SECURITY MARKETS WITH PRICE LIMITS: A BAYESIAN APPROACH

Several financial markets impose daily price limits on individual securities. Once a price limit is triggered, investors observe either the limit floor or ceiling, but cannot know with certainty what the true equilibrium price would have been in the absence of such limits. The price limits in most exchanges are typically based on a percentage change from the previous day's closing price, and can be expressed as return limits. We develop a Bayesian forecasting model in the presence of return limits, assuming that security returns are governed by identically and independently shifted-exponential random variables with an unknown parameter. The unique features of our Bayesian model are the derivations of the posterior and predictive densities. Several numerical predictions are generated and depicted graphically. Our main theoretical result with policy implications is that when return-limit regulations are tightened, the price-discovery process is impeded and investor's welfare is reduced.Price limits, return predictions, asset pricing, Bayesian analysis

FAIR ACTUARIAL VALUES FOR DEDUCTIBLE INSURANCE POLICIES IN THE PRESENCE OF PARAMETER UNCERTAINTY

This paper derives the multi-period fair actuarial values for six deductible insurance policies offered in today's insurance markets. The loss in any given period is generated by the Weibull distribution with a known shape parameter but an unknown scale parameter. The insurer is assumed to be a Bayesian decision maker, in the sense that he/she learns sequentially about the unknown scale parameter by observing the realizations of the filed claims. It is shown that the insurer's underlying predictive loss distributions belong to the Burr family, and the multi-period actuarially fair policy value can be derived. With a proper loading, an insurance premium can be quoted. Our major contribution is the analytical derivations of the fair actuarial values for deductible insurance policies in the presence of parameter uncertainty and Bayesian learning.Weibull loss distribution, Bayesian learning, Burr predictive loss distribution, fair actuarial values, deductible insurance policies

Pricing futures on geometric indexes: A discrete time approach

Several futures contracts are written against an underlying asset that is a geometric, rather than arithmetic, index. These contracts include: the US Dollar Index futures, the CRB-17 futures, and the Value Line geometric index futures. Due to the geometric averaging, the standard cost-of-carry futures pricing formula is improper for pricing these futures contracts. We assume that asset prices are lognormally distributed, and capital markets are complete. Using the concepts of equivalent martingale measure and the risk-neutral valuation relationships in conjunction with discrete time methodology, we derive closed-form pricing formulas for these contracts. Our pricing formulas are consistent with the ones obtained via a continuous time paradigm. Copyright Springer Science+Business Media, LLC 2007Geometric indexes, Futures pricing, Risk-neutral valuation, Discrete time model,

A new paradigm for forecasting security returns in a market regulated by price limits

Bayesian forecasting, Security returns, Price limits, C11, C53, G10,