1,128 research outputs found
On the Exponentiation of Interval Matrices
The numerical computation of the exponentiation of a real matrix has been intensively studied. The main objective of a good numerical method is to deal with round-off errors and computational cost. The situation is more complicated when dealing with interval matrices exponentiation: Indeed, the main problem will now be the dependency loss of the different occurrences of the variables due to interval evaluation, which may lead to so wide enclosures that they are useless. In this paper, the problem of computing a sharp enclosure of the interval matrix exponential is proved to be NP-hard. Then the scaling and squaring method is adapted to interval matrices and shown to drastically reduce the dependency loss w.r.t. the interval evaluation of the Taylor series
Moment Methods for Exotic Volatility Derivatives
The latest generation of volatility derivatives goes beyond variance and
volatility swaps and probes our ability to price realized variance and sojourn
times along bridges for the underlying stock price process. In this paper, we
give an operator algebraic treatment of this problem based on Dyson expansions
and moment methods and discuss applications to exotic volatility derivatives.
The methods are quite flexible and allow for a specification of the underlying
process which is semi-parametric or even non-parametric, including
state-dependent local volatility, jumps, stochastic volatility and regime
switching. We find that volatility derivatives are particularly well suited to
be treated with moment methods, whereby one extrapolates the distribution of
the relevant path functionals on the basis of a few moments. We consider a
number of exotics such as variance knockouts, conditional corridor variance
swaps, gamma swaps and variance swaptions and give valuation formulas in
detail
Customisable arithmetic hardware designs
Imperial Users onl
A Matrix Approach to Numerical Solution of the DGLAP Evolution Equations
A matrix-based approach to numerical integration of the DGLAP evolution
equations is presented. The method arises naturally on discretisation of the
Bjorken x variable, a necessary procedure for numerical integration. Owing to
peculiar properties of the matrices involved, the resulting equations take on a
particularly simple form and may be solved in closed analytical form in the
variable t=ln(alpha_0/alpha). Such an approach affords parametrisation via data
x bins, rather than fixed functional forms. Thus, with the aid of the full
correlation matrix, appraisal of the behaviour in different x regions is
rendered more transparent and free of pollution from unphysical
cross-correlations inherent to functional parametrisations. Computationally,
the entire programme results in greater speed and stability; the matrix
representation developed is extremely compact. Moreover, since the parameter
dependence is linear, fitting is very stable and may be performed analytically
in a single pass over the data values.Comment: 13 pages, no figures, typeset with revtex4 and uses packages:
acromake, amssym
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