Market option prices in last 20 years confirmed deviations from the Black and Scholes (BS) models assumptions, especially on the BS implied volatility. Implied binomialtrees (IBT) models capture the variations of the implied volatility known as \volatility smile". They provide a discrete...

In January 2005 the EU-wide CO2 emissions trading system (EU-ETS) has formally entered into operation.Within the new trading system, the right to emit a particular amount of CO2 becomes a tradable commodity - called EU Allowances (EUAs) - and affected companies, traders and investors will face...

We present solutions to some discounted optimal stopping problems for the maximum process in a model driven by a Brownian motion and a compound Poisson process with exponential jumps. The method of proof is based on reducing the initial problems to integro-differential free-boundary problems...

We present a solution to some discounted optimal stopping problem for the maximum of a geometric Brownian motion on a finite time interval. The method of proof is based on reducing the initial optimal stopping problem with the continuation region determined by an increasing continuous boundary...

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...

The calibration of option pricing models leads to the minimization of an error functional. We show that its usual specification as a root mean squared error implies fluctuating exotics prices and possibly wrong prices...

State price density (SPD) contains important information concerning market expectations. In existing literature, a constrained estimator of the SPD is found by nonlinear least squares in a suitable Sobolev space...

We present a closed form solution to the perpetual American double barrier call option problem in a model driven by a Brownian motion and a compound Poissonprocess with exponential jumps. The method of proof is based on reducing the initialirregular optimal stopping problem to an...

A new algorithm for finding value functions of finite horizon optimal stopping problems in one-dimensional diffusion models is presented. It is based on a time discretization of the corresponding integral equation. The proposed iterative procedure for solving the discretized integral equation...