This paper examines the pricing of options by approximating extensions of the Black-Scholes setup in which volatility follows a separate diffusion process. It gereralizes the well-known binomial model, constructing a discrete two-dimensional lattice. We discuss convergence issues extensively and...

Viewing binomial models as a discrete approximation of the respective continuous models, the interest focuses on the notions of convergence and especially "fast" convergence of prices. Though many authors were proposing new models, none of them could successfully explain better performance for...

Binomial models, which rebuild the continuous setup in the limit, serve for approximative valuation of options, especially where formulas cannot be derived mathematically. Even with the valuation of European call options distorting irregularities occur. For this case, sources of convergence...

The historical returns on equity index options are well known to be strikingly negative. That is typically explained either by investors having convex marginal utility over stock returns (e.g. crash/variance aversion) or by intermediaries demanding a premium for hedging risk. This paper examines...

This paper reviews recent developments in macro and finance on the relationship between financial risk and the real economy. We focus on three specific topics: the term structure of uncertainty, time variation - and specifically the long-term decline - in the variance risk premium, and time...

In this paper we study Binomial Models with random time steps. We explain, how calculating values for European and American Call and Put options is straightforward for the Random-Time Binomial Model. We present the conditions to ensure weak-convergence to the Black-Scholes setup and convergence...

The extension of the Black-Scholes option pricing theory to the valuation of barrier options is reconsidered. Working in the binomial framework of CRR we show how various types of barrier options can be priced either by backward induction or by closed binomial formulas. We also consider...

The finding of clustered volatility and ARCH effects is ubiquitous in financial data. This paper presents a possible explanation of this phenomenon within a multi-agent framework of speculative activity. In the model, both chartist and fundamentalist strategies are considered with agents...

This paper reports statistical analyses performed on simulated data from a stochastic multi-agent model of speculative behaviour in a financial market. The price dynamics resulting from this artificial market process exhibits the same type of scaling laws as do empirical data from stock markets...

We develop a new approach to pricing and hedging contingent claims in incomplete markets. Mimicking as closely as possible in an incomplete markets framework the no--arbitrage arguments that have been developed in complete markets leads us to defining the concept of pseudo--arbitrage. Building...