Calibration to American options: numerical investigation of the de-Americanization method.

American options are the reference instruments for the model calibration of a large and important class of single stocks. For this task, a fast and accurate pricing algorithm is indispensable. The literature mainly discusses pricing methods for American options that are based on Monte Carlo, tree and partial differential equation methods. We present an alternative approach that has become popular under the name de-Americanization in the financial industry. The method is easy to implement and enjoys fast run-times (compared to a direct calibration to American options). Since it is based on ad hoc simplifications, however, theoretical results guaranteeing reliability are not available. To quantify the resulting methodological risk, we empirically test the performance of the de-Americanization method for calibration. We classify the scenarios in which de-Americanization performs very well. However, we also identify the cases where de-Americanization oversimplifies and can result in large errors

The Short-Time Behaviour of VIX Implied Volatilities in a Multifactor Stochastic Volatility Framework

We consider a modelling setup where the VIX index dynamics are explicitly computable as a smooth transformation of a purely diffusive, multidimensional Markov process. The framework is general enough to embed many popular stochastic volatility models. We develop closed-form expansions and sharp error bounds for VIX futures, options and implied volatilities. In particular, we derive exact asymptotic results for VIX implied volatilities, and their sensitivities, in the joint limit of short time-to-maturity and small log-moneyness. The obtained expansions are explicit, based on elementary functions and they neatly uncover how the VIX skew depends on the specific choice of the volatility and the vol-of-vol processes. Our results are based on perturbation techniques applied to the infinitesimal generator of the underlying process. This methodology has been previously adopted to derive approximations of equity (SPX) options. However, the generalizations needed to cover the case of VIX options are by no means straightforward as the dynamics of the underlying VIX futures are not explicitly known. To illustrate the accuracy of our technique, we provide numerical implementations for a selection of model specifications

Variance-of-variance risk premium

This article explores the premium for bearing the variance risk of the VIX index, called the variance-of-variance risk premium. I find that during the sample period from 2006 until 2014 trading strategies exploiting the difference between the implied and realized variance of the VIX index yield average excess returns of − 24.16% per month, with an alpha of − 16.98% after adjusting for Fama–French and Carhart risk factors as well as accounting for variance risk (both highly significant). The article provides further evidence of risk premium characteristics using corridor variance swaps and compares empirical results with the predictions of reduced-form and structural benchmark models

Interest Rate Volatility and Risk Management: Evidence from CBOE Treasury Options

This paper investigates US Treasury market volatility and develops new ways of dealing with the underlying interest rate volatility risk. We adopt an innovative approach which is based on a class of model-free interest rate volatility (VXI) indices we derive from options traded on the CBOE. The empirical analysis indicates substantial interest rate volatility risk for medium-term instruments which declines to the levels of the equity market only as the tenor increases to 30 years. We show that this risk appears to be priced in the market and has a significant time-varying relationship with equity volatility risk. US Treasury market volatility is appealing from an investment diversification perspective since the VXI indices are negatively correlated with the levels of interest rates and of equity market implied volatility indices, respectively. Although VXI indices are affected by macroeconomic and monetary news, they are only partially spanned by information contained in the yield curve. Motivated by our results on the magnitude and the nature of interest rate volatility risk and by the phenomenal recent growth of the equity volatility derivative market, we propose the use of our VXI indices as benchmarks for monitoring, securitizing, managing and trading interest rate volatility risk. As a first step in this direction, we describe a framework of one-factor equilibrium models for pricing VXI futures and options on the basis of empirically favored mean-reverting jump-diffusions