153 research outputs found
Pricing Bermudan options under local L\'evy models with default
We consider a defaultable asset whose risk-neutral pricing dynamics are
described by an exponential L\'evy-type martingale. This class of models allows
for a local volatility, local default intensity and a locally dependent L\'evy
measure. We present a pricing method for Bermudan options based on an
analytical approximation of the characteristic function combined with the COS
method. Due to a special form of the obtained characteristic function the price
can be computed using a Fast Fourier Transform-based algorithm resulting in a
fast and accurate calculation. The Greeks can be computed at almost no
additional computational cost. Error bounds for the approximation of the
characteristic function as well as for the total option price are given
Pricing options and computing implied volatilities using neural networks
This paper proposes a data-driven approach, by means of an Artificial Neural
Network (ANN), to value financial options and to calculate implied volatilities
with the aim of accelerating the corresponding numerical methods. With ANNs
being universal function approximators, this method trains an optimized ANN on
a data set generated by a sophisticated financial model, and runs the trained
ANN as an agent of the original solver in a fast and efficient way. We test
this approach on three different types of solvers, including the analytic
solution for the Black-Scholes equation, the COS method for the Heston
stochastic volatility model and Brent's iterative root-finding method for the
calculation of implied volatilities. The numerical results show that the ANN
solver can reduce the computing time significantly
D-TIPO: Deep time-inconsistent portfolio optimization with stocks and options
In this paper, we propose a machine learning algorithm for time-inconsistent
portfolio optimization. The proposed algorithm builds upon neural network based
trading schemes, in which the asset allocation at each time point is determined
by a a neural network. The loss function is given by an empirical version of
the objective function of the portfolio optimization problem. Moreover, various
trading constraints are naturally fulfilled by choosing appropriate activation
functions in the output layers of the neural networks. Besides this, our main
contribution is to add options to the portfolio of risky assets and a risk-free
bond and using additional neural networks to determine the amount allocated
into the options as well as their strike prices.
We consider objective functions more in line with the rational preference of
an investor than the classical mean-variance, apply realistic trading
constraints and model the assets with a correlated jump-diffusion SDE. With an
incomplete market and a more involved objective function, we show that it is
beneficial to add options to the portfolio. Moreover, it is shown that adding
options leads to a more constant stock allocation with less demand for drastic
re-allocations.Comment: 27 pages, 7 figure
A neural network-based framework for financial model calibration
A data-driven approach called CaNN (Calibration Neural Network) is proposed
to calibrate financial asset price models using an Artificial Neural Network
(ANN). Determining optimal values of the model parameters is formulated as
training hidden neurons within a machine learning framework, based on available
financial option prices. The framework consists of two parts: a forward pass in
which we train the weights of the ANN off-line, valuing options under many
different asset model parameter settings; and a backward pass, in which we
evaluate the trained ANN-solver on-line, aiming to find the weights of the
neurons in the input layer. The rapid on-line learning of implied volatility by
ANNs, in combination with the use of an adapted parallel global optimization
method, tackles the computation bottleneck and provides a fast and reliable
technique for calibrating model parameters while avoiding, as much as possible,
getting stuck in local minima. Numerical experiments confirm that this
machine-learning framework can be employed to calibrate parameters of
high-dimensional stochastic volatility models efficiently and accurately.Comment: 34 pages, 9 figures, 11 table
On local Fourier analysis of multigrid methods for PDEs with jumping and random coefficients
In this paper, we propose a novel non-standard Local Fourier Analysis (LFA)
variant for accurately predicting the multigrid convergence of problems with
random and jumping coefficients. This LFA method is based on a specific basis
of the Fourier space rather than the commonly used Fourier modes. To show the
utility of this analysis, we consider, as an example, a simple cell-centered
multigrid method for solving a steady-state single phase flow problem in a
random porous medium. We successfully demonstrate the prediction capability of
the proposed LFA using a number of challenging benchmark problems. The
information provided by this analysis helps us to estimate a-priori the time
needed for solving certain uncertainty quantification problems by means of a
multigrid multilevel Monte Carlo method
- …