CWMs and estimating key contract parameters. We argue that CWMs could become the optimal home financing instrument for many households. Our contribution provides insight on how to improve the financial system and mitigate systemic risk by eliminating negative feedback loops in the economy. Demand for housing increases if Automatic Workout Mortgage (AWM) is used and attains maxima for those intending to reverse-mortgage a 40 \% of equity (without workout) and about 80 \% of equity (with AWM). We therefore assert that AWM is particularly suited for those who intend to sell or reverse-mortgage a significant fraction of their home equity before retirement. Insurance provided via AWM inhibis precautionary saving motives by making housing more attractive to risk averse borrowers. Consumption is reduced as more housing is purchased and borrowing increased. AWM improves expected utility by a dollar equivalent of about \$40,000 to \$55,000, which represents up to 55\% of the initial value of the house (\$100,000 in our simulations).

Indifference fee rate for variable annuities
Ricardo Romo Romero (Université d'Evry Val D'Essone, France)
Joint work with Thomas Lim and Etienne Chevalier

Thursday June 5, 17:00-17:30 | session 9.7 | Insurance | room I

Variable annuities play an increasingly important role in helping individual investors to achieve a secure retirement. The present work provides an analysis of the variable annuity policy. Especially, we focus on the valuation of the guaranteed minimum death benefits and the guaranteed minimum living benefits. We assume that the fee rate is fixed at the beginning of the contract. We then define and derive indifference fee rates for the insurer based on indifference pricing theory. It consists in solving two stochastic control problems. For that we apply recent results on backward stochastic differential equations with jumps and provide a verification theorem which gives the optimal strategy in each case. We numerically evaluate indifference fees, applying a Monte Carlo method and a dichotomy algorithm. We conclude our study with numerical illustrations of sensibilities of indifference fees with respect to parameters.

Continuous Time Perpetuities and the Time Reversal of Diffusions
Scott Robertson (Carnegie Mellon University, USA)
Joint work with Constantinos Kardaras

Thursday June 5, 17:30-18:00 | session 9.7 | Insurance | room I

We consider the problem of obtaining the distribution of a continuous time perpetuity, where the non-discounted cash flow rate is determined by an ergodic diffusion. Using results regarding the time reversal and erdodicity of (potentially degenerate) diffusions, we identify the distribution of the perpetuity with the invariant measure associated to a certain (different) ergodic diffusion. This enables efficient estimation of the distribution via simulation and, in certain instances, an explicit formula for the distribution. Using Occupancy Time Large Deviations Principles and results concerning Couplings of diffusions, rates of convergence are obtained for estimating the distribution, thus providing upper bounds for how long simulations must be run.