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Resultados filtrados por Publicador: Universidade Cornell

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

Walker, Michael B.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 09/03/2014 Português
Relevância na Pesquisa
16.99%
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...

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

Otto, Matthias
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
16.99%
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...

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

Framstad, Nils Chr.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
16.99%
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/

On stochastic calculus related to financial assets without semimartingales

Coviello, Rosanna; Di Girolami, Cristina; Russo, Francesco
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 10/02/2011 Português
Relevância na Pesquisa
16.99%
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.

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

Challet, Damien
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
16.99%
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

Financial markets with volatility uncertainty

Vorbrink, Joerg
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
16.99%
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.

To sigmoid-based functional description of the volatility smile

Itkin, Andrey
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
16.99%
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

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

Strobl, Karl
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 10/01/2000 Português
Relevância na Pesquisa
16.99%
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...

On the Existence of Martingale Measures in Jump Diffusion Market Models

Mancin, Jacopo; Runggaldier, Wolfgang J.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 26/11/2015 Português
Relevância na Pesquisa
16.99%
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

Robust valuation and risk measurement under model uncertainty

Xu, Yuhong
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 30/07/2014 Português
Relevância na Pesquisa
16.99%
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

Binary market models with memory

Inoue, Akihiko; Nakano, Yumiharu; Anh, Vo
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 09/08/2004 Português
Relevância na Pesquisa
16.99%
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

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

Bianchetti, Marco
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...

Binary markets under transaction costs

Cordero, Fernando; Klein, Irene; Ostafe, Lavinia
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 24/09/2012 Português
Relevância na Pesquisa
16.99%
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.