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Resultados filtrados por Publicador: Universidade Cornell

## Admissible Trading Strategies under Transaction Costs

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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A well known result in stochastic analysis reads as follows: for an
$\mathbb{R}$-valued super-martingale $X = (X_t)_{0\leq t \leq T}$ such that the
terminal value $X_T$ is non-negative, we have that the entire process $X$ is
non-negative. An analogous result holds true in the no arbitrage theory of
mathematical finance: under the assumption of no arbitrage, a portfolio process
$x+(H\cdot S)$ verifying $x+(H\cdot S)_T\geq 0$ also satisfies $x+(H\cdot
S)_t\geq 0,$ for all $0 \leq t \leq T$.
In the present paper we derive an analogous result in the presence of
transaction costs. A counter-example reveals that the consideration of
transaction costs makes things more delicate than in the frictionless setting.; Comment: Paper has been expanded by inserting section 2 The num\'eraire-free
setting

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## One-Factor Term Structure without Forward Rates

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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We construct a no-arbitrage model of bond prices where the long bond is used
as a numeraire. We develop bond prices and their dynamics without developing
any model for the spot rate or forward rates. The model is arbitrage free and
all nominal interest rates remain positive in the model. We give examples where
our model does not have a spot rate; other examples include both spot and
forward rates.

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## A Market Test for the Positivity of Arrow-Debreu Prices

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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We derive tractable necessary and sufficient conditions for the absence of
buy-and-hold arbitrage opportunities in a perfectly liquid, one period market.
We formulate the positivity of Arrow-Debreu prices as a generalized moment
problem to show that this no arbitrage condition is equivalent to the positive
semidefiniteness of matrices formed by the market price of tradeable securities
and their products. We apply this result to a market with multiple assets and
basket call options.; Comment: New version, fixes a few minor errors and typos

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## Pricing Queries Approximately Optimally

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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Data as a commodity has always been purchased and sold. Recently, web
services that are data marketplaces have emerged that match data buyers with
data sellers. So far there are no guidelines how to price queries against a
database. We consider the recently proposed query-based pricing framework of
Koutris et al and ask the question of computing optimal input prices in this
framework by formulating a buyer utility model.
We establish the interesting and deep equivalence between arbitrage-freeness
in the query-pricing framework and envy-freeness in pricing theory for
appropriately chosen buyer valuations. Given the approximation hardness results
from envy-free pricing we then develop logarithmic approximation pricing
algorithms exploiting the max flow interpretation of the arbitrage-free pricing
for the restricted query language proposed by Koutris et al. We propose a novel
polynomial-time logarithmic approximation pricing scheme and show that our new
scheme performs better than the existing envy-free pricing algorithms
instance-by-instance. We also present a faster pricing algorithm that is always
greater than the existing solutions, but worse than our previous scheme. We
experimentally show how our pricing algorithms perform with respect to the
existing envy-free pricing algorithms and to the optimal exponentially
computable solution...

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## When roll-overs do not qualify as num\'eraire: bond markets beyond short rate paradigms

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 30/09/2013
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We investigate default-free bond markets where the standard relationship
between a possibly existing bank account process and the term structure of bond
prices is broken, i.e. the bank account process is not a valid num\'eraire. We
argue that this feature is not the exception but rather the rule in bond
markets when starting with, e.g., terminal bonds as num\'eraires.
Our setting are general c\`adl\`ag processes as bond prices, where we employ
directly methods from large financial markets. Moreover, we do not restrict
price process to be semimartingales, which allows for example to consider
markets driven by fractional Brownian motion. In the core of the article we
relate the appropriate no arbitrage assumptions (NAFL), i.e. no asymptotic free
lunch, to the existence of an equivalent local martingale measure with respect
to the terminal bond as num\'eraire, and no arbitrage opportunities of the
first kind (NAA1) to the existence of a supermartingale deflator, respectively.
In all settings we obtain existence of a generalized bank account as a limit of
convex combinations of roll-over bonds.
Additionally we provide an alternative definition of the concept of a
num\'eraire, leading to a possibly interesting connection to bubbles. If we can
construct a bank account process through roll-overs...

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## Pricing and Hedging GLWB in the Heston and in the Black-Scholes with Stochastic Interest Rate Models

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 09/09/2015
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Valuing Guaranteed Lifelong Withdrawal Benefit (GLWB) has attracted
significant attention from both the academic field and real world financial
markets. As remarked by Forsyth and Vetzal the Black and Scholes framework
seems to be inappropriate for such long maturity products. They propose to use
a regime switching model. Alternatively, we propose here to use a stochastic
volatility model (Heston model) and a Black Scholes model with stochastic
interest rate (Hull White model). For this purpose we present four numerical
methods for pricing GLWB variables annuities: a hybrid tree-finite difference
method and a hybrid Monte Carlo method, an ADI finite difference scheme, and a
standard Monte Carlo method. These methods are used to determine the
no-arbitrage fee for the most popular versions of the GLWB contract, and to
calculate the Greeks used in hedging. Both constant withdrawal and optimal
withdrawal (including lapsation) strategies are considered. Numerical results
are presented which demonstrate the sensitivity of the no-arbitrage fee to
economic, contractual and longevity assumptions.

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## On a Heath-Jarrow-Morton approach for stock options

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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This paper aims at transferring the philosophy behind Heath-Jarrow-Morton to
the modelling of call options with all strikes and maturities. Contrary to the
approach by Carmona and Nadtochiy (2009) and related to the recent contribution
Carmona and Nadtochiy (2012) by the same authors, the key parametrisation of
our approach involves time-inhomogeneous L\'evy processes instead of local
volatility models. We provide necessary and sufficient conditions for absence
of arbitrage. Moreover we discuss the construction of arbitrage-free models.
Specifically, we prove their existence and uniqueness given basic building
blocks.

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## The fundamental theorem of asset pricing under proportional transaction costs

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 15/10/2007
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We extend the fundamental theorem of asset pricing to a model where the risky
stock is subject to proportional transaction costs in the form of bid-ask
spreads and the bank account has different interest rates for borrowing and
lending. We show that such a model is free of arbitrage if and only if one can
embed in it a friction-free model that is itself free of arbitrage, in the
sense that there exists an artificial friction-free price for the stock between
its bid and ask prices and an artificial interest rate between the borrowing
and lending interest rates such that, if one discounts this stock price by this
interest rate, then the resulting process is a martingale under some
non-degenerate probability measure. Restricting ourselves to the simple case of
a finite number of time steps and a finite number of possible outcomes for the
stock price, the proof follows by combining classical arguments based on
finite-dimensional separation theorems with duality results from linear
optimisation.

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## D-Brane solutions under market panic

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 30/06/2013
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The relativistic quantum mechanic approach is used to develop a stock market
dynamics. The relativistic is conceptional here as the meaning of big external
volatility or volatility shock on a financial market. We used a differential
geometry approach with the parallel transport of the prices to obtain a direct
shift of the stock price movement. The prices are represented here as electrons
with different spin orientation. Up and down orientations of the spin particle
are likened here as an increase or a decrease of stock prices. The paralel
transport of stock prices is enriched about Riemann curvature which describes
some arbitrage opportunities in the market. To solve the stock-price dynamics,
we used the Dirac equation for bispinors on the spherical brane-world. We found
that when a spherical brane is abbreviated to the disk on the equator, we
converge to the ideal behaviour of financial market where Black Scholes as well
as semi-classical equations are sufficient. Full spherical brane-world
scenarios can descibe a non-equilibrium market behaviour were all arbitrage
opportunities as well as transaction costs are take into account.; Comment: 11 pages, 3 figures. arXiv admin note: text overlap with
arXiv:hep-th/0412306, arXiv:physics/0205053...

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## Model-independent Superhedging under Portfolio Constraints

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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In a discrete-time market, we study model-independent superhedging, while the
semi-static superhedging portfolio consists of {\it three} parts: static
positions in liquidly traded vanilla calls, static positions in other tradable,
yet possibly less liquid, exotic options, and a dynamic trading strategy in
risky assets under certain constraints. By considering the limit order book of
each tradable exotic option and employing the Monge-Kantorovich theory of
optimal transport, we establish a general superhedging duality, which admits a
natural connection to convex risk measures. With the aid of this duality, we
derive a model-independent version of the fundamental theorem of asset pricing.
The notion "finite optimal arbitrage profit", weaker than no-arbitrage, is also
introduced. It is worth noting that our method covers a large class of Delta
constraints as well as Gamma constraint.; Comment: 29 pages

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## Financial instability from local market measures

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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We study the emergence of instabilities in a stylized model of a financial
market, when different market actors calculate prices according to different
(local) market measures. We derive typical properties for ensembles of large
random markets using techniques borrowed from statistical mechanics of
disordered systems. We show that, depending on the number of financial
instruments available and on the heterogeneity of local measures, the market
moves from an arbitrage-free phase to an unstable one, where the complexity of
the market - as measured by the diversity of financial instruments - increases,
and arbitrage opportunities arise. A sharp transition separates the two phases.
Focusing on two different classes of local measures inspired by real markets
strategies, we are able to analytically compute the critical lines,
corroborating our findings with numerical simulations.; Comment: 17 pages, 4 figures

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## BSDEs driven by a multi-dimensional martingale and their applications to market models with funding costs

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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We establish some well-posedness and comparison results for BSDEs driven by
one- and multi-dimensional martingales. On the one hand, our approach is
largely motivated by results and methods developed in Carbone et al. (2008) and
El Karoui and Huang (1997). On the other hand, our results are also motivated
by the recent developments in arbitrage pricing theory under funding costs and
collateralization. A new version of the comparison theorem for BSDEs driven by
a multi-dimensional martingale is established and applied to the pricing and
hedging BSDEs studied in Bielecki and Rutkowski (2014) and Nie and Rutkowski
(2014). This allows us to obtain the existence and uniqueness results for
unilateral prices and to demonstrate the existence of no-arbitrage bounds for a
collateralized contract when both agents have non-negative initial endowments.

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