This paper develops a closed form risk-neutral valuation model for pricing Europeanstyle options when the underlying has a mixture of transformed-normaldistributions. Specifically, we introduce the mixture of g distributions, which containsthe mixture of normal and lognormal distributions as a...

The gamma class of distributions encompasses several important distributionseither as special or limiting cases, or through simple transformations. In this paper,we established the link between the real and the risk neutral distributions, andprovided a formal proof for the existence of the risk...

This analysis reveals the restricted scope of approaches which utilise arbitrage based arguments toprice contingent claims whose payoffs are determined by the outcome of non-zero-sum valuationgames between financial market participants. Many examples of such model formulations can befound, for...

This paper proposes a new explanation for the smile and skewness effects in implied volatilities. Starting from a microeconomic equilibrium approach, we develop a diffusion model for stock prices explicitly incorporating the technical demand induced by hedging strategies. This leads to a...

The basic model of financial economics is the Samuelson model of geometric Brownian motion because of the celebrated Black-Scholes formula for pricing the call option. The asset volatility is a linear function of the asset value and the model guarantees positive asset prices. We show that the...

Let X be a seminmartingale and Teta the space of all predictable X-integrable processes teta such that integral tetat dX is inthe space S square of semimartingales. We consider the problem of approximating a given random variable H element of L square (P) by the sum of a constant c and a...

In this survey we discuss models with level-dependent and stochastic volatility from the viewpoint of erivative asset analysis. Both classes of models are generalisations of the classical Black-Scholes model; they have been developed in an effort to build models that are flexible enough to cope...

Starting with observable annually compounded forward rates we derive a term structure model of interest rates. The model relies upon the assumption that a specific set of annually compounded forward rates is log-normally distributed. We derive solutions for interest rate caps and floors as well...

In this paper a stochastic volatility model is presented that directly prescribes the stochastic development of the implied Black-Scholes volatilities of a set of given standard options. Thus the model is able to capture the stochastic movements of a full term structure of implied volatilities....

We study the problem of convergence of discrete-time option values to continuous-time option values. While previous papers typically concentrate on the approximation of geometric Brownian motion by a binomial tree, we consider here the case where the model is incomplete in both continuos and...