We study asymptotics of forward-start option prices and the forward implied volatility smile using the theory of sharp large deviations (and refinements). In Chapter 1 we give some intuition and insight into forward volatility and provide motivation for the study of forward smile asymptotics. We numerically analyse no-arbitrage bounds for the forward smile given calibration to the marginal dist...

This paper examines the ability of GARCH(1,1) and GARCH(1,1) + Implied Volatility models to forecast stock market volatility on the FTSE100 index. Comparing the volatility forecasts with the implied volatility of the corresponding at-the-money index option contract, it is investigated whether successful volatility trading models can be developed. An at-the-money index call was bought/sold if th...

Volatility is an integral and inescapable variable of financial engineering, modeling, and finance theory itself Classical financial economics proxies volatility for risk itself, as it becomes difficult to predict future price realizations of a given asset when that asset exhibits significant price volatility over a given time. However, the nature of volatility as it is explained by classical f...

In this paper, we assess the efficiency, information content and unbiasedness of volatility forecasts based on the VIX/VXN implied volatility indexes, RiskMetrics and GARCHtype models at the 5-, 10and 22-day time horizon. Our empirical application focuses on the S&P100 and NASDAQ100 indexes. We also deal with the information content of the competing volatility forecasts in a market risk (VaR ty...

Multiscale stochastic volatility models have been developed as an efficient way to capture the principle effects on derivative pricing and portfolio optimization of randomly varying volatility. The recent book Fouque, Papanicolaou, Sircar and Sølna (2011, CUP) analyzes models in which the volatility of the underlying is driven by two diffusions – one fast mean-reverting and one slow-varying, an...

We analyze the implied volatility skews generated by displaced lognormal diffusions. In particular, we prove the global monotonicity of implied volatility, and an at-the-money bound on the steepness of downward volatility skews, under displaced lognormal dynamics, which therefore cannot reproduce some features observed in equity markets. A variant, the displaced anti-lognormal, overcomes the st...

In this paper we investigate implied volatility patterns in the Shifted Square Root Diffusion (SSRD) model as functions of the model parameters. We begin by recalling the Credit Default Swap (CDS) options market model that is consistent with a market Black-like formula, thus introducing a notion of implied volatility for CDS options. We examine implied volatilies coming from SSRD prices and cha...

Multiscale stochastic volatility models have been developed as an efficient way to capture the principle effects on derivative pricing and portfolio optimization of randomly varying volatility. The recent book Fouque, Papanicolaou, Sircar and Sølna (2011, CUP) analyzes models in which the volatility of the underlying is driven by two diffusions – one fast mean-reverting and one slow-varying, an...