466 research outputs found
Arbitrage-free SVI volatility surfaces
In this article, we show how to calibrate the widely-used SVI
parameterization of the implied volatility surface in such a way as to
guarantee the absence of static arbitrage. In particular, we exhibit a large
class of arbitrage-free SVI volatility surfaces with a simple closed-form
representation. We demonstrate the high quality of typical SVI fits with a
numerical example using recent SPX options data.Comment: 25 pages, 6 figures Corrected some typos. Extended bibliography.
Paper restructured, Main theorem (Theorem 4.1) improved. Proof of Theorem 4.3
amende
Drift dependence of optimal trade execution strategies under transient price impact
We give a complete solution to the problem of minimizing the expected
liquidity costs in presence of a general drift when the underlying market
impact model has linear transient price impact with exponential resilience. It
turns out that this problem is well-posed only if the drift is absolutely
continuous. Optimal strategies often do not exist, and when they do, they
depend strongly on the derivative of the drift. Our approach uses elements from
singular stochastic control, even though the problem is essentially
non-Markovian due to the transience of price impact and the lack in Markovian
structure of the underlying price process. As a corollary, we give a complete
solution to the minimization of a certain cost-risk criterion in our setting
Jets in Effective Theory: Summing Phase Space Logs
We demonstrate how to resum phase space logarithms in the Sterman-Weinberg
(SW) dijet decay rate within the context of Soft Collinear Effective theory
(SCET). An operator basis corresponding to two and three jet events is defined
in SCET and renormalized. We obtain the RGE of the two and three jet operators
and run the operators from the scale to the phase space scale . This phase space scale, where is the
cone half angle of the jet, defines the angular region of the jet. At we determine the mixing of the three and two jet operators. We
combine these results with the running of the two jet shape function, which we
run down to an energy cut scale . This defines the resumed SW
dijet decay rate in the context of SCET. The approach outlined here
demonstrates how to establish a jet definition in the context of SCET. This
allows a program of systematically improving the theoretical precision of jet
phenomenology to be carried out.Comment: 25 pages, 4 figures, V2: Typos fixed, writing clarified, detail on
PSRG added. Matching onto jet definition changed to taking place at collinear
scal
Time-Changed Fast Mean-Reverting Stochastic Volatility Models
We introduce a class of randomly time-changed fast mean-reverting stochastic
volatility models and, using spectral theory and singular perturbation
techniques, we derive an approximation for the prices of European options in
this setting. Three examples of random time-changes are provided and the
implied volatility surfaces induced by these time-changes are examined as a
function of the model parameters. Three key features of our framework are that
we are able to incorporate jumps into the price process of the underlying
asset, allow for the leverage effect, and accommodate multiple factors of
volatility, which operate on different time-scales
An Optimal Execution Problem with Market Impact
We study an optimal execution problem in a continuous-time market model that
considers market impact. We formulate the problem as a stochastic control
problem and investigate properties of the corresponding value function. We find
that right-continuity at the time origin is associated with the strength of
market impact for large sales, otherwise the value function is continuous.
Moreover, we show the semi-group property (Bellman principle) and characterise
the value function as a viscosity solution of the corresponding
Hamilton-Jacobi-Bellman equation. We introduce some examples where the forms of
the optimal strategies change completely, depending on the amount of the
trader's security holdings and where optimal strategies in the Black-Scholes
type market with nonlinear market impact are not block liquidation but gradual
liquidation, even when the trader is risk-neutral.Comment: 36 pages, 8 figures, a modified version of the article "An optimal
execution problem with market impact" in Finance and Stochastics (2014
On small time asymptotics for rough differential equations driven by fractional Brownian motions
We survey existing results concerning the study in small times of the density
of the solution of a rough differential equation driven by fractional Brownian
motions. We also slightly improve existing results and discuss some possible
applications to mathematical finance.Comment: This is a survey paper, submitted to proceedings in the memory of
Peter Laurenc
Light--like Wilson loops and gauge invariance of Yang--Mills theory in 1+1 dimensions
A light-like Wilson loop is computed in perturbation theory up to for pure Yang--Mills theory in 1+1 dimensions, using Feynman and
light--cone gauges to check its gauge invariance. After dimensional
regularization in intermediate steps, a finite gauge invariant result is
obtained, which however does not exhibit abelian exponentiation. Our result is
at variance with the common belief that pure Yang--Mills theory is free in 1+1
dimensions, apart perhaps from topological effects.Comment: 10 pages, plain TeX, DFPD 94/TH/
On planar gluon amplitudes/Wilson loops duality
There is growing evidence that on-shell gluon scattering amplitudes in planar
N=4 SYM theory are equivalent to Wilson loops evaluated over contours
consisting of straight, light-like segments defined by the momenta of the
external gluons. This equivalence was first suggested at strong coupling using
the AdS/CFT correspondence and has since been verified at weak coupling to one
loop in perturbation theory. Here we perform an explicit two-loop calculation
of the Wilson loop dual to the four-gluon scattering amplitude and demonstrate
that the relation holds beyond one loop. We also propose an anomalous conformal
Ward identity which uniquely fixes the form of the finite part (up to an
additive constant) of the Wilson loop dual to four- and five-gluon amplitudes,
in complete agreement with the BDS conjecture for the multi-gluon MHV
amplitudes.Comment: 16 pages, 1 figure. v2: minor correction
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