Partial Derivative Approach for Option Pricing in a Simple Stochastic Volatility Model

We study a market model in which the volatility of the stock may jump at a random time from a fixed value to another fixed value. This model was already described in the literature. We present a new approach to the problem, based on partial derivative equations, which gives a different perspective to the problem. Within our framework we can easily consider several prescriptions for the market price of volatility risk, and interpret their financial meaning. Thus, we recover solutions previously cited in the literature as well as obtain new ones.Comment: 21 pages, 3 figures, submitted for publicatio

Malliavin calculus in finance

This article is an introduction to Malliavin Calculus for practitioners. We treat one specific application to the calculation of greeks in Finance. We consider also the kernel density method to compute greeks and an extension of the Vega index called the local vega index.Malliavin claculus, computational finance, Greeks, Monte Carlo methods, kernel density method

All-sky search algorithms for monochromatic signals in resonant bar GW detector data

In this paper we design and develop several filtering strategies for the analysis of data generated by a resonant bar Gravitational Wave (GW) antenna, with the goal to assess the presence (or absence) in them of long duration monochromatic GW signals, as well as their eventual amplitude and frequency, within the sensitivity band of the detector. Such signals are most likely generated in the fast rotation of slightly asymmetric spinning stars. We shall develop the practical procedures, together with the study of their statistical properties, which will provide us with useful information on each technique's performance. The selection of candidate events will then be established according to threshold-crossing probabilities, based on the Neyman-Pearson criterion. In particular, it will be shown that our approach, based on phase estimation, presents better signal-to-noise ratio than the most common one of pure spectral analysis.Comment: 17 pages, 10 PS figures, psbox, MNRAS TeX, submitted to MNRAS, revised 22-june-1998, full quality figures available compressed at ftp://fismat.ffn.ub.es/pub/papers/gr-qc/fig_9804026.zi

Merge of two oppositely biased Wiener processes

We introduce a technique to merge two biased Brownian motions into a single regular process. The outcome follows a stochastic differential equation with a constant diffusion coefficient and a non-linear drift. The emerging stochastic process has outstanding properties, such as spatial and temporal translational invariance of its mean squared displacement, and can be efficiently simulated via a random walk with site-dependent one-step transition probabilities.Comment: 6 pages, no figure

Invariance in Quantum Walks

In this Chapter, we present some interesting properties of quantum walks on the line. We concentrate our attention in the emergence of invariance and provide some insights into the ultimate origin of the observed behavior. In the first part of the Chapter, we review the building blocks of the quantum-mechanical version of the standard random walk in one dimension. The most distinctive difference between random and quantum walks is the replacement of the random coin in the former by the action of a unitary operator upon some internal property of the later. We provide explicit expressions for the solution to the problem when the most general form for the homogeneous unitary operator is considered, and we analyze several key features of the system as the presence of symmetries or stationary limits. After that, we analyze the consequences of letting the properties of the coin operator change from site to site, and from time step to time step. In spite of this lack of homogeneity, the probabilistic properties of the motion of the walker can remain unaltered if the coin variability is chosen adequately. Finally, we show how this invariance can be connected to the gauge freedom of electromagnetism