| 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.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 tradable, an additional arbitrage condition has to be introduced and implies additional parameter restrictions.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. |
