73,614 research outputs found
Robust pricing--hedging duality for American options in discrete time financial markets
We investigate pricing-hedging duality for American options in discrete time
financial models where some assets are traded dynamically and others, e.g. a
family of European options, only statically. In the first part of the paper we
consider an abstract setting, which includes the classical case with a fixed
reference probability measure as well as the robust framework with a
non-dominated family of probability measures. Our first insight is that by
considering a (universal) enlargement of the space, we can see American options
as European options and recover the pricing-hedging duality, which may fail in
the original formulation. This may be seen as a weak formulation of the
original problem. Our second insight is that lack of duality is caused by the
lack of dynamic consistency and hence a different enlargement with dynamic
consistency is sufficient to recover duality: it is enough to consider
(fictitious) extensions of the market in which all the assets are traded
dynamically. In the second part of the paper we study two important examples of
robust framework: the setup of Bouchard and Nutz (2015) and the martingale
optimal transport setup of Beiglb\"ock et al. (2013), and show that our general
results apply in both cases and allow us to obtain pricing-hedging duality for
American options.Comment: 29 page
Incorporating statistical model error into the calculation of acceptability prices of contingent claims
The determination of acceptability prices of contingent claims requires the
choice of a stochastic model for the underlying asset price dynamics. Given
this model, optimal bid and ask prices can be found by stochastic optimization.
However, the model for the underlying asset price process is typically based on
data and found by a statistical estimation procedure. We define a confidence
set of possible estimated models by a nonparametric neighborhood of a baseline
model. This neighborhood serves as ambiguity set for a multi-stage stochastic
optimization problem under model uncertainty. We obtain distributionally robust
solutions of the acceptability pricing problem and derive the dual problem
formulation. Moreover, we prove a general large deviations result for the
nested distance, which allows to relate the bid and ask prices under model
ambiguity to the quality of the observed data.Comment: 27 pages, 2 figure
Preliminary remarks on option pricing and dynamic hedging
An elementary arbitrage principle and the existence of trends in financial
time series, which is based on a theorem published in 1995 by P. Cartier and Y.
Perrin, lead to a new understanding of option pricing and dynamic hedging.
Intricate problems related to violent behaviors of the underlying, like the
existence of jumps, become then quite straightforward by incorporating them
into the trends. Several convincing computer experiments are reported.Comment: 1st International Conference on Systems and Computer Science,
Villeneuve d'Ascq : France (2012
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
From Black-Scholes to Online Learning: Dynamic Hedging under Adversarial Environments
We consider a non-stochastic online learning approach to price financial
options by modeling the market dynamic as a repeated game between the nature
(adversary) and the investor. We demonstrate that such framework yields
analogous structure as the Black-Scholes model, the widely popular option
pricing model in stochastic finance, for both European and American options
with convex payoffs. In the case of non-convex options, we construct
approximate pricing algorithms, and demonstrate that their efficiency can be
analyzed through the introduction of an artificial probability measure, in
parallel to the so-called risk-neutral measure in the finance literature, even
though our framework is completely adversarial. Continuous-time convergence
results and extensions to incorporate price jumps are also presented
Robust pricing and hedging under trading restrictions and the emergence of local martingale models
We consider the pricing of derivatives in a setting with trading
restrictions, but without any probabilistic assumptions on the underlying
model, in discrete and continuous time. In particular, we assume that European
put or call options are traded at certain maturities, and the forward price
implied by these option prices may be strictly decreasing in time. In discrete
time, when call options are traded, the short-selling restrictions ensure no
arbitrage, and we show that classical duality holds between the smallest
super-replication price and the supremum over expectations of the payoff over
all supermartingale measures. More surprisingly in the case where the only
vanilla options are put options, we show that there is a duality gap. Embedding
the discrete time model into a continuous time setup, we make a connection with
(strict) local-martingale models, and derive framework and results often seen
in the literature on financial bubbles. This connection suggests a certain
natural interpretation of many existing results in the literature on financial
bubbles
Model-independent pricing with insider information: a Skorokhod embedding approach
In this paper, we consider the pricing and hedging of a financial derivative
for an insider trader, in a model-independent setting. In particular, we
suppose that the insider wants to act in a way which is independent of any
modelling assumptions, but that she observes market information in the form of
the prices of vanilla call options on the asset. We also assume that both the
insider's information, which takes the form of a set of impossible paths, and
the payoff of the derivative are time-invariant. This setup allows us to adapt
recent work of Beiglboeck, Cox and Huesmann (2016) to prove duality results and
a monotonicity principle, which enables us to determine geometric properties of
the optimal models. Moreover, we show that this setup is powerful, in that we
are able to find analytic and numerical solutions to certain pricing and
hedging problems
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