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Resultados filtrados por Publicador: Universidade Cornell

## Modelling Credit Default Swaps: Market-Standard Vs Incomplete-Market Models

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 09/03/2014
Português

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Recently, incomplete-market techniques have been used to develop a model
applicable to credit default swaps (CDSs) with results obtained that are quite
different from those obtained using the market-standard model. This article
makes use of the new incomplete-market model to further study CDS hedging and
extends the model so that it is capable treating single-name CDS portfolios.
Also, a hedge called the vanilla hedge is described, and with it, analytic
results are obtained explaining the striking features of the plot of
no-arbitrage bounds versus CDS maturity for illiquid CDSs. The valuation
process that follows from the incomplete-market model is an integrated
modelling and risk management procedure, that first uses the model to find the
arbitrage-free range of fair prices, and then requires risk management
professionals for both the buyer and the seller to find, as a basis for
negotiation, prices that both respect the range of fair prices determined by
the model, and also benefit their firms. Finally, in a section on numerical
results, the striking behavior of the no-arbitrage bounds as a function of CDS
maturity is illustrated, and several examples describe the reduction in risk by
the hedging of single-name CDS portfolios.; Comment: 19 pages...

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## Stochastic relaxational dynamics applied to finance: towards non-equilibrium option pricing theory

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

16.99%

#Condensed Matter - Statistical Mechanics#Quantitative Finance - Computational Finance#Quantitative Finance - Pricing of Securities

Non-equilibrium phenomena occur not only in physical world, but also in
finance. In this work, stochastic relaxational dynamics (together with path
integrals) is applied to option pricing theory. A recently proposed model (by
Ilinski et al.) considers fluctuations around this equilibrium state by
introducing a relaxational dynamics with random noise for intermediate
deviations called ``virtual'' arbitrage returns. In this work, the model is
incorporated within a martingale pricing method for derivatives on securities
(e.g. stocks) in incomplete markets using a mapping to option pricing theory
with stochastic interest rates. Using a famous result by Merton and with some
help from the path integral method, exact pricing formulas for European call
and put options under the influence of virtual arbitrage returns (or
intermediate deviations from economic equilibrium) are derived where only the
final integration over initial arbitrage returns needs to be performed
numerically. This result is complemented by a discussion of the hedging
strategy associated to a derivative, which replicates the final payoff but
turns out to be not self-financing in the real world, but self-financing {\it
when summed over the derivative's remaining life time}. Numerical examples are
given which underline the fact that an additional positive risk premium (with
respect to the Black-Scholes values) is found reflecting extra hedging costs
due to intermediate deviations from economic equilibrium.; Comment: 21 pages...

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## On free lunches in random walk markets with short-sale constraints and small transaction costs, and weak convergence to Gaussian continuous-time processes

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

16.99%

#Quantitative Finance - Computational Finance#Mathematics - Probability#Quantitative Finance - Portfolio Management#91G99, 60B10 (Primary), 60E05, 60F05 (Secondary)

This paper considers a sequence of discrete-time random walk markets with a
safe and a single risky investment opportunity, and gives conditions for the
existence of arbitrages or free lunches with vanishing risk, of the form of
waiting to buy and selling the next period, with no shorting, and furthermore
for weak convergence of the random walk to a Gaussian continuous-time
stochastic process. The conditions are given in terms of the kernel
representation with respect to ordinary Brownian motion and the discretisation
chosen. Arbitrage and free lunch with vanishing risk examples are established
where the continuous-time analogue is arbitrage-free under small transaction
costs - including for the semimartingale modifications of fractional Brownian
motion suggested in the seminal Rogers (1997) article proving arbitrage in fBm
models.; Comment: To appear in the Brazilian Journal of Probability and Statistics,
http://www.imstat.org/bjps/

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## On stochastic calculus related to financial assets without semimartingales

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 10/02/2011
Português

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This paper does not suppose a priori that the evolution of the price of a
financial asset is a semimartingale. Since possible strategies of investors are
self-financing, previous prices are forced to be finite quadratic variation
processes. The non-arbitrage property is not excluded if the class
$\mathcal{A}$ of admissible strategies is restricted. The classical notion of
martingale is replaced with the notion of $\mathcal{A}$-martingale. A calculus
related to $\mathcal{A}$-martingales with some examples is developed. Some
applications to no-arbitrage, viability, hedging and the maximization of the
utility of an insider are expanded. We finally revisit some no arbitrage
conditions of Bender-Sottinen-Valkeila type.

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## The tick-by-tick dynamical consistency of price impact in limit order books

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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#Physics - Physics and Society#Condensed Matter - Statistical Mechanics#Quantitative Finance - Trading and Market Microstructure

Constant price impact functions, much used in financial literature, are shown
to give rise to paradoxical outcomes since they do not allow for proper
predictability removal: for instance the exploitation of a single large trade
whose size and time of execution are known in advance to some insider leaves
the arbitrage opportunity unchanged, which allows arbitrage exploitation
multiple times. We argue that chain arbitrage exploitation should not exist,
which provides an a contrario consistency criterion. Remarkably, all the stocks
investigated in Paris Stock Exchange have dynamically consistent price impact
functions. Both the bid-ask spread and the feedback of sequential same-side
market orders onto both sides of the order book are essential to ensure
consistency at the smallest time scale.; Comment: 21 pages, 10 figures

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## Financial markets with volatility uncertainty

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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We investigate financial markets under model risk caused by uncertain
volatilities. For this purpose we consider a financial market that features
volatility uncertainty. To have a mathematical consistent framework we use the
notion of G-expectation and its corresponding G-Brownian motion recently
introduced by Peng (2007). Our financial market consists of a riskless asset
and a risky stock with price process modeled by a geometric G-Brownian motion.
We adapt the notion of arbitrage to this more complex situation and consider
stock price dynamics which exclude arbitrage opportunities. Due to volatility
uncertainty the market is not complete any more. We establish the interval of
no-arbitrage prices for general European contingent claims and deduce explicit
results in a Markovian setting.

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## To sigmoid-based functional description of the volatility smile

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

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#Quantitative Finance - Mathematical Finance#Quantitative Finance - Computational Finance#Quantitative Finance - General Finance

We propose a new static parameterization of the implied volatility surface
which is constructed by using polynomials of sigmoid functions combined with
some other terms. This parameterization is flexible enough to fit market
implied volatilities which demonstrate smile or skew. An arbitrage-free
calibration algorithm is considered that constructs the implied volatility
surface as a grid in the strike-expiration space and guarantees a lack of
arbitrage at every node of this grid. We also demonstrate how to construct an
arbitrage-free interpolation and extrapolation in time, as well as build a
local volatility and implied pdf surfaces. Asymptotic behavior of this
parameterization is discussed, as well as results on stability of the
calibrated parameters are presented. Numerical examples show robustness of the
proposed approach in building all these surfaces as well as demonstrate a
better quality of the fit as compared with some known models.; Comment: 32 pages, 18 figures, 5 tables

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## On the Consistency of the Deterministic Local Volatility Function Model ('implied tree')

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 10/01/2000
Português

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#Condensed Matter - Statistical Mechanics#Mathematics - Analysis of PDEs#Physics - Data Analysis, Statistics and Probability#Quantitative Finance - Statistical Finance

We show that the frequent claim that the implied tree prices exotic options
consistently with the market is untrue if the local volatilities are subject to
change and the market is arbitrage-free. In the process, we analyse -- in the
most general context -- the impact of stochastic variables on the P&L of a
hedged portfolio, and we conclude that no model can a priori be expected to
price all exotics in line with the vanilla options market. Calibration of an
assumed underlying process from vanilla options alone must not be overly
restrictive, yet still unique, and relevant to all exotic options of interest.
For the implied tree we show that the calibration to real-world prices allows
us to only price vanilla options themselves correctly. This is usually
attributed to the incompleteness of the market under traditional stochastic
(local) volatility models. We show that some `weakly' stochastic volatility
models without quadratic variation of the volatilities avoid the incompleteness
problems, but they introduce arbitrage. More generally, we find that any
stochastic tradable either has quadratic variation -- and therefore a
$\Ga$-like P&L on instruments with non-linear exposure to that asset -- or it
introduces arbitrage opportunities.; Comment: LaTeX...

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## On the Existence of Martingale Measures in Jump Diffusion Market Models

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 26/11/2015
Português

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In the context of jump-diffusion market models we construct examples that
satisfy the weaker no-arbitrage condition of NA1 (NUPBR), but not NFLVR. We
show that in these examples the only candidate for the density process of an
equivalent local martingale measure is a supermartingale that is not a
martingale, not even a local martingale. This candidate is given by the
supermartingale deflator resulting from the inverse of the discounted growth
optimal portfolio. In particular, we con- sider an example with constraints on
the portfolio that go beyond the standard ones for admissibility.; Comment: A version has appeared in "Arbitrage, Credit and Informational
Risks", Peking University Series in Mathematics Vol.5, World Scientific 2014.
Arbitrage, Credit and Informational Risks, (C. Hillairet, M. Jeanblanc, Y.
Jiao, eds.). Peking University Series in Mathematics, Vol.5, World Scientific
Publishing Co. Pte. Ltd., 2014, pp.29-51

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## Robust valuation and risk measurement under model uncertainty

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 30/07/2014
Português

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#Quantitative Finance - Pricing of Securities#91G20, 91B24, 91B26, 91B28, 91G80, 60H05, 60H10, 60H30

Model uncertainty is a type of inevitable financial risk. Mistakes on the
choice of pricing model may cause great financial losses. In this paper we
investigate financial markets with mean-volatility uncertainty. Models for
stock markets and option markets with uncertain prior distribution are
established by Peng's G-stochastic calculus. The process of stock price is
described by generalized geometric G-Brownian motion in which the mean
uncertainty may move together with or regardless of the volatility uncertainty.
On the hedging market, the upper price of an (exotic) option is derived
following the Black-Scholes-Barenblatt equation. It is interesting that the
corresponding Barenblatt equation does not depend on the risk preference of
investors and the mean-uncertainty of underlying stocks. Hence under some
appropriate sublinear expectation, neither the risk preference of investors nor
the mean-uncertainty of underlying stocks pose effects on our super and
subhedging strategies. Appropriate definitions of arbitrage for super and
sub-hedging strategies are presented such that the super and sub-hedging prices
are reasonable. Especially the condition of arbitrage for sub-hedging strategy
fills the gap of the theory of arbitrage under model uncertainty. Finally we
show that the term $K$ of finite-variance arising in the super-hedging strategy
is interpreted as the max Profit\&Loss of being short a delta-hedged option.
The ask-bid spread is in fact the accumulation of summation of the superhedging
$P\&L$ and the subhedging $P\&L $.; Comment: 29 pages

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## Binary market models with memory

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 09/08/2004
Português

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We construct a binary market model with memory that approximates a
continuous-time market model driven by a Gaussian process equivalent to
Brownian motion. We give a sufficient conditions for the binary market to be
arbitrage-free. In a case when arbitrage opportunities exist, we present the
rate at which the arbitrage probability tends to zero as the number of periods
goes to infinity.; Comment: 13 pages

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## Two Curves, One Price: Pricing & Hedging Interest Rate Derivatives Decoupling Forwarding and Discounting Yield Curves

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

16.99%

We revisit the problem of pricing and hedging plain vanilla single-currency
interest rate derivatives using multiple distinct yield curves for market
coherent estimation of discount factors and forward rates with different
underlying rate tenors.
Within such double-curve-single-currency framework, adopted by the market
after the credit-crunch crisis started in summer 2007, standard single-curve
no-arbitrage relations are no longer valid, and can be recovered by taking
properly into account the forward basis bootstrapped from market basis swaps.
Numerical results show that the resulting forward basis curves may display a
richer micro-term structure that may induce appreciable effects on the price of
interest rate instruments.
By recurring to the foreign-currency analogy we also derive generalised
no-arbitrage double-curve market-like formulas for basic plain vanilla interest
rate derivatives, FRAs, swaps, caps/floors and swaptions in particular. These
expressions include a quanto adjustment typical of cross-currency derivatives,
naturally originated by the change between the numeraires associated to the two
yield curves, that carries on a volatility and correlation dependence.
Numerical scenarios confirm that such correction can be non negligible...

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## Binary markets under transaction costs

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 24/09/2012
Português

Relevância na Pesquisa

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The goal of this work is to study binary market models with transaction
costs, and to characterize their arbitrage opportunities. It has been already
shown that the absence of arbitrage is related to the existence of
\lambda-consistent price systems (\lambda-CPS), and, for this reason, we aim to
provide conditions under which such systems exist. More precisely, we give a
characterization for the smallest transaction cost \lambda_c (called "critical"
\lambda) starting from which one can construct a \lambda-consistent price
system. We also provide an expression for the set M(\lambda) of all probability
measures inducing \lambda-CPS. We show in particular that in the transition
phase "\lambda=\lambda_c" these sets are empty if and only if the frictionless
market admits arbitrage opportunities. As an application, we obtain an explicit
formula for \lambda_c depending only on the parameters of the model for
homogeneous and also for some semi-homogeneous binary markets.

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