364 research outputs found
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
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