National drought insurance for Malawi

Malawi has experienced several catastrophic droughts over the past few decades. The impact of these shocks has been far reaching, and the resulting macroeconomic instability has been a major constraint to growth and poverty reduction in Malawi. This paper describes a weather risk management tool that has been developed to help the government manage the financial impact of drought-related national maize production shortfalls. The instrument is an index-based weather derivative contract designed to transfer the financial risk of severe and catastrophic national drought that adversely impacts the government's budget to the international risk markets. Because rainfall and maize yields are highly correlated, changes in rainfall -- its timing, cumulative amount, and distribution -- can act as an accurate proxy for maize losses. An index has been constructed using rainfall data from 23 weather stations throughout Malawi and uses daily rainfall as an input to predict maize yields and therefore production throughout the country. The index picks up the well documented historical drought events in 2005, 1995, 1994, and 1992 and a weather derivative contract based on such an index would have triggered timely cash payouts to the government in those years. This innovative risk management instrument was pioneered in 2008/2009 by the Government of Malawi, with the assistance of the World Bank, and was a first for a sovereign entity in Africa. Several piloting seasons will be necessary to understand the scope and limitations of such contracts, and their role in the government's strategy, contingency planning, and operational drought response framework.Debt Markets,Hazard Risk Management,Banks&Banking Reform,Labor Policies,Insurance&Risk Mitigation

Relaxation of quantum states under energy perturbations

The energy-based stochastic extension of the Schrodinger equation is perhaps the simplest mathematically rigourous and physically plausible model for the reduction of the wave function. In this article we apply a new simulation methodology for the stochastic framework to analyse formulae for the dynamics of a particle confined to a square-well potential. We consider the situation when the width of the well is expanded instantaneously. Through this example we are able to illustrate in detail how a quantum system responds to an energy perturbation, and the mechanism, according to the stochastic evolutionary law, by which the system relaxes spontaneously into one of the stable eigenstates of the Hamiltonian. We examine in particular how the expectation value of the Hamiltonian and the probability distribution for the position of the particle change in time. An analytic expression for the typical timescale of relaxation is derived. We also consider the small perturbation limit, and discuss the relation between the stochastic framework and the quantum adiabatic theorem

Dynamical pricing of weather derivatives

The dynamics of temperature can be modelled by means of a stochastic process known as fractional Brownian motion. Based on this empirical observation, we characterize temperature dynamics by a fractional Ornstein-Uhlenbeck process. This model is used to price two types of contingent claims: one based on heating and cooling degree days, and one based on cumulative temperature. We derive analytic expressions for the expected discounted payoffs of such derivatives, and discuss the dependence of the results on the fractionality of the temperature dynamics.