This paper provides and empirical examination of four European equity indices between 1991 and 2005. We investigate the ability of fifteen different GARCH models to capture the characteristics of historical daily returns effectively and generate realistic implied volatility skews. Using many...

Arbitrage-free price bounds for convertible bonds are obtained assuming a stochastic volatility process for the common stock that lies within a band but makes few other assumptions about volatility dynamics. Equity-linked hazard rates, stochastic interest rates and different assumptions about...

This paper presents two applications of cointegration based trading strategies: a classic index tracking strategy and a long-short equity market neutral strategy. As opposed to other traditional index tracking or long-short equity strategies, the portfolio optimisation is based on cointegration...

1997 three papers that introduced very similar lognormal diffusion processes for interest rates appeared virtuously simultaneously. These models, now commonly called the 'LIBOR models' are based on either lognormal diffusions of forward rates as in Brace, Gatarek & Musiela (1997) and Miltersen,...

GARCH processes constitute the major area of time series variance analysis hence the limit of these processes is of considerable interest for continuous time volatility modelling. The limit of the GARCH(1,1) model is fundamental for limits of other GARCH processes yet it has been the subject of...

Normal mixture (NM) GARCH models are better able to account for leptokurtosis in financial data and offer a more intuitive and tractable framework for risk analysis and option pricing than student’s t-GARCH models. We present a general, symmetric parameterisation for NM-GARCH(1,1) models,...

This paper explores the properties of a European spread option valuation method for correlated assets when the marginal distribution each asset return is assumed to be a mixture of normal distributions. In this ‘bivariate normal mixture’ (BNM) approach no-arbitrage option values are just...

This paper presents a new approach to aggregating market and credit risks in large complex financial firms, banks in particular. By identifying risk factors that are common to many business activities, dependencies between different risk types across various lines of business can be properly...

The assumption that the probability distribution of returns is independent of the current level of the asset price is an intuitive property for option pricing models on financial assets. This ‘scale invariance’ feature is common to the Black-Scholes (1973) model, most stochastic volatility...

Contrary to popular belief, the diffusion limit of a GARCH variance process is not a diffusion model unless one makes a very specific assumption that cannot be generalized. In fact, the normal GARCH(1,1) prices of European call and puts are identical to the Black-Scholes prices based on the...