In an incomplete market framework, contingent claims are of particular interest since they improve the market efficiency. This paper addresses the problem of market completeness when trading in contingent claims is allowed. We extend recent results by Bajeux and Rochet (1996) in a stochastic...

We study the critical price of an American put option near expiration in the Black-Scholes model. Our main result is an estimate for the difference &Pmacr; ("t")- "K" between the critical price at time "t" and the exercise price as "t" approaches the maturity of the option. Copyright 1995 Blackwell...

This article deals with the estimation of continuous-time stochastic volatility models of option pricing. We argue that option prices are much more informative about the parameters than are asset prices. This is confirmed in a Monte Carlo experiment that compares two very simple strategies based...

We define (d,n)-coherent risk measures as set-valued maps from <InlineEquation ID="Equ1"> <EquationSource Format="TEX">$L^\infty_d$</EquationSource> </InlineEquation> into <InlineEquation ID="Equ2"> <EquationSource Format="TEX">$\mathbb{R}^n$</EquationSource> </InlineEquation> satisfying some axioms. We show that this definition is a convenient extension of the real-valued risk measures introduced by Artzner et al. [2]. We then discuss the aggregation issue, i.e., the...</equationsource></inlineequation></equationsource></inlineequation>

This paper presents an original probabilistic method for the numerical computations of Greeks (i.e. price sensitivities) in finance. Our approach is based on the {\it integration-by-parts} formula, which lies at the core of the theory of variational stochastic calculus, as developed in the...

We consider a multivariate financial market with transaction costs as in Kabanov. We study the problem of finding the minimal initial capital needed to hedge, without risk, European-type contingent claims. We prove that the value of this stochastic control problem is given by the cost of the...