In this dissertation, a financial market consisting of a risk free bank account, a risky stock, a set of zero coupon bonds and a set of European type contingent claim will be considered and an entirely new type of model, a Stochastic Conditional Distribution(SCD) Model belonging to the class of 'Dynamic Market Models', will be developed. Contrary to classical equity market models with stochastic short rate and stochastic volatility, the objective of a dynamic market model is to describe the dynamics of a financial market essentially by prescribing the evolution of the pricing measure under the risk neutral measure used by market participants to price the assets traded in the market. Recent advances in this literature have prescribed the dynamics of the risk neutral measure indirectly through for example the dynamics of the local volatility surface or the Black-Scholes implied volatility. In the framework of a Stochastic Conditional Distribution model developed here, the dynamics of the risk neutral measure is prescribed much more directly by prescribing the dynamics of the conditional cumulants of the log return to the risky asset for all time horizons. Prescribing the dynamics of the cumulants is also motivated by the fact that these can be extracted in a model free way and hence are, unlike the short rate and the volatility, directly observable from market data.

When developing an SCD model, it will become clear that prescribing the dynamics of the first two cumulants will pin down both the stochastic short rate and stochastic volatility and all higher order cumulants will effectively also be pinned down by the dynamics of the first two cumulants. Prescribing the dynamics of the cumulants for all horizons at once implies that an SCD model can be interpreted as a term structure model of the cumulants and in that perspective, it is no surprise that the main theoretical result of this dissertation will be a set of conditions on the drift of the first two cumulants insuring that the model is well-specified. It is also shown how in an SCD model, it is easy to switch measure to the forward measure allowing for the computation of prices of contingent claims even if the short rate is stochastic by finding the dynamics of zero coupon bonds in the market and changing the cumulants accordingly. If the additional assumption is made, that the market is driven by a set of factors, it will be possible to compute higher order cumulants by recursively solving a set of PDE's.

In general, a wide range of SCD models can be constructed and in this dissertation a specific SCD factor model will be constructed, a special case of which is the much celebrated Heston model, in which both higher order cumulants and the term structure of interest rates can be found explicitly and prices of European call and put options can be approximated to arbitrary precision using a very fast algorithm. Both the static and time-series behavior of this model will be extensively studied including properties of the term structure of interest rates, the term structure of the cumulants and the Black-Scholes implied volatility surface. The model will be able to generate a skew in the Black-Scholes implied volatility, is very flexible and able to account for a wide range of market conditions.

To be able to use the model in practice and to truly use the fact that this is a dynamic model, it should be possible to estimate the parameters of the model from observed conditional cumulants and that problem will also be addressed. This problem is complicated by the fact that the factors driving the market are not observable, but nevertheless a search algorithm can be constructed which estimates the parameters of the model very well and most importantly facilitates extracting the latent factors. This in turn will allow for the validity of the model to be verified by investigating if the time-series properties of the factors and checking if these are consistent with the assumptions of the model.