The 1987 stock market crash occurred with minimal impact on observable economic variables (e.g., consumption), yet dramatically and permanently changed the shape of the implied volatility curve for equity index options. Here, we propose a general equilibrium model that captures many salient...

The 1987 market crash was associated with a dramatic and permanent steepening of the implied volatility curve for equity index options, despite minimal changes in aggregate consumption. We explain these events within a general equilibrium framework in which expected endowment growth and economic...

We explore convenient analytic properties of distributions constructed as mixtures of scaled and shifted t-distributions. A feature that makes this family particularly desirable for econometric applications is that it possesses closed-form expressions for its anti-derivatives (e.g., the...

Based on criteria of mathematical simplicity and consistency with empirical market data, a stochastic volatility model is constructed, the volatility process being driven by fractional noise. Price return statistics and asymptotic behavior are derived from the model and compared with data....

The state price density is a second derivative of the discounted European options prices with respect to the strike price. We use Maximum Likelihood method to derive a simple estimator of the curve such that it is decreasing, convex and its second derivative integrates to one. Confidence...

In this paper we compare the price of an option with one year maturity of the German stock index DAX for several volatility models including long memory and leverage effects. We compute the price by applying a present value scheme as well as the Black-Scholes and Hull-White formulas which...

In this paper we apply statistical inference techniques to build neural network models which are able to explain the prices of call options written on the German stock index DAX. By testing for the explanatory power of several input variables serving as network inputs, some insight into the...

With the celebrated model of Black and Scholes in 1973 the development of modern option pricing models started. One of the assumptions of the Black and Scholes model is that the risky asset evolves according to a geometric Brownian motion which implies normally distributed log-returns. As...

The mainstream model of option pricing is based on an exogenously given process of price movements. The implication of this assumption is that price movements are not affected by actions of market participants. However, if we assume that there are indeed impacts on the price movements it no...

Many economic and econometric applications require the integration of functions lacking a closed form antiderivative, which is therefore a task that can only be solved by numerical methods. We propose a new family of probability densities that can be used as substitutes and have the property of...