Signed path dependence in financial markets : applications and implications

Despite decades of studies, there is still no consensus on what type of serial dependence, if any, might be present in risky asset returns. The serial dependence structure in asset returns is complex and challenging to study, it varies over time, it varies over observed time resolution, it varies by asset type, it varies with liquidity and exchange and it even varies in statistical structure. The focus of the work in this thesis is to capture a previously unexplored notion of serial dependence that is applicable to any asset class and can be both parameteric or non-parameteric depending on the modelling approach preferred. The aim of this research is to develop new approaches by providing a model-free definition of serial dependence based on how the sign of cumulative innovations for a given lookback horizon correlates with the future cumulative innovations for a given forecast horizon. This concept is then theoretically validated on well-known time series model classes and used to build a predictive econometric model for future market returns, which is applied to empirical forecasting by means of a profit seeking trading strategy. The empirical experiment revealed strong evidence of serial dependence in equity markets, being statistically and economically significant even in the presence of trading costs. Subsequently, this thesis provides an empirical study of the prices of Energy Commodities, Gold and Copper in the futures markets and demonstrates that, for these assets, the level of asymmetry of asset returns varies through time and can be forecast using past returns. A new time series model is proposed based on this phenomenon, also empirically validated. The thesis concludes by embedding into option pricing theory the findings of previous chapters pertaining to signed path dependence structure. This is achieved by devising a model-free empirical risk-neutral distribution based on Polynomial Chaos Expansion and Stochastic Bridge Interpolators that includes information from the entire set of observable European call option prices under all available strikes and maturities for a given underlying asset, whilst the real-world measure includes the effects of serial dependence based on the sign of previous returns. The risk premium behaviour is subsequently inferred from the two distributions using the Radon-Nikodym derivative of the empirical riskneutral distribution with respect to the modelled real-world distribution.