687 research outputs found
Convergence of Heston to SVI
In this short note, we prove by an appropriate change of variables that the
SVI implied volatility parameterization presented in Gatheral's book and the
large-time asymptotic of the Heston implied volatility agree algebraically,
thus confirming a conjecture from Gatheral as well as providing a simpler
expression for the asymptotic implied volatility in the Heston model. We show
how this result can help in interpreting SVI parameters.Comment: 5 page
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
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
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
A generalization of the rational rough Heston approximation
We extend the rational approximation of the solution of the rough Heston
fractional ODE in [GR19] to the case of the Mittag-Leffler kernel. We provide
numerical evidence of the convergence of the solution
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