8 research outputs found
Fluctuation symmetries for work and heat
We consider a particle dragged through a medium at constant temperature as
described by a Langevin equation with a time-dependent potential. The
time-dependence is specified by an external protocol. We give conditions on
potential and protocol under which the dissipative work satisfies an exact
symmetry in its fluctuations for all times. We also present counter examples to
that exact fluctuation symmetry when our conditions are not satisfied. Finally,
we consider the dissipated heat which differs from the work by a temporal
boundary term. We explain when and why there can be a correction to the
standard fluctuation theorem due to the unboundedness of that temporal
boundary. However, the corrected fluctuation symmetry has again a general
validity.Comment: 10 pages, 4 figures (v2: minor typographic corrections
Vanna-Volga methods applied to FX derivatives : from theory to market practice
We study Vanna-Volga methods which are used to price first generation exotic
options in the Foreign Exchange market. They are based on a rescaling of the
correction to the Black-Scholes price through the so-called `probability of
survival' and the `expected first exit time'. Since the methods rely heavily on
the appropriate treatment of market data we also provide a summary of the
relevant conventions. We offer a justification of the core technique for the
case of vanilla options and show how to adapt it to the pricing of exotic
options. Our results are compared to a large collection of indicative market
prices and to more sophisticated models. Finally we propose a simple
calibration method based on one-touch prices that allows the Vanna-Volga
results to be in line with our pool of market data
Average error exponent in Gallager low-density parity-check codes
We present a theoretical method for a direct evaluation of the average error exponent in Gallager error-correcting codes using methods of statistical physics. Results for the binary symmetric channel(BSC)are presented for codes of both finite and infinite connectivity
Cavity approach for real variables on diluted graphs and application to synchronization in small-world lattices
We study XY spin systems on small world lattices for a variety of graph
structures, e.g. Poisson and scale-free, superimposed upon a one dimensional
chain. In order to solve this model we extend the cavity method in the one
pure-state approximation to deal with real-valued dynamical variables. We find
that small-world architectures significantly enlarge the region in parameter
space where synchronization occurs. We contrast the results of population
dynamics performed on a truncated set of cavity fields with Monte Carlo
simulations and find excellent agreement. Further, we investigate the
appearance of replica symmetry breaking in the spin-glass phase by numerically
analyzing the proliferation of pure states in the message passing equations.Comment: 10 pages, 3 figure
VANNA-VOLGA METHODS APPLIED TO FX DERIVATIVES: FROM THEORY TO MARKET PRACTICE
We study Vanna-Volga methods which are used to price first generation exotic options in the Foreign Exchange market. They are based on a rescaling of the correction to the Black–Scholes price through the so-called "probability of survival" and the "expected first exit time". Since the methods rely heavily on the appropriate treatment of market data we also provide a summary of the relevant conventions. We offer a justification of the core technique for the case of vanilla options and show how to adapt it to the pricing of exotic options. Our results are compared to a large collection of indicative market prices and to more sophisticated models. Finally we propose a simple calibration method based on one-touch prices that allows the Vanna-Volga results to be in line with our pool of market data.Vanna-Volga, Foreign Exchange, exotic options, market conventions
Vanna-Volga methods applied to FX derivatives: from theory to market practice
We study Vanna-Volga methods which are used to price first generation exotic options in the Foreign Exchange market. They are based on a rescaling of the correction to the Black-Scholes price through the so-called `probability of survival' and the `expected first exit time'. Since the methods rely heavily on the appropriate treatment of market data we also provide a summary of the relevant conventions. We offer a justification of the core technique for the case of vanilla options and show how to adapt it to the pricing of exotic options. Our results are compared to a large collection of indicative market prices and to more sophisticated models. Finally we propose a simple calibration method based on one-touch prices that allows the Vanna-Volga results to be in line with our pool of market data.Vanna-Volga; Foreign Exchange; exotic options; market conventions.