Option pricing models are calibrated to market data of plain vanillas by minimization of an error functional. From the economic viewpoint, there are several possibilities to measure the error between the market and the model. These different specifications of the error give rise to different...

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. We propose a simple and natural method to overcome these problems, illustrate...

We study the problem of finding the minimal initial capital needed in order to hedge without risk a barrier option when the vector of proportions of wealth invested in each risky asset is constraint to lie in a closed convex domain. In the context of a Brownian diffusion model, we provide a PDE...

The pricing accuracy and pricing performance of local volatility models crucially depends on absence of arbitrage in the implied volatility surface: an input implied volatility surface that is not arbitrage-free invariably results in negative transition probabilities and/ or negative local...

We propose a new method to estimate the empirical pricing kernel based on option data. We estimate the pricing kernel nonparametrically by using the ratio of the risk-neutral density estimator and the subjective density estimator. The risk-neutral density is approximated by a weighted kernel...

Here we develop methods for efficient pricing multidimensional discrete time American and Bermudan options by using regression based algorithms together with a new approach towards constructing upper bounds for the price of the option. Applying the sample space with payoffs at the optimal...

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

We present an explicit solution to the formulated in [17] optimal stopping problem for a geometric compound Poisson process with exponential jumps. The method of proof is based on reducing the initial problem to an integro-differential free-boundary problem where the smooth fit may break down...

In this paper, we study the statistical properties of the moneyness scaling transformation by Leung and Sircar (2015). This transformation adjusts the moneyness coordinate of the implied volatility smile in an attempt to remove the discrepancy between the IV smiles for levered and unlevered ETF...

In the ideal Black-Scholes world, financial time series are assumed 1) stationary (time homogeneous) and 2) having conditionally normal distribution given the past. These two assumptions have been widely-used in many methods such as the RiskMetrics, one risk management method considered as...