Using a suitable Hull and White type formula we develop a methodology to obtain a second order approximation to the implied volatility for very short maturities. Using this approximation we accurately calibrate the full set of parameters of the Heston model. One of the reasons that makes our...

We present a method to develop simple option pricing approximation formulas for a fractional Heston model, where the volatility process is defined by means of a fractional integration of a diffusion process. This model preserves the short-time behaviour of the Heston model, at the same time it...

This paper analyses the robustness of Least-Squares Monte Carlo, a technique recently proposed by Longstaff and Schwartz (2001) for pricing American options. This method is based on least-squares regressions in which the explanatory variables are certain polynomial functions. We analyze the...

In this paper we use Malliavin calculus techniques to obtain an expression for the short-time behavior of the at-the-money implied volatility skew for a generalization of the Bates model, where the volatility does not need to be neither a difussion, nor a Markov process as the examples in...

We see that the price of an european call option in a stochastic volatility framework can be decomposed in the sum of four terms, which identify the main features of the market that affect to option prices: the expected future volatility, the correlation between the volatility and the noise...

Executive compensation packages are often valued in an inconsistent manner: while employee stock options (ESOs) are typically valued ex-ante, cash bonuses are valued ex-post. This renders the existing valuation models of employee compensation packages theoretically unsatisfactory and,...

We develop a general error analysis framework for the Monte Carlo simulation of densities for functionals in Wiener space. We also study variance reduction methods with the help of Malliavin derivatives. For this, we give some general heuristic principles which are applied to diffusion...

In this paper we address a problem arising in risk management; namely the study of price variations of different contingent claims in the Black-Scholes model due to anticipating future events. The method we propose to use is an extension of the classical Vega index, i.e. the price derivative...

By means of Malliavin Calculus we see that the classical Hull and White formula for option pricing can be extended to the case where the noise driving the volatility process is correlated with the noise driving the stock prices. This extension will allow us to construct option pricing...

This paper presents a two-factor (Vasicek-CIR) model of the term structure of interest rates and develops its pricing and empirical properties. We assume that default free discount bond prices are determined by the time to maturity and two factors, the long-term interest rate and the spread....