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Ensaios em finanças quantitativas: apreçamento de derivativos multidimensionais via processos de Lévy, e topologia e propagação do risco sistêmico; Essays in quantitative finance: multidimensional derivative pricing via Lévy processes, and systemic risk topology na risk propagation

Santos, Edson Bastos e
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Tese de Doutorado Formato: application/pdf
Publicado em 24/03/2010 Português
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Este estudo contempla dois ensaios em finanças quantitativas, relacionados, respectivamente, a modelos de apreçamento e risco sistêmico. No Capitulo 1, e apresentado uma alternativa para modelar opções multidimensionais, cujas estruturas de ganhos e perdas dependam das trajetórias dos processos dos preços dos ativos objetos. A modelagem sugerida considera os processos de Levy, uma classe de processos estocásticos bastante ampla, que permite a existência de saltos (descontinuidades) no processo dos preços dos ativos financeiros, e tem como caso particular o movimento Browniano. Para escrever a dependência entre os processos, os conceitos estáticos de copulas ordinárias são estendidos para o contexto dos processos de Levy, levando em consideração a medida de Levy, que caracteriza o comportamento dos saltos. São realizados estudos comparativos entre as copulas dinâmicas de Clayton e de Frank, no apreçamento dos contratos derivativos do tipo asiático, utilizando-se processos gama e técnicas de simulação de Monte Carlo. No Capitulo 2, a estrutura e dinâmica interbancária das exposições mutuas entre as instituições financeiras no Brasil e explorada bem como o capital destas reservas, utilizando um conjunto de dados únicos que considera vários períodos entre 2007 e 2008. Para isto e mostrado que a rede de exposições pode ser modelada adequadamente como um gráfico estocástico dirigido de escala - livre (ponderada) seguindo distribuições que apresentam caudas grossas. A relação entre as conexões das instituições financeiras e seu colchão-de-capital também são investigados neste estudo. Finalmente...

Econometric Asset Pricing Modelling

Bertholon, H.; Monfort, A.; Pegoraro, F.
Fonte: Oxford University Press Publicador: Oxford University Press
Tipo: Artigo de Revista Científica Formato: text/html
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The purpose of this paper is to propose a general econometric approach to no-arbitrage asset pricing modelling based on three main ingredients: (i) the historical discrete-time dynamics of the factor representing the information, (ii) the stochastic discount factor (SDF), and (iii) the discrete-time risk-neutral (RN) factor dynamics. Retaining an exponential-affine specification of the SDF, its modelling is equivalent to the specification of the risk-sensitivity vector and of the short rate, if the latter is neither exogenous nor a known function of the factor. In this general framework, we distinguish three modelling strategies: the direct modelling, the RN constrained direct modelling, and the back modelling. In all the approaches, we study the internal consistency conditions (ICCs), implied by the absence of arbitrage opportunity assumption, and the identification problem. The general modelling strategies are applied to two important domains: security market models and term structure of interest rates models. In these contexts, we stress the usefulness (and we suggest the use) of the RN constrained direct modelling and of the back modelling approaches, both allowing us to conciliate a flexible (non-Car) historical dynamics and a Car (compound autoregressive) RN dynamics leading to explicit or quasi-explicit pricing formulas for various derivative products. Moreover...

A Nonparametric Approach to Pricing and Hedging Derivative Securities via Learning Networks

Hutchinson, James M.; Lo, Andrew; Poggio, Tomaso
Fonte: MIT - Massachusetts Institute of Technology Publicador: MIT - Massachusetts Institute of Technology
Formato: 397765 bytes; 1887637 bytes; application/octet-stream; application/pdf
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We propose a nonparametric method for estimating derivative financial asset pricing formulae using learning networks. To demonstrate feasibility, we first simulate Black-Scholes option prices and show that learning networks can recover the Black-Scholes formula from a two-year training set of daily options prices, and that the resulting network formula can be used successfully to both price and delta-hedge options out-of-sample. For comparison, we estimate models using four popular methods: ordinary least squares, radial basis functions, multilayer perceptrons, and projection pursuit. To illustrate practical relevance, we also apply our approach to S&P 500 futures options data from 1987 to 1991.

International Asset Allocations and Capital Flows : The Benchmark Effect

Raddatz, Claudio; Schmukler, Sergio L.; Williams, Tomas
Fonte: World Bank, Washington, DC Publicador: World Bank, Washington, DC
Português
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This paper studies channels through which well-known benchmark indexes impact asset allocations and capital flows across countries. The study uses unique monthly micro-level data of benchmark compositions and mutual fund investments during 1996-2012. Benchmarks have important effects on equity and bond mutual fund portfolios across funds with different degrees of activism. Benchmarks explain, on average, around 70 percent of country allocations and have significant impact even on active funds. Benchmark effects are important after controlling for industry, macroeconomic, and country-specific, time-varying effects. Reverse causality does not drive the results. Exogenous, pre-announced changes in benchmarks result in movements in asset allocations mostly when these changes are implemented (not when announced). By impacting country allocations, benchmarks affect capital flows across countries through direct and indirect channels, including contagion. They explain apparently counterintuitive movements in capital flows...

Esscher transforms and consumption-based models

Badescu, A.; Elliott, R.; Siu, T.
Fonte: Elsevier Science BV Publicador: Elsevier Science BV
Tipo: Artigo de Revista Científica
Publicado em //2009 Português
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The Esscher transform is an important tool in actuarial science. Since the pioneering work of Gerber and Shiu (1994), the use of the Esscher transform for option valuation has also been investigated extensively. However, the relationships between the asset pricing model based on the Esscher transform and some fundamental equilibrium-based asset pricing models, such as consumption-based models, have so far not been well-explored. In this paper, we attempt to bridge the gap between consumption-based models and asset pricing models based on Esscher-type transformations in a discrete-time setting. Based on certain assumptions for the distributions of asset returns, changes in aggregate consumptions and returns on the market portfolio, we construct pricing measures that are consistent with those arising from Esscher-type transformations. Explicit relationships between the market price of risk, and the risk preference parameters are derived for some particular cases.; http://www.elsevier.com/wps/find/journaldescription.cws_home/505554/description#description; Alex Badescu, Robert J. Elliott and Tak Kuen Siu

Asset pricing using finite state Markov chain stochastic discount functions

Van Der Hoek, J.; Elliott, R.
Fonte: Marcel Dekker Inc Publicador: Marcel Dekker Inc
Tipo: Artigo de Revista Científica
Publicado em //2012 Português
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This article fuses two pieces of theory to make a tractable model for asset pricing. The first is the theory of asset pricing using a stochastic discounting function (SDF). This will be reviewed. The second is to model uncertainty in an economy using a Markov chain. Using the semi-martingale dynamics for the chain these models can be calibrated and asset valuations derived. Interest rate models, stock price models, futures pricing, exchange rates can all be introduced endogenously in this framework.; John van der Hoek and Robert J. Elliott

Arbitrage-Based Pricing when Volatility is Stochastic.

Bossaerts, P.; Ghysels, E.; Gourieroux, C.
Fonte: Université de Montréal Publicador: Université de Montréal
Tipo: Artigo de Revista Científica Formato: 2019964 bytes; application/pdf
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The paper investigates the pricing of derivative securities with calendar-time maturities.

Pricing Derivatives on Multiscale Diffusions: an Eigenfunction Expansion Approach

Lorig, Matthew
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
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Using tools from spectral analysis, singular and regular perturbation theory, we develop a systematic method for analytically computing the approximate price of a derivative-asset. The payoff of the derivative-asset may be path-dependent. Additionally, the process underlying the derivative may exhibit killing (i.e. jump to default) as well as combined local/nonlocal stochastic volatility. The nonlocal component of volatility is multiscale, in the sense that it is driven by one fast-varying and one slow-varying factor. The flexibility of our modeling framework is contrasted by the simplicity of our method. We reduce the derivative pricing problem to that of solving a single eigenvalue equation. Once the eigenvalue equation is solved, the approximate price of a derivative can be calculated formulaically. To illustrate our method, we calculate the approximate price of three derivative-assets: a vanilla option on a defaultable stock, a path-dependent option on a non-defaultable stock, and a bond in a short-rate model.

Coherent CVA and FVA with Liability Side Pricing of Derivatives

Lou, Wujiang
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 24/10/2015 Português
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This article presents FVA and CVA of a bilateral derivative in a coherent manner, based on recent developments in fair value accounting and ISDA standards. We argue that a derivative liability, after primary risk factors being hedged, resembles in economics an issued variable funding note, and should be priced at the market rate of the issuer's debt. For the purpose of determining the fair value, the party on the liability side is economically neutral to make a deposit to the other party, which earns his current debt rate and effectively provides funding and hedging for the party holding the derivative asset. The newly derived partial differential equation for an option discounts the derivative's receivable part with counterparty's curve and payable part with own financing curve. The price difference from the counterparty risk free price, or total counterparty risk adjustment, is precisely defined by discounting the product of the risk free price and the credit spread at the local liability curve. Subsequently the adjustment can be broken into a default risk component -- CVA and a funding component -- FVA, consistent with a simple note's fair value treatment and in accordance with the usual understanding of a bond's credit spread consisting of a CDS spread and a basis. As for FVA...

An Information-Based Framework for Asset Pricing: X-Factor Theory and its Applications

Macrina, Andrea
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 14/07/2008 Português
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A new framework for asset pricing based on modelling the information available to market participants is presented. Each asset is characterised by the cash flows it generates. Each cash flow is expressed as a function of one or more independent random variables called market factors or "X-factors". Each X-factor is associated with a "market information process", the values of which become available to market participants. In addition to true information about the X-factor, the information process contains an independent "noise" term modelled here by a Brownian bridge. The information process thus gives partial information about the X-factor, and the value of the market factor is only revealed at the termination of the process. The market filtration is assumed to be generated by the information processes associated with the X-factors. The price of an asset is given by the risk-neutral expectation of the sum of the discounted cash flows, conditional on the information available from the filtration. The theory is developed in some detail, with a variety of applications to credit risk management, share prices, interest rates, and inflation. A number of new exactly solvable models are obtained for the price processes of various types of assets and derivative securities; and a novel mechanism is proposed to account for the dynamics of stochastic volatility and dynamic correlation. A discrete-time version of the information-based framework is also developed...

Non-Parametric Extraction of Implied Asset Price Distributions

Healy, Jerome V.; Dixon, Maurice; Read, Brian J.; Cai, Fang Fang
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 26/07/2006 Português
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Extracting the risk neutral density (RND) function from option prices is well defined in principle, but is very sensitive to errors in practice. For risk management, knowledge of the entire RND provides more information for Value-at-Risk (VaR) calculations than implied volatility alone [1]. Typically, RNDs are deduced from option prices by making a distributional assumption, or relying on implied volatility [2]. We present a fully non-parametric method for extracting RNDs from observed option prices. The aim is to obtain a continuous, smooth, monotonic, and convex pricing function that is twice differentiable. Thus, irregularities such as negative probabilities that afflict many existing RND estimation techniques are reduced. Our method employs neural networks to obtain a smoothed pricing function, and a central finite difference approximation to the second derivative to extract the required gradients. This novel technique was successfully applied to a large set of FTSE 100 daily European exercise (ESX) put options data and as an Ansatz to the corresponding set of American exercise (SEI) put options. The results of paired t-tests showed significant differences between RNDs extracted from ESX and SEI option data, reflecting the distorting impact of early exercise possibility for the latter. In particular...

Mirror-time diffusion discount model of options pricing

Levin, Pavel
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
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The proposed model modifies option pricing formulas for the basic case of log-normal probability distribution providing correspondence to formulated criteria of efficiency and completeness. The model is self-calibrating by historic volatility data; it maintains the constant expected value at maturity of the hedged instantaneously self-financing portfolio. The payoff variance dependent on random stock price at maturity obtained under an equivalent martingale measure is taken as a condition for introduced "mirror-time" derivative diffusion discount process. Introduced ksi-return distribution, correspondent to the found general solution of backward drift-diffusion equation and normalized by theoretical diffusion coefficient, does not contain so-called "long tails" and unbiased for considered 2004-2007 S&P 100 index data. The model theoretically yields skews correspondent to practical term structure for interest rate derivatives. The method allows increasing the number of asset price probability distribution parameters.; Comment: 22 pages, 3 figures

Valuation of asset and volatility derivatives using decoupled time-changed L\'evy processes

Torricelli, Lorenzo
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
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In this paper we propose a general derivative pricing framework which employs decoupled time-changed (DTC) L\'evy processes to model the underlying asset of contingent claims. A DTC L\'evy process is a generalized time-changed L\'evy process whose continuous and pure jump parts are allowed to follow separate random time scalings; we devise the martingale structure for a DTC L\'evy-driven asset and revisit many popular models which fall under this framework. Postulating different time changes for the underlying L\'evy decomposition allows to introduce asset price models consistent with the assumption of a correlated pair of continuous and jump market activities; we study one illustrative DTC model having this property by assuming that the instantaneous activity rates follow the the so-called Wishart process. The theory developed is applied to the problem of pricing claims depending not only on the price or the volatility of an underlying asset, but also to more sophisticated derivatives that pay-off on the joint performance of these two financial variables, like the target volatility option (TVO). We solve the pricing problem through a Fourier-inversion method; numerical computations validating our technique are provided.; Comment: 30 Pages...

Adapted Downhill Simplex Method for Pricing Convertible Bonds

Mishchenko, Kateryna; Mishchenko, Volodymyr; Malyarenko, Anatoliy
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 01/10/2007 Português
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The paper is devoted to modeling optimal exercise strategies of the behavior of investors and issuers working with convertible bonds. This implies solution of the problems of stock price modeling, payoff computation and min-max optimization. Stock prices (underlying asset) were modeled under the assumption of the geometric Brownian motion of their values. The Monte Carlo method was used for calculating the real payoff which is the objective function. The min-max optimization problem was solved using the derivative-free Downhill Simplex method. The performed numerical experiments allowed to formulate recommendations for the choice of appropriate size of the initial simplex in the Downhill Simplex Method, the number of generated trajectories of underlying asset, the size of the problem and initial trajectories of the behavior of investors and issuers.; Comment: 18 pages, 8 figures

A Fourier transform method for spread option pricing

Hurd, T. R.; Zhou, Zhuowei
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 20/02/2009 Português
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Spread options are a fundamental class of derivative contract written on multiple assets, and are widely used in a range of financial markets. There is a long history of approximation methods for computing such products, but as yet there is no preferred approach that is accurate, efficient and flexible enough to apply in general models. The present paper introduces a new formula for general spread option pricing based on Fourier analysis of the spread option payoff function. Our detailed investigation proves the effectiveness of a fast Fourier transform implementation of this formula for the computation of prices. It is found to be easy to implement, stable, efficient and applicable in a wide variety of asset pricing models.; Comment: 16 pages, 3 figures

Pricing formulas, model error and hedging derivative portfolios

Hurd, T. R.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 31/08/2001 Português
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We propose a method for extending a given asset pricing formula to account for two additional sources of risk: the risk associated with future changes in market--calibrated parameters and the remaining risk associated with idiosyncratic variations in the individual assets described by the formula. The paper makes simple and natural assumptions for how these risks behave. These extra risks should always be included when using the formula as a basis for portfolio management. We investigate an idealized typical portfolio problem, and argue that a rational and workable trading strategy can be based on minimizing the quadratic risk over the time intervals between trades. The example of the variance gamma pricing formula for equity derivatives is explored, and the method is seen to yield tractable decision strategies in this case.; Comment: 16 pages, 1 figure

Minimax Option Pricing Meets Black-Scholes in the Limit

Abernethy, Jacob; Frongillo, Rafael M.; Wibisono, Andre
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 12/02/2012 Português
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Option contracts are a type of financial derivative that allow investors to hedge risk and speculate on the variation of an asset's future market price. In short, an option has a particular payout that is based on the market price for an asset on a given date in the future. In 1973, Black and Scholes proposed a valuation model for options that essentially estimates the tail risk of the asset price under the assumption that the price will fluctuate according to geometric Brownian motion. More recently, DeMarzo et al., among others, have proposed more robust valuation schemes, where we can even assume an adversary chooses the price fluctuations. This framework can be considered as a sequential two-player zero-sum game between the investor and Nature. We analyze the value of this game in the limit, where the investor can trade at smaller and smaller time intervals. Under weak assumptions on the actions of Nature (an adversary), we show that the minimax option price asymptotically approaches exactly the Black-Scholes valuation. The key piece of our analysis is showing that Nature's minimax optimal dual strategy converges to geometric Brownian motion in the limit.; Comment: 19 pages

Pricing Options in Incomplete Equity Markets via the Instantaneous Sharpe Ratio

Bayraktar, Erhan; Young, Virginia R.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
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We use a continuous version of the standard deviation premium principle for pricing in incomplete equity markets by assuming that the investor issuing an unhedgeable derivative security requires compensation for this risk in the form of a pre-specified instantaneous Sharpe ratio. First, we apply our method to price options on non-traded assets for which there is a traded asset that is correlated to the non-traded asset. Our main contribution to this particular problem is to show that our seller/buyer prices are the upper/lower good deal bounds of Cochrane and Sa\'{a}-Requejo (2000) and of Bj\"{o}rk and Slinko (2006) and to determine the analytical properties of these prices. Second, we apply our method to price options in the presence of stochastic volatility. Our main contribution to this problem is to show that the instantaneous Sharpe ratio, an integral ingredient in our methodology, is the negative of the market price of volatility risk, as defined in Fouque, Papanicolaou, and Sircar (2000).; Comment: Keywords: Pricing derivative securities, incomplete markets, Sharpe ratio, correlated assets, stochastic volatility, non-linear partial differential equations, good deal bounds

A One-Factor Conditionally Linear Commodity Pricing Model under Partial Information

Kato, Takashi; Sekine, Jun; Yamamoto, Hiromitsu
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 17/06/2014 Português
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A one-factor asset pricing model with an Ornstein--Uhlenbeck process as its state variable is studied under partial information: the mean-reverting level and the mean-reverting speed parameters are modeled as hidden/unobservable stochastic variables. No-arbitrage pricing formulas for derivative securities written on a liquid asset and exponential utility indifference pricing formulas for derivative securities written on an illiquid asset are presented. Moreover, a conditionally linear filtering result is introduced to compute the pricing/hedging formulas and the Bayesian estimators of the hidden variables.; Comment: 21 pages

Continuous-time stochastic analysis of optimal experimentation and of derivative asset pricing.

Rady, Sven
Fonte: London School of Economics and Political Science Thesis Publicador: London School of Economics and Political Science Thesis
Tipo: Thesis; NonPeerReviewed Formato: application/pdf
Publicado em //1995 Português
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This thesis applies continuous-time stochastic techniques to problems in economics of information and financial economics. The first part of the thesis uses non-linear filtering and stochastic control theory to study a continuous-time model of optimal experimentation by a monopolist who faces an unknown demand curve subject to random changes. It is shown that different probabilities of a demand curve switch can lead to qualitatively very different optimal behaviour. Moreover, the dependence of the optimal policy on these switching probabilities is discontinuous. This suggests that a market or an economy embedded in a changing environment may alter its behaviour dramatically if the volatility of the environment passes a critical threshold. The second part of the thesis studies continuous-time models of derivative asset pricing. First, a review of the so-called direct approach to debt option pricing emphasises the principal modeling problems of this approach and highlights the shortcomings of certain models proposed in the literature. Next, the connection between martingale measures and numeraire portfolios is exploited in problems of option pricing with strict upper and lower bounds on the underlying financial variable. This leads to a new decomposition of option prices in terms of exercise probabilities calculated under particular martingale measures and allows a simple proof of certain generalisations of the Black-Scholes option price formula. Finally...