We show how to set up a forward rate model in the presence of volatility uncertainty by using the theory of G …

volatility-induced stationarity. Our model employs a level-dependent conditional volatility that maintains stationarity despite …

, leading to the so called "unspanned stochastic volatility puzzle". Additional volatility factors seem to be needed to explain … volatility from a nonparametric perspective …

, leading to the so called "unspanned stochastic volatility puzzle". Additional volatility factors seem to be needed to explain … volatility from a nonparametric perspective …

SABR stochastic volatility model is appealing for modeling smile and skew of option prices. Hagan, who first proposed … hedges. Here I prove a new exact closed formula for the joint probability density of underlying and volatility processes … stochastic volatility extensions, I will show how to specify a unified SABR-LMM with a smile, where the term structure of skew is …

, futures and forwards, option pricing under jumps and stochastic volatility, and the market valuation of corporate securities …

range of volatility assumptions. It shows that, if the market price of risk is a function only of the short rate and time, a …

of implied intensity rather than the conventional implied volatility. Our preliminary empirical work finds intensity …