In this paper, we propose AR-GARCH (autoregression-generalized autoregressive conditional heteroskedasticity) models to fit and forecast mortality rates for a given age by two alternative approaches. Specifically, one approach is to fit a time series of mortality rates for some age to an...

Motivated by the empirical findings that asset returns or volatilities are predictable, this paper studies the pricing of European options on stock or volatility, the instantaneous changes of which depend upon an autoregressive moving average (ARMA) process. The pricing formula of an ARMA-type...

This study empirically tests the performance of the Future Option model with Basis Risk (FOBR) proposed by Wang et al. (2005). The Black (1976) model is used as the competing model in this empirical test. The basis risk is the only difference between the two competing models and is therefore...

For the valuation of reverse mortgages with tenure payments, this article proposes a specific analytic valuation framework with mortality risk, interest rate risk, and housing price risk that helps determine fair premiums when the present value of premiums equals the present value of contingent...

Assuming that a futures price is a function of the underlying asset and the basis, and that a Brownian bridge process drives the basis, this article provides the closed-form solution of futures with basis risk (FBR). The Brownian bridge process ensures that the basis is zero at the maturity of a...

Under a no-arbitrage assumption, the futures price converges to the spot price at the maturity of the futures contract, where the basis equals zero. Assuming that the basis process follows a modified Brownian bridge process with a zero basis at maturity, we derive the closed-form solutions of...

In the classical Lee-Carter model, the mortality indices that are assumed to be a random walk model with drift are normally distributed. However, for the long-term mortality data, the error terms of the Lee-Carter model and the mortality indices have tails thicker than those of a normal...