Andreas Kaeck

Stochastic Volatility Jump‐Diffusions for European Equity Index Dynamics

Major research on equity index dynamics has investigated only US indices (usually the S&P 500) and has provided contradictory results. In this paper a clarification and extension of that previous research is given. We find that European equity indices have quite different dynamics from the S&P 500. Each of the European indices considered may be satisfactorily modelled using either an affine model with price and volatility jumps or a GARCH volatility process without jumps. The S&P 500 dynamics are much more difficult to capture in a jump-diffusion framework.

Does Model Fit Matter for Hedging? Evidence from FTSE 100 Options

This paper implements a variety of different calibration methods applied to the Heston model and examines their effect on the performance of standard and minimum-variance hedging of vanilla options on the FTSE 100 index. Simple adjustments to the Black-Scholes-Merton model are used as a benchmark. Our empirical findings apply to delta, delta-gamma or delta-vega hedging and they are robust to varying the option maturities and moneyness, and to different market regimes. On the methodological side, an efficient technique for simultaneous calibration to option price and implied volatility index data is introduced.

Regimes in CDS Spreads: A Markov Switching Model of iTraxx Europe Indices

This paper investigates the determinants of the iTraxx CDS Europe indices, finding strong evidence that they are regime dependent. During volatile periods credit spreads become highly sensitive to stock volatility and more sensitive to this than to stock returns. They are also almost immune to interest rates changes. During tranquil periods credit spreads are more sensitive to stock returns than to volatility and most indices are sensitive to interest rate moves. However for companies in the financial sector interest rates have no significant influence in either regime. We also found some evidence that raising interest rates can decrease the probability of credit spreads entering a volatile period. Our findings are useful for policy makers and, since equity hedge ratios based on single-state models cannot capture the regime dependent behaviour of credit spreads, our results may also help traders to improve the efficiency of hedging credit default swaps. Finally, the volatility clustering and autocorrelation that we have identified in the price dynamics of iTraxx indices should prove useful for pricing the iTraxx options that are now being actively traded over-the-counter.

Stochastic Volatility Jump-Diffusions for Equity Index Dynamics

This paper examines the ability of twelve different continuous-time two-factor models with mean-reverting stochastic volatility to capture the dynamics of the S&P 500 and three European equity indices. The stochastic volatility models are the square root variance, GARCH, and log volatility diffusions, and each is augmented with price and volatility jump extensions. Parameter estimation is by Markov Chain Monte Carlo using daily spot index returns from 1987 to 2010. For each index we find that GARCH diffusions augmented with correlated price and volatility jumps outperform other specifications with respect to all the tests we perform. The European indices have similar dynamics, which are relatively easy to capture using several of our specifications, but the S&P 500 index has different dynamics and here the GARCH-jump specification is very clearly superior.

Informed Trading in the Index Option Market

We propose a structural vector autoregressive (VAR) model of informed trading in option markets to analyze whether investors use options to trade on private information about the underlying price and/or the underlyings volatility. We decompose option order flow into exposures to the underlying asset (through the option delta) and its volatility (through the option vega). Our proposed methodological framework facilitates meaningfully aggregation of option order flows for different strike prices and maturities, and increases statistical power to identify informed trading. A fitted model confirms that S&P500 option trades are indeed informative about changes in both the underlying and volatility.

A parsimonious parametric model for generating margin requirements for futures

Abstract Major exchanges employ the Standard Portfolio Analysis of Risk (SPAN) software to measure maintenance margins. However, its methodology has become cumbersome and opaque, having evolved over several decades and by now it requires that several hundred parameter values are re-set every day. We present a new, parsimonious parametric model for calculating margin requirements for futures which has a rigorous econometric foundation, being derived entirely from the median tail loss (MTL) of the returns distribution. This facilitates maximum likelihood volatility model calibration and state-of-the-art backtests. Then the parameters of the margin scheme which overlays the MTL may be calibrated using a variety of objectives. We examine three such objectives, including two which are designed to generate margins which mimic SPAN.