Here we develop an approach for efficient pricing discrete-time American and Bermudan options which employs the fact that such options are equivalent to theEuropean ones with a consumption, combined with analysis of the market model over a small number of steps ahead. This approach allows...

The calibration of financial models has become rather important topic in recent years mainly because of the need to price increasingly complex options in a consistent way. The choice of the underlying model is crucial for the good performance of any calibration procedure. Recent empirical...

We investigate the problem of calibrating an exponential Lévy model based on market prices of vanilla options. We show that this inverse problem is in general severely ill-posed and we derive exact minimax rates of convergence. The estimation procedure we propose is based on the explicit...

Implied volatility is one of the key issues in modern quantitative finance, since plain vanilla option prices contain vital information for pricing and hedging of exotic and illiquid options. European plain vanilla options are nowadays widely traded, which results in a great amount of...

Trading, hedging and risk analysis of complex option portfolios depend on accurate pricing models. The modelling of implied volatilities (IV) plays an important role, since volatility is the crucial parameter in the Black-Scholes (BS) pricing formula. It is well known from empirical studies that...

Many of the concepts in theoretical and empirical finance developed over thepast decades - including the classical portfolio theory, the Black-Scholes-Mertonoption pricing model and the RiskMetrics variance-covariance approach toValue at Risk (VaR) - rest upon the assumption that asset returns...

Options are financial derivatives that, conditional on the price of an underlyingasset, constitute a right to transfer the ownership of this underlying. Morespecifically, a European call and put options give their owner the right to buyand sell, respectively, at a fixed strike price at a given...

The doctoral thesis of Louis Bachelier (1900) is widely considered as the seminal work inoption pricing theory. However, only a few years later, 1908, Vinzenz Bronzin, who wasa professor of actuarial science at the Accademia di Commercio e Nautica in Trieste,published a booklet (in German) on...