Implied volatilities are frequently used to quote the prices of options. The implied volatility of a European option on a particular asset as a function of strike price and time to maturity is known as the asset's volatility surface. Traders monitor movements in volatility surfaces closely. In...

This article shows that the one-state-variable interest-rate models of Vasicek (1977) and Cox, Ingersoll, and Ross (1985b) can be extended so that they are consistent with both the current term structure of interest rates and either the current volatilities of all spot interest rates or the...

This paper presents a generalized version of the lattice approach to pricing options. It shows how the control variate technique can produce significant improvements in the efficiency of the approach. The control variate technique is illustrated using American puts on dividend and nondividend...

The first part of this paper presents a general approach to valuing a financial institution's contracts when there is credit risk. The approach uses contingent claims pricing theory and is particularly appropriate for an off-balance sheet contract, such as a swap, that can have either a positive...

We propose a methodology for assessing model risk and apply it to the implied volatility function (IVF) model. This is a popular model among traders for valuing exotic options. Our research is different from other tests of the IVF model in that we reflect the traders' practice of using the model...