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## Approximation of forward curve models in commodity markets with arbitrage-free finite dimensional models

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 18/12/2015
Português

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In this paper we show how to approximate a Heath-Jarrow-Morton dynamics for
the forward prices in commodity markets with arbitrage-free models which have a
finite dimensional state space. Moreover, we recover a closed form
representation of the forward price dynamics in the approximation models and
derive the rate of convergence uniformly over an interval of time to maturity
to the true dynamics under certain additional smoothness conditions. In the
Markovian case we can strengthen the convergence to be uniform over time as
well. Our results are based on the construction of a convenient Riesz basis on
the state space of the term structure dynamics.

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## A microscopic model of triangular arbitrage

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 24/02/2006
Português

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We introduce a microscopic model which describes the dynamics of each dealer
in multiple foreign exchange markets, taking account of the triangular
arbitrage transaction. The model reproduces the interaction among the markets
well. We explore the relation between the parameters of the present microscopic
model and the spring constant of a macroscopic model that we proposed
previously.; Comment: 17 pages, 14 figures

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## No-Arbitrage Pricing for Dividend-Paying Securities in Discrete-Time Markets with Transaction Costs

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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We prove a version of First Fundamental Theorem of Asset Pricing under
transaction costs for discrete-time markets with dividend-paying securities.
Specifically, we show that the no-arbitrage condition under the efficient
friction assumption is equivalent to the existence of a risk-neutral measure.
We derive dual representations for the superhedging ask and subhedging bid
price processes of a derivative contract. Our results are illustrated with a
vanilla credit default swap contract.; Comment: Forthcoming in Mathematical Finance

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## Default times, non arbitrage conditions and change of probability measures

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 21/12/2008
Português

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In this paper we give a financial justification, based on non arbitrage
conditions, of the $(H)$ hypothesis in default time modelling. We also show how
the $(H)$ hypothesis is affected by an equivalent change of probability
measure. The main technique used here is the theory of progressive enlargements
of filtrations.

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## Arbitrage-free Pricing of Credit Index Options: The no-armageddon pricing measure and the role of correlation after the subprime crisis

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 22/12/2008
Português

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In this work we consider three problems of the standard market approach to
pricing of credit index options: the definition of the index spread is not
valid in general, the usually considered payoff leads to a pricing which is not
always defined, and the candidate numeraire one would use to define a pricing
measure is not strictly positive, which would lead to a non-equivalent pricing
measure.
We give a general mathematical solution to the three problems, based on a
novel way of modeling the flow of information through the definition of a new
subfiltration. Using this subfiltration, we take into account consistently the
possibility of default of all names in the portfolio, that is neglected in the
standard market approach. We show that, while the related mispricing can be
negligible for standard options in normal market conditions, it can become
highly relevant for different options or in stressed market conditions.
In particular, we show on 2007 market data that after the subprime credit
crisis the mispricing of the market formula compared to the no arbitrage
formula we propose has become financially relevant even for the liquid
Crossover Index Options.; Comment: Updated version accepted for publication in Mathematical Finance

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## On the no-arbitrage market and continuity in the Hurst parameter

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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We consider a market with fractional Brownian motion with stochastic
integrals generated by the Riemann sums. We found that this market is arbitrage
free if admissible strategies that are using observations with an arbitrarily
small delay. Moreover, we found that this approach eliminates the discontinuity
of the stochastic integrals with respect to the Hurst parameter H at H=1/2.; Comment: arXiv admin note: text overlap with arXiv:1509.06112

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## How Non-Arbitrage, Viability and Num\'eraire Portfolio are Related

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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#Quantitative Finance - General Finance#Mathematics - Optimization and Control#Mathematics - Probability#Quantitative Finance - Portfolio Management

This paper proposes two approaches that quantify the exact relationship among
the viability, the absence of arbitrage, and/or the existence of the
num\'eraire portfolio under minimal assumptions and for general continuous-time
market models. Precisely, our first and principal contribution proves the
equivalence among the No-Unbounded-Profit-with-Bounded-Risk condition (NUPBR
hereafter), the existence of the num\'eraire portfolio, and the existence of
the optimal portfolio under an equivalent probability measure for any "nice"
utility and positive initial capital. Herein, a 'nice" utility is any smooth
von Neumann-Morgenstern utility satisfying Inada's conditions and the
elasticity assumptions of Kramkov and Schachermayer. Furthermore, the
equivalent probability measure ---under which the utility maximization problems
have solutions--- can be chosen as close to the real-world probability measure
as we want (but might not be equal). Without changing the underlying
probability measure and under mild assumptions, our second contribution proves
that the NUPBR is equivalent to the "{\it local}" existence of the optimal
portfolio. This constitutes an alternative to the first contribution, if one
insists on working under the real-world probability. These two contributions
lead naturally to new types of viability that we call weak and local
viabilities.; Comment: 21 pages

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## Optimal strategies for operating energy storage in an arbitrage market

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 02/12/2014
Português

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We characterize profit-maximizing operating strategies, over some time
horizon [0,T], for an energy store which is trading in an arbitrage market. Our
theory allows for leakage, operating inefficiencies, operating constraints and
general cost functions. In the special case where the operating cost of a store
depends only on its instantaneous power output (or input), we present an
algorithm to determine the optimal strategies. A key feature is that this
algorithm is localized in time, in the sense that the action of the store at a
time t only requires information about electricity prices over some subinterval
of time [t,t_k] contained within [t,T]. To introduce more complex storage
models, we discuss methods for an example which includes minimum switching
times between modes of operation.; Comment: 19 pages, 1 figure. Submitted to SIAM Journal on Control and
Optimization

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## Statistical Arbitrage and Optimal Trading with Transaction Costs in Futures Markets

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 22/01/2008
Português

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#Quantitative Finance - Trading and Market Microstructure#Mathematics - Optimization and Control#Mathematics - Probability#91B28#91B70#90C46#60G44

We consider the Brownian market model and the problem of expected utility
maximization of terminal wealth. We, specifically, examine the problem of
maximizing the utility of terminal wealth under the presence of transaction
costs of a fund/agent investing in futures markets. We offer some preliminary
remarks about statistical arbitrage strategies and we set the framework for
futures markets, and introduce concepts such as margin, gearing and slippage.
The setting is of discrete time, and the price evolution of the futures prices
is modelled as discrete random sequence involving Ito's sums. We assume the
drift and the Brownian motion driving the return process are non-observable and
the transaction costs are represented by the bid-ask spread. We provide
explicit solution to the optimal portfolio process, and we offer an example
using logarithmic utility.; Comment: 28 pages, submitted to journal

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## Arbitrage in markets with bid-ask spreads

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 12/07/2014
Português

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#Quantitative Finance - Pricing of Securities#Mathematics - Probability#Quantitative Finance - Portfolio Management#91G80, 60G42, 60G40, 91B25

In this paper a finite discrete time market with an arbitrary state space and
bid-ask spreads is considered. The notion of an equivalent bid-ask martingale
measure (EBAMM) is introduced and the fundamental theorem of asset pricing is
proved using (EBAMM) as an equivalent condition for no-arbitrage. The
Cox-Ross-Rubinstein model with bid-ask spreads is presented as an application
of our results.; Comment: 18 pages, 3 figures

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## How to account for virtual arbitrage in the standard derivative pricing

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 03/02/1999
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In this short note we show how virtual arbitrage opportunities can be
modelled and included in the standard derivative pricing without changing the
general framework.; Comment: Latex, 6 pages, Proschal'nii poklon

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## Arbitrage Pricing of Multi-person Game Contingent Claims

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 12/05/2014
Português

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We introduce a class of financial contracts involving several parties by
extending the notion of a two-person game option (see Kifer (2000)) to a
contract in which an arbitrary number of parties is involved and each of them
is allowed to make a wide array of decisions at any time, not restricted to
simply `exercising the option'. The collection of decisions by all parties then
determines the contract's settlement date as well as the terminal payoff for
each party. We provide sufficient conditions under which a multi-person game
option has a unique arbitrage price, which is additive with respect to any
partition of the contract.

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## No-arbitrage in discrete-time markets with proportional transaction costs and general information structure

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 04/01/2005
Português

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#Mathematics - Probability#Quantitative Finance - Computational Finance#AMS (2000) Subject Classification: 91B28, 60G42

We discuss the no-arbitrage conditions in a general framework for
discrete-time models of financial markets with proportional transaction costs
and general information structure. We extend the results of Kabanov and al.
(2002), Kabanov and al. (2003) and Schachermayer (2004) to the case where
bid-ask spreads are not known with certainty. In the "no-friction" case, we
retrieve the result of Kabanov and Stricker (2003).

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## Arbitrage risk induced by transaction costs

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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We discuss the time evolution of quotation of stocks and commodities and show
that they form an Ising chain. We show that transaction costs induce arbitrage
risk that usually is neglected. The full analysis of the portfolio theory is
computationally complex but the latest development in quantum computation
theory suggests that such a task can be performed on quantum computers.; Comment: 9 pages, LaTeX

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## Generalizations of Functionally Generated Portfolios with Applications to Statistical Arbitrage

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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The theory of functionally generated portfolios (FGPs) is an aspect of the
continuous-time, continuous-path Stochastic Portfolio Theory of Robert
Fernholz. FGPs have been formulated to yield a master equation - a description
of their return relative to a passive (buy-and-hold) benchmark portfolio
serving as the num\'eraire. This description has proven to be analytically very
useful, as it is both pathwise and free of stochastic integrals. Here we
generalize the class of FGPs in several ways: (1) the num\'eraire may be any
strictly positive wealth process, not necessarily the market portfolio or even
a passive portfolio; (2) generating functions may be stochastically dynamic,
adjusting to changing market conditions through an auxiliary continuous-path
stochastic argument of finite variation. These generalizations do not forfeit
the important tractability properties of the associated master equation. We
show how these generalizations can be usefully applied to scenario analysis,
statistical arbitrage, portfolio risk immunization, and the theory of mirror
portfolios.; Comment: 22 pages

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## Non-Arbitrage under a Class of Honest Times

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 01/04/2014
Português

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This paper addresses the question of non-arbitrage (precisely
No-Unbounded-Profit-with-Bounded-Risk, NUPBR hereafter) after a specific random
time. This study completes the one of Aksamit et al.
\cite{aksamit/choulli/deng/jeanblanc}, devoted to the study before the random
time, by elaborating results for the part after the random time under
consideration. We restrict our attention to honest times, and we characterize
the pairs of market and honest time for which the resulting model preserves the
NUPBR property. Furthermore, we characterize the honest times that preserve the
NUPBR property. These findings are essentially based on new stochastic results
that are interesting in themselves. Furthermore, we construct explicitly local
martingale deflators for a large class of processes.; Comment: 31 pages. arXiv admin note: text overlap with arXiv:1310.1142

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## The optimal control of storage for arbitrage and buffering, with energy applications

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 18/09/2015
Português

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We study the optimal control of storage which is used for both arbitrage and
buffering against unexpected events, with particular applications to the
control of energy systems in a stochastic and typically time-heterogeneous
environment. Our philosophy is that of viewing the problem as being formally
one of stochastic dynamic programming, but of using coupling arguments to
provide good estimates of the costs of failing to provide necessary levels of
buffering. The problem of control then reduces to that of the solution,
dynamically in time, of a deterministic optimisation problem which must be
periodically re-solved. We show that the optimal control then proceeds locally
in time, in the sense that the optimal decision at each time $t$ depends only
on a knowledge of the future costs and stochastic evolution of the system for a
time horizon which typically extends only a little way beyond $t$. The approach
is thus both computationally tractable and suitable for the management of
systems over indefinitely extended periods of time. We develop also the
associated strong Lagrangian theory (which may be used to assist in the optimal
dimensioning of storage), and we provide characterisations of optimal control
policies. We give examples based on Great Britain electricity price data.; Comment: 25 pages...

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## The fractional volatility model: No-arbitrage, leverage and risk measures

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 16/07/2010
Português

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#Quantitative Finance - Pricing of Securities#Mathematics - Probability#Quantitative Finance - Statistical Finance

Based on a criterium of mathematical simplicity and consistency with
empirical market data, a stochastic volatility model has been obtained with the
volatility process driven by fractional noise. Depending on whether the
stochasticity generators of log-price and volatility are independent or are the
same, two versions of the model are obtained with different leverage behavior.
Here, the no-arbitrage and incompleteness properties of the model are studied.
Some risk measures are also discussed in this framework.; Comment: 12 pages latex

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## Pathwise no-arbitrage in a class of Delta hedging strategies

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 30/10/2015
Português

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We consider a strictly pathwise setting for Delta hedging exotic options,
based on F\"ollmer's pathwise It\=o calculus. Price trajectories are
$d$-dimensional continuous functions whose pathwise quadratic variations and
covariations are determined by a given local-volatility matrix. The existence
of Delta hedging strategies in this pathwise setting is established via an
existence result for a recursive scheme of parabolic Cauchy problems. Our main
result establishes the nonexistence of pathwise arbitrage opportunities in a
class of strategies containing these Delta hedging strategies and under
relatively mild conditions on the local-volatility matrix.

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## The fairest price of an asset in an environment of temporary arbitrage

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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In practice there are temporary arbitrage opportunities arising from the fact
that prices for a given asset at different stock exchanges are not
instantaneously the same. We will show that even in such an environment there
exists a ``fairest measure'' (instead of a martingale measure), albeit not
necessarily unique. For this end, we define and analyse quantitative notions of
unfairness in complete as well as incomplete market settings.; Comment: minor changes to introduction and abstract

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