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's volatility is a linear function of the asset value and the model garantees positive asset prices. In this paper it...

In this paper a new credit risk model for credit derivatives is presented. The model is based upon the Libor market modelling framework for default-free interest rates. We model effective default-free forward rates and effective forward credit spreads as lognormal diffusion processes, and...

We consider two sequences of Markov chains inducing equivalent measures on the discrete path space. We establish conditions under which these two measures converge weakly to measures induced on the Wiener space by weak solutions of two SDEs, which are unique in the sense of probability law. We...

We study the pricing and hedging of derivative securities with uncertainty about the volatility of the underlying asset. Rather than taking all models from a prespecified class equally seriously, we penalise less plausible ones based on their "distance" to a reference local volatility model. In...

In a tractable stochastic volatility model, we identify the price of the smile as the price of the unspanned risks traded in SPX option markets. The price of the smile reflects two persistent volatility and skewness risks, which imply a downward sloping term structure of low-frequency variance...

Supported by empirical examples, this paper provides a theoretical analysis on the impacts of using a suboptimal information set for the estimation of the empirical pricing kernel and, more in general, for the validity of the fundamental theorems of asset pricing. While inferring the...

We propose a nonparametric Bayesian approach for the estimation of the pricing kernel. Historical stock returns and option market data are combined through the Dirichlet Process (DP) to construct an option-adjusted physical measure. The precision parameter of the DP process is calibrated to the...

A new method to retrieve the risk-neutral probability measure from observed option prices is developed and a closed form pricing formula for European options is obtained by employing a modified Gram-Charlier series expansion, known as the Gauss-Hermite expansion. This expansion converges for...

This paper makes use of an integrated benchmark modeling framework that allows us to derive term structure equations for bond and forward prices. The benchmark or numeraire is chosen to be the growth optimal portfolio (GOP). For deterministic short rate the solution of the bond term structure...