One-factor no-arbitrage models of the short rate are important tools for valuing interest rate derivatives. Trees are often used to implement the models and fit them to the initial term structure. This paper generalizes existing tree building procedures so that a very wide range of interest rate...

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...

We employ neural networks to understand volatility surface movements. We first use daily data on options on the S&P 500 index to derive a relationship between the expected change in implied volatility and three variables: the return on the index, the moneyness of the option, and the remaining...