Author Description

The S & P 500 Index is a leading indicator of U.S. equities and is meant to reflect the risk and return on the U.S. stock market. Many derivatives based on the S & P 500 are available to investors. The S & P 500 Futures of the Chicago Mercantile Exchange and the S & P 500 Index Options of the Chicago Board Options Exchange are both actively traded. This thesis argues that the S & P 500 Index is only a summary statistic designed to reflect the evolution of the stock market. It is not the value of a self-financed tradable portfolio, and its modifications do not coincide with changes of the value of any mimicking portfolio, due to the particular way the S & P 500 Index is computed and maintained. Therefore, the Spot-Futures Parity and the Put-Call Parity do not hold for the S & P 500 Index and its derivatives. Furthermore, its derivatives cannot be priced by using the standard option pricing models, which assume that the underlying asset is tradable. Chapter One analyzes why the S & P 500 Index does not represent the value of a self-financed tradable portfolio and why it cannot be replaced by the value of a tracker such as the SPDR. In particular, we show that the nonlinear and extreme risk dynamics of the SPDR and of the S & P 500 Index are very different. Chapter Two provides empirical evidence that the non-tradability of the S & P 500 Index can explain the Put-Call Parity deviations. Even after controlling for the liquidity risk of the options, we find that the Put-Call Parity implied dividends depend significantly on the option strike. In Chapter Three, we develop an affine multi-factor model to price coherently various derivatives such as forwards and futures written on the S & P 500 Index, and European put and call options written on the S & P 500 Index and on the S & P 500 futures. We consider the cases when the underlying asset is self-financed and tradable and when it is not, and show the difference between them. When the underlying asset is self-financed and