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## Fundamental Theorem of Asset Pricing under Transaction costs and Model uncertainty

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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We prove the Fundamental Theorem of Asset Pricing for a discrete time
financial market where trading is subject to proportional transaction cost and
the asset price dynamic is modeled by a family of probability measures,
possibly non-dominated. Using a backward-forward scheme, we show that when the
market consists of a money market account and a single stock, no-arbitrage in a
quasi-sure sense is equivalent to the existence of a suitable family of
consistent price systems. We also show that when the market consists of
multiple dynamically traded assets and satisfies \emph{efficient friction},
strict no-arbitrage in a quasi-sure sense is equivalent to the existence of a
suitable family of strictly consistent price systems.; Comment: Final version. To appear in Mathematics of Operations Research

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## Trajectory based models. Evaluation of minmax pricing bounds

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 03/11/2015
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The paper studies market models based on trajectory spaces, properties of
such models are obtained without recourse to probabilistic assumptions. For a
given European option, an interval of rational prices exists under a more
general condition than the usual no-arbitrage requirement. The paper develops
computational results in order to evaluate the option bounds; the global minmax
optimization, defining the price interval, is reduced to a local minmax
optimization via dynamic programming. A general class of trajectory sets is
described for which the market model introduced by Britten Jones and Neuberger
is nested as a particular case. We also develop a market model based on an
operational setting constraining market movements and investor's portfolio
rebalances. Numerical examples are presented, the effect of the presence of
arbitrage on the price bounds is illustrated.; Comment: 45 pages, 15 figures

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## Communication Strategies for Low-Latency Trading

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 27/04/2015
Português

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The possibility of latency arbitrage in financial markets has led to the
deployment of high-speed communication links between distant financial centers.
These links are noisy and so there is a need for coding. In this paper, we
develop a gametheoretic model of trading behavior where two traders compete to
capture latency arbitrage opportunities using binary signalling. Different
coding schemes are strategies that trade off between reliability and latency.
When one trader has a better channel, the second trader should not compete.
With statistically identical channels, we find there are two different regimes
of channel noise for which: there is a unique Nash equilibrium yielding ties;
and there are two Nash equilibria with different winners.; Comment: Will appear in IEEE International Symposium on Information Theory
(ISIT), 2015

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## Financial Models with Defaultable Num\'eraires

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 13/11/2015
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#Quantitative Finance - Pricing of Securities#Mathematics - Probability#60G48, 60H99, 91B24, 91B25, 91B70, 91G20, 91G40

Financial models are studied where each asset may potentially lose value
relative to any other. To this end, the paradigm of a pre-determined
num\'eraire is abandoned in favour of a symmetrical point of view where all
assets have equal priority. This approach yields novel versions of the
Fundamental Theorems of Asset Pricing, which clarify and extend non-classical
pricing formulas used in the financial community. Furthermore, conditioning on
non-devaluation, each asset can serve as proper num\'eraire and a classical
no-arbitrage condition can be formulated. It is shown when and how these local
conditions can be aggregated to a global no-arbitrage condition.

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## Dynamic Conic Finance via Backward Stochastic Difference Equations

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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#Quantitative Finance - Pricing of Securities#Mathematics - Probability#Quantitative Finance - Risk Management#91B30, 60G30, 91B06, 62P05

We present an arbitrage free theoretical framework for modeling bid and ask
prices of dividend paying securities in a discrete time setup using theory of
dynamic acceptability indices. In the first part of the paper we develop the
theory of dynamic subscale invariant performance measures, on a general
probability space, and discrete time setup. We prove a representation theorem
of such measures in terms of a family of dynamic convex risk measures, and
provide a representation of dynamic risk measures in terms of g-expectations,
and solutions of BS$\Delta$Es with convex drivers. We study the existence and
uniqueness of the solutions, and derive a comparison theorem for corresponding
BS$\Delta$Es.
In the second part of the paper we discuss a market model for dividend paying
securities by introducing the pricing operators that are defined in terms of
dynamic acceptability indices, and find various properties of these operators.
Using these pricing operators, we define the bid and ask prices for the
underlying securities and then for derivatives in this market. We show that the
obtained market model is arbitrage free, and we also prove a series of
properties of these prices.; Comment: 65 pages

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## Bilateral counterparty risk valuation with stochastic dynamical models and application to Credit Default Swaps

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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We introduce the general arbitrage-free valuation framework for counterparty
risk adjustments in presence of bilateral default risk, including default of
the investor. We illustrate the symmetry in the valuation and show that the
adjustment involves a long position in a put option plus a short position in a
call option, both with zero strike and written on the residual net value of the
contract at the relevant default times. We allow for correlation between the
default times of the investor, counterparty and underlying portfolio risk
factors. We use arbitrage-free stochastic dynamical models. We then specialize
our analysis to Credit Default Swaps (CDS) as underlying portfolio,
generalizing the work of Brigo and Chourdakis (2008) [5] who deal with
unilateral and asymmetric counterparty risk. We introduce stochastic intensity
models and a trivariate copula function on the default times exponential
variables to model default dependence. Similarly to [5], we find that both
default correlation and credit spread volatilities have a relevant and
structured impact on the adjustment. Differently from [5], the two parties will
now agree on the credit valuation adjustment. We study a case involving British
Airways, Lehman Brothers and Royal Dutch Shell...

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## A note on the theory of fast money flow dynamics

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 14/06/2010
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The gauge theory of arbitrage was introduced by Ilinski in
[arXiv:hep-th/9710148] and applied to fast money flows in
[arXiv:cond-mat/9902044]. The theory of fast money flow dynamics attempts to
model the evolution of currency exchange rates and stock prices on short, e.g.\
intra-day, time scales. It has been used to explain some of the heuristic
trading rules, known as technical analysis, that are used by professional
traders in the equity and foreign exchange markets. A critique of some of the
underlying assumptions of the gauge theory of arbitrage was presented by
Sornette in [arXiv:cond-mat/9804045]. In this paper, we present a critique of
the theory of fast money flow dynamics, which was not examined by Sornette. We
demonstrate that the choice of the input parameters used in
[arXiv:cond-mat/9902044] results in sinusoidal oscillations of the exchange
rate, in conflict with the results presented in [arXiv:cond-mat/9902044]. We
also find that the dynamics predicted by the theory are generally unstable in
most realistic situations, with the exchange rate tending to zero or infinity
exponentially.; Comment: accepted for publication in The European Physical Journal B

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## Outperforming the market portfolio with a given probability

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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#Quantitative Finance - Computational Finance#Mathematics - Analysis of PDEs#Mathematics - Optimization and Control#Mathematics - Probability#Quantitative Finance - Portfolio Management

Our goal is to resolve a problem proposed by Fernholz and Karatzas [On
optimal arbitrage (2008) Columbia Univ.]: to characterize the minimum amount of
initial capital with which an investor can beat the market portfolio with a
certain probability, as a function of the market configuration and time to
maturity. We show that this value function is the smallest nonnegative
viscosity supersolution of a nonlinear PDE. As in Fernholz and Karatzas [On
optimal arbitrage (2008) Columbia Univ.], we do not assume the existence of an
equivalent local martingale measure, but merely the existence of a local
martingale deflator.; Comment: Published in at http://dx.doi.org/10.1214/11-AAP799 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org)

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## On the range of admissible term-structures

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 01/04/2014
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In this paper, we analyze the diversity of term structure functions (e.g.,
yield curves, swap curves, credit curves) constructed in a process which
complies with some admissible properties: arbitrage-freeness, ability to fit
market quotes and a certain degree of smooth- ness. When present values of
building instruments are expressed as linear combinations of some primary
quantities such as zero-coupon bonds, discount factor, or survival probabilit-
ies, arbitrage-free bounds can be derived for those quantities at the most
liquid maturities. As a matter of example, we present an iterative procedure
that allows to compute model-free bounds for OIS-implied discount rates and
CDS-implied default probabilities. We then show how mean-reverting term
structure models can be used as generators of admissible curves. This framework
is based on a particular specification of the mean-reverting level which al-
lows to perfectly reproduce market quotes of standard vanilla interest-rate and
default-risky securities while preserving a certain degree of smoothness. The
numerical results suggest that, for both OIS discounting curves and CDS credit
curves, the operational task of term- structure construction may be associated
with a significant degree of uncertainty.

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## Diverse Market Models of Competing Brownian Particles with Splits and Mergers

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 02/04/2014
Português

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We study models of regulatory breakup, in the spirit of Strong and Fouque
(2011) but with a fluctuating number of companies. An important class of market
models is based on systems of competing Brownian particles: each company has a
capitalization whose logarithm behaves as a Brownian motion with drift and
diffusion coefficients depending on its current rank. We study such models with
a fluctuating number of companies: If at some moment the share of the total
market capitalization of a company reaches a fixed level, then the company is
split into two parts of random size. Companies are also allowed to merge, when
an exponential clock rings. We find conditions under which this system is
non-explosive (that is, the number of companies remains finite at all times)
and diverse, yet does not admit arbitrage opportunities.; Comment: 22 pages. Keywords: competing Brownian particles, splits, mergers,
diverse markets, arbitrage opportunity, portfolio

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## Phenomenology of the Interest Rate Curve

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 15/12/1997
Português

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This paper contains a phenomenological description of the whole U.S. forward
rate curve (FRC), based on an data in the period 1990-1996. We find that the
average FRC (measured from the spot rate) grows as the square-root of the
maturity, with a prefactor which is comparable to the spot rate volatility.
This suggests that forward rate market prices include a risk premium,
comparable to the probable changes of the spot rate between now and maturity,
which can be understood as a `Value-at-Risk' type of pricing. The
instantaneous FRC however departs form a simple square-root law. The distortion
is maximum around one year, and reflects the market anticipation of a local
trend on the spot rate. This anticipated trend is shown to be calibrated on the
past behaviour of the spot itself. We show that this is consistent with the
volatility `hump' around one year found by several authors (and which we
confirm). Finally, the number of independent components needed to interpret
most of the FRC fluctuations is found to be small. We rationalize this by
showing that the dynamical evolution of the FRC contains a stabilizing second
derivative (line tension) term, which tends to suppress short scale distortions
of the FRC. This shape dependent term could lead...

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## B-spline techniques for volatility modeling

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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This paper is devoted to the application of B-splines to volatility modeling,
specifically the calibration of the leverage function in stochastic local
volatility models and the parameterization of an arbitrage-free implied
volatility surface calibrated to sparse option data. We use an extension of
classical B-splines obtained by including basis functions with infinite
support. We first come back to the application of shape-constrained B-splines
to the estimation of conditional expectations, not merely from a scatter plot
but also from the given marginal distributions. An application is the Monte
Carlo calibration of stochastic local volatility models by Markov projection.
Then we present a new technique for the calibration of an implied volatility
surface to sparse option data. We use a B-spline parameterization of the
Radon-Nikodym derivative of the underlying's risk-neutral probability density
with respect to a roughly calibrated base model. We show that this method
provides smooth arbitrage-free implied volatility surfaces. Finally, we sketch
a Galerkin method with B-spline finite elements to the solution of the partial
differential equation satisfied by the Radon-Nikodym derivative.; Comment: 25 pages

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## Portfolio optimisation beyond semimartingales: shadow prices and fractional Brownian motion

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 10/05/2015
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#Quantitative Finance - Mathematical Finance#Quantitative Finance - Portfolio Management#91G10, 60G22, 93E20, 60G48

While absence of arbitrage in frictionless financial markets requires price
processes to be semimartingales, non-semimartingales can be used to model
prices in an arbitrage-free way, if proportional transaction costs are taken
into account. In this paper, we show, for a class of price processes which are
not necessarily semimartingales, the existence of an optimal trading strategy
for utility maximisation under transaction costs by establishing the existence
of a so-called shadow price. This is a semimartingale price process, taking
values in the bid ask spread, such that frictionless trading for that price
process leads to the same optimal strategy and utility as the original problem
under transaction costs. Our results combine arguments from convex duality with
the stickiness condition introduced by P. Guasoni. They apply in particular to
exponential utility and geometric fractional Brownian motion. In this case, the
shadow price is an Ito process. As a consequence we obtain a rather surprising
result on the pathwise behaviour of fractional Brownian motion: the
trajectories may touch an Ito process in a one-sided manner without reflection.; Comment: 29 pages

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## Arbitrages in a Progressive Enlargement Setting

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 09/12/2013
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This paper completes the analysis of Choulli et al. Non-Arbitrage up to
Random Horizons and after Honest Times for Semimartingale Models and contains
two principal contributions. The first contribution consists in providing and
analysing many practical examples of market models that admit classical
arbitrages while they preserve the No Unbounded Profit with Bounded Risk (NUPBR
hereafter) under random horizon and when an honest time is incorporated for
particular cases of models. For these markets, we calculate explicitly the
arbitrage opportunities. The second contribution lies in providing simple
proofs for the stability of the No Unbounded Profit with Bounded Risk under
random horizon and after honest time satisfying additional important condition
for particular cases of models.

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## Self-Financing, Replicating Hedging Strategies, an incomplete thermodynamic analogy

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 14/03/2002
Português

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In the theory of riskfree hedges in continuous time finance, one can start
with the delta-hedge and derive the option pricing equation, or one can start
with the replicating, self-financing hedging strategy and derive both the
delta-hedge and the option pricing partial differential equation. Approximately
reversible trading is implicitly assumed in both cases. The option pricing
equation is not restricted to the standard Black-Scholes equation when
nontrivial volatility is assumed, but produces option pricing in agreement with
the empirical distribution for the right choice of volatility in a stochastic
description of fluctuations. The replicating, self-financing hedging strategy
provides us with an incomplete analogy with thermodynamics where liquidity
plays the role of the heat bath, the absence of arbitrage is analgous to
thermal equilibrium, but there is no role played by the entropy of the returns
distribution, which cannot reach a maximum/equilibrium. We emphasize strongly
that the no-arbitrage assumption is not an equilibrium assumption, as is taught
in economics, but provides only an incomplete, very limited analogy with the
idea of thermal equilibrium.; Comment: 10 pages, no figures

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## A note on the Fundamental Theorem of Asset Pricing under model uncertainty

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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We show that the results of ArXiv:1305.6008 on the Fundamental Theorem of
Asset Pricing and the super-hedging theorem can be extended to the case in
which the options available for static hedging (\emph{hedging options}) are
quoted with bid-ask spreads. In this set-up, we need to work with the notion of
\emph{robust no-arbitrage} which turns out to be equivalent to no-arbitrage
under the additional assumption that hedging options with non-zero spread are
\emph{non-redundant}. A key result is the closedness of the set of attainable
claims, which requires a new proof in our setting.; Comment: Final version. To appear in Risks

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## On pricing kernels, information and risk

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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We discuss the finding that cross-sectional characteristic based models have
yielded portfolios with higher excess monthly returns but lower risk than their
arbitrage pricing theory counterparts in an analysis of equity returns of
stocks listed on the JSE. Under the assumption of general no-arbitrage
conditions, we argue that evidence in favour of characteristic based pricing
implies that information is more likely assimilated by means of nonlinear
pricing kernels for the markets considered.; Comment: 20 pages, 3 figures, 1 table

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## Implicit transaction costs and the fundamental theorems of asset pricing

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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This paper studies arbitrage pricing theory in ?financial markets with
transaction costs. We extend the existing theory to include the more realistic
possibility that the price at which the investors trade is dependent on the
traded volume. The investors in the market always buy at the ask and sell at
the bid price. Transaction costs are composed of three terms, one is able to
capture the implicit transaction costs, the second the price impact and the
last the bid-ask spread impact. Moreover, a new definition of a self-financing
portfolio is obtained. The self-financing condition suggests that continuous
trading is possible, but is restricted to predictable trading strategies having
c?adl?ag (right-continuous with left limits) and c?agl?ad (left-continuous with
right limits) paths of bounded quadratic variation and of ?finitely many jumps.
That is, c?adl?ag and c?agl?ad predictable trading strategies of infinite
variation, with?finitely many jumps and of ?finite quadratic variation are
allowed in our setting. Restricting ourselves to c?agl?ad predictable trading
strategies, we show that the existence of an equivalent probability measure is
equivalent to the absence of arbitrage opportunities, so that the first
fundamental theorem of asset pricing (FFTAP) holds. It is also shown that...

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## Kinetic properties in inhomogeneous self-aware media

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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The new framework for finance is proposed. This framework based on three
known approaches in econophysics. Assumptions of the framework are the
following: 1. For the majority of situations market follows non-arbitrage
condition. 2. For the small number of situations market influenced by the
actions of big firms. 3. If actions of big players lead to the arbitrage
opportunity, small players could self-organize to take advantage of this
opportunity. The framework is an attempt to combine approaches of Bouchaud,
Gabaix, Sornette, Stanley and coauthors. Suggested framework is applied for the
analysis of market impact models, behavior of big players, self-organization of
market firm and volatility description.; Comment: Chapter 23 of the book "Transport processes in macroscopically
disordered media (From mean field theory to percolation)" accepted for
publication by Springer [32 pages, 1 figure, 2 tables]

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## Consistent Long-Term Yield Curve Prediction

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 09/03/2012
Português

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We present an arbitrage-free non-parametric yield curve prediction model
which takes the full (discretized) yield curve as state variable. We believe
that absence of arbitrage is an important model feature in case of highly
correlated data, as it is the case for interest rates. Furthermore, the model
structure allows to separate clearly the tasks of estimating the volatility
structure and of calibrating market prices of risk. The empirical part includes
tests on modeling assumptions, back testing and a comparison with the
Vasi\v{c}ek short rate model.

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