The Cox, Ross, and Rubinstein binomial model is generalized to the multinomial case. Limits are investigated and shown to yield the Black-Scholes formula in the case of continuous sample paths for a wide variety of complete market structures. In the discontinuous case a Merton-type formula is...

Contingent claims with payoffs depending on finitely many asset prices are modeled as elements of a separable Hilbert space. Under fairly general conditions, including market completeness, it is shown that one may change measure to a reference measure under which asset prices are Gaussian and...

European call options are priced when the uncertainty driving the stock price follows the V. G. stochastic process (Madan and Seneta 1990). The incomplete markets equilibrium change of measure is approximated and identified using the log return mean. variance, and kurtosis. An exact equilibrium...

The Financial Crisis accelerated a latent Fiscal Crisis that had been brewing in many Western countries. The paper outlines the causes of the Financial Crisis, and how this increased expenditure and reduced revenues for many Western governments. But these additional fiscal stresses merely...

We combine two approaches to the pricing kernel, one empirical and one theoretical, which relax the restriction that the objective return distribution and risk neutral distribution share the same volatility and higher order moments. The empirical approach provides estimates for the evolution of...

Regulators charged with monitoring systemic risk need to focus on sentiment as well as narrowly defined measures of systemic risk. This chapter describes techniques for jointly monitoring the co-evolution of sentiment and systemic risk. To measure systemic risk, we use Marginal Expected...