6,515 research outputs found
Smart expansion and fast calibration for jump diffusion
Using Malliavin calculus techniques, we derive an analytical formula for the
price of European options, for any model including local volatility and Poisson
jump process. We show that the accuracy of the formula depends on the
smoothness of the payoff function. Our approach relies on an asymptotic
expansion related to small diffusion and small jump frequency/size. Our formula
has excellent accuracy (the error on implied Black-Scholes volatilities for
call option is smaller than 2 bp for various strikes and maturities).
Additionally, model calibration becomes very rapid.Comment: in Finance and Stochastics (2009) a paraitr
Smart expansion and fast calibration for jump diffusion
Using Malliavin calculus techniques, we derive an analytical formula for the price of European options, for any model including local volatility and Poisson jump process. We show that the accuracy of the formula depends on the smoothness of the payoff function. Our approach relies on an asymptotic expansion related to small diffusion and small jump frequency/size. Our formula has excellent accuracy (the error on implied Black-Scholes volatilities for call option is smaller than 2 bp for various strikes and maturities). Additionally, model calibration becomes very rapid.asymptotic expansion; Malliavin calculus; volatility skew and smile; small diffusion process; small jump frequency/size
The learning curve in a competitive industry.
We consider the learning curve in an industry with free entry and exit, and price-taking firms. A unique equilibrium exists if the fixed cost is positive. While equilibrium profits are zero, mature firms earn rents on their learning, and, if costs are convex, no firm can profitably enter after the date the industry begins. Under some cost and demand conditions, however, firms may have to exit the market despite their experience gained earlier. Furthermore identical firms facing the same prices may produce different quantities. The market outcome is always socially efficient, even if dictates that firms exit after learning. Finally, actual and optimal industry concentration does not always increase in the intensity of learning.Learning curve; Industry evolution; Perfect competition;
Closed forms for European options in a local volatility model
Because of its very general formulation, the local volatility model does not have an analytical solution for European options. In this article, we present a new methodology to derive closed form solutions for the price of any European options. The formula results from an asymptotic expansion, terms of which are Black-Scholes price and related Greeks. The accuracy of the formula depends on the payoff smoothness and it converges with very few terms.
Semiconservative Replication in the Quasispecies Model
This paper extends Eigen's quasispecies equations to account for the
semiconservative nature of DNA replication. We solve the equations in the limit
of infinite sequence length for the simplest case of a static, sharply peaked
fitness landscape. We show that the error catastrophe occurs when , the
product of sequence length and per base pair mismatch probability, exceeds , where is the first order growth rate
constant of the viable ``master'' sequence (with all other sequences having a
first-order growth rate constant of ). This is in contrast to the result
of for conservative replication. In particular, as ,
the error catastrophe is never reached for conservative replication, while for
semiconservative replication the critical approaches .
Semiconservative replication is therefore considerably less robust than
conservative replication to the effect of replication errors. We also show that
the mean equilibrium fitness of a semiconservatively replicating system is
given by below the error catastrophe, in contrast to
the standard result of for conservative replication (derived by
Kimura and Maruyama in 1966).Comment: 15 pages, 7 figures, to be submitted to Phys. Rev.
Energy conservation and numerical stability for the reduced MHD models of the non-linear JOREK code
In this paper we present a rigorous derivation of the reduced MHD models with
and without parallel velocity that are implemented in the non-linear MHD code
JOREK. The model we obtain contains some terms that have been neglected in the
implementation but might be relevant in the non-linear phase. These are
necessary to guarantee exact conservation with respect to the full MHD energy.
For the second part of this work, we have replaced the linearized time stepping
of JOREK by a non-linear solver based on the Inexact Newton method including
adaptive time stepping. We demonstrate that this approach is more robust
especially with respect to numerical errors in the saturation phase of an
instability and allows to use larger time steps in the non-linear phase
A general kinetic model for the photothermal oxidation of polypropylene
A general kinetic model for the photothermal oxidation of polypropylene has been derived from the basic auto-oxidation mechanistic scheme in which the main sources of radicals are the thermolysis and photolysis of the most unstable species, i.e hydroperoxides. Thermolysis is a uni- or bi-molecular reaction whose rate constant obeys an Arrhenius law. In contrast, photolysis is exclusively a unimolecular reaction and its rate constant is independent of temperature. According to the quantum theory, this latter is proportional to the energy absorbed by photosensitive species and thus, accounts for the impact of UV-light intensity and wavelength on the global oxidation kinetics. The validity of this model has been checked on iPP films homogeneously oxidized in air over a wide range of temperatures and UV-light sources. It gives access to the concentration changes of: (i) primary (hydroperoxides) and secondary (carbonyls) oxidation products, (ii) double bonds, (iii) chain scissions and crosslinking nodes, but also to the subsequent changes in molecular masses. These calculations are in full agreement with the photolysis results reported by Carlsson and Wiles in the 70s [1–3]. However, the model seems to be only valid for UV-light energies equivalent to about 10 suns as upper boundary, presumably because of multiphotonic excitations or chromophores photosensitization (i.e. termolecular photo-physical reactions), both enhanced at high irradiances
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