This paper shows how to recover stochastic volatility models (SVMs) from market models for the VIX futures term structure. Market models have more flexibility for fitting of curves than do SVMs, and therefore they are better-suited for pricing VIX futures and derivatives. But the VIX itself is a...

We consider nonlinear filtering applications to target tracking based on a vector of multi-scaled models where some of the processes are rapidly mean reverting to their local equilibria. We focus attention on target tracking problems because multiple scaled models with fast mean-reversion (FMR)...

We formulate and analyze an inverse problem using derivatives prices to obtain an implied filtering density on volatility's hidden state. Stochastic volatility is the unobserved state in a hidden Markov model (HMM), and can be tracked using Bayesian filtering. However, derivative data can be...

Volatility products have become popular in the past 15 years as a hedge against market uncertainty. In particular, there is growing interest in options on the VIX volatility index. A number of recent empirical studies examine whether there is significantly greater risk premium in VIX option...

We consider the problem of filtering and control in the setting of portfolio optimization in financial markets with random factors that are not directly observable. The example that we present is a commodities portfolio where yields on futures contracts are observed with some noise. Through the...