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Constructing good deals in discrete time arbitrage-free dynamic pricing models

Balbás, Beatriz; Balbás, Raquel
Fonte: Instituto Politécnico de Lisboa Publicador: Instituto Politécnico de Lisboa
Tipo: Conferência ou Objeto de Conferência
Publicado em /07/2011 Português
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Recent literature has proved that many classical pricing models (Black and Scholes, Heston, etc.) and risk measures (V aR, CV aR, etc.) may lead to “pathological meaningless situations”, since traders can build sequences of portfolios whose risk leveltends to −infinity and whose expected return tends to +infinity, i.e., (risk = −infinity, return = +infinity). Such a sequence of strategies may be called “good deal”. This paper focuses on the risk measures V aR and CV aR and analyzes this caveat in a discrete time complete pricing model. Under quite general conditions the explicit expression of a good deal is given, and its sensitivity with respect to some possible measurement errors is provided too. We point out that a critical property is the absence of short sales. In such a case we first construct a “shadow riskless asset” (SRA) without short sales and then the good deal is given by borrowing more and more money so as to invest in the SRA. It is also shown that the SRA is interested by itself, even if there are short selling restrictions.

The Behavior of Savings and Asset Prices When Preferences and Beliefs are Heterogeneous

Zeckhauser, Richard Jay; Tran, Ngoc-Khanh
Fonte: John F. Kennedy School of Government, Harvard University Publicador: John F. Kennedy School of Government, Harvard University
Tipo: Research Paper or Report
Português
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Movements in asset prices are a major risk confronting individuals. This paper establishes new asset pricing results when agents differ in risk preference, time preference and/or expectations. It shows that risk tolerance is a critical concept driving savings decisions, consumption allocations, prices and return volatilities. Surprisingly, due to the equilibrium risk sharing, the precautionary savings motive in the aggregate can vastly exceed that of even the most prudent actual agent in the economy. Consequently, a low real interest rate, resulting from large aggregate savings, can prevail with reasonable risk aversions for all agents. One downside of a large aggregate savings motive is that savings rates become extremely sensitive to output fluctuation. Thus, the same mechanism that produces realistically low interest rates tends to make them unrealistically volatile. A powerful isomorphism allows differences in time preference and expectations to be swept away in the analysis, yielding an equivalent economy whose agents differ merely in risk aversion. These results hold great potential to simplify the analysis of heterogeneous-agent economies, as we demonstrate in quantifying how asset prices move and bounding their volatilities. All results are obtained in closed form for any number of agents possessing additively separable preferences in an endowment economy.

Liquidity Clienteles : Transaction Costs and Investment Decisions of Individual Investors

Anginer, Deniz
Fonte: Banco Mundial Publicador: Banco Mundial
Tipo: Publications & Research :: Policy Research Working Paper
Português
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Theoretical papers link the liquidity premium to the optimal trading decisions of investors facing transaction costs. In particular, investors' holding periods determine how transaction costs are amortized and priced in asset returns. Using a unique data set containing two million trades, this paper investigates the relationship between holding periods and transaction costs for 66,000 households from a large discount brokerage. The author finds that transaction costs are an important determinant of investors' holding periods, after controlling for household and stock characteristics. The relationship between holding periods and transaction costs is stronger among more sophisticated investors. Households with longer holding periods earn significantly higher returns after amortized transaction costs, and households that have holding periods that are positively related to transaction costs earn both higher gross and net returns. The author shows that there is correlation in the demand for liquid assets across households and...

Building proxies that capture time-variation in expected returns using a VAR approach

Sousa, Ricardo M.
Fonte: Routledge Publicador: Routledge
Tipo: Artigo de Revista Científica
Publicado em //2011 Português
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I use the consumer's budget constraint to derive a relationship between stock market returns, the residuals of the trend relationship among consumption, aggregate wealth, and labour income, and three major sources of risk: future changes in the housing consumption share, future labour income growth, and future consumption growth. I model the joint dynamics of changes in the housing consumption share, consumption growth, wealth growth, income growth, asset returns, consumptionwealth ratio and dividend-price ratio, and show that asset returns largely reflect expectations about long-run risk. On the other hand, unexpected shocks play a negligible role in the context of forecasting future asset returns. Combining the intertemporal budget constraint and the forecasting properties of an informative Vector-Autogression (VAR), one can, therefore, generate the predictability of many economically motivated variables developed in the literature on asset pricing, and accommodate the implications of a wide class of optimal models of consumer behaviour without imposing a functional form on preferences.; Fundação para a Ciência e a Tecnologia (FCT) SFRH/BD/12985/2003

Essays in Financial Economics and Econometrics

Bates, Brandon
Fonte: Harvard University Publicador: Harvard University
Tipo: Thesis or Dissertation
Português
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In the first essay, I study the power of predictive regressions in a world of forecastable returns and find it to be quite poor. Using a simple model, I investigate the properties of short- and long-horizon regressions. The mechanisms biasing coefficients in short-horizon regressions differ from those affecting longer horizons. Further, I demonstrate that R\(^2s\) are biased and give an estimable bias correction. A calibration exercise shows sample lengths will be insufficient to determine what predicts asset returns until beyond the year 2100. The problem is not isolated to highly persistent predictors; even modestly persistent predictors have difficulties. Further, long-horizon regressions have inferior power relative to their single-period counterparts. These results present a predicament. If return predictability exists, then our ability to identify its source using predictive regressions alone is exceedingly poor. The second essay, written with James Stock and Mark Watson, considers the estimation of approximate dynamic factor models when there is temporal instability in the factors, factor loadings, and errors. We demonstrate that estimators for the factors and for the number of those factors are consistent for their population values even when affected by these instabilities. Further...

Intertemporal Substitutability, Risk Aversion and Asset Prices

Pepin, Dominique
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
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Is the elasticity of intertemporal substitution (EIS) more or less than one? This question can be answered by confronting theoretical results of asset pricing models with investor behaviour during episodes of stock market panic. If we consider these episodes as periods of high risk aversion, then lower asset prices are in fact associated with higher risk aversion. However, according to theoretical models, risky asset price is an increasing function of the coefficient of risk aversion only if the EIS exceeds unity. It may therefore be concluded that the EIS must be more than one to reconcile theory with the observed stock price decline during periods of panic.

Mean-Variance Hedging for Pricing European Options Under Assumption of Non-continuous Trading

Nikulin, Vladimir
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 25/04/2010 Português
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We consider a portfolio with call option and the corresponding underlying asset under the standard assumption that stock-market price represents a random variable with lognormal distribution. Minimizing the variance (hedging risk) of the portfolio on the date of maturity of the call option we find a fraction of the asset per unit call option. As a direct consequence we derive the statistically fair lookback call option price in explicit form. In contrast to the famous Black-Scholes theory, any portfolio can not be regarded as risk-free because no additional transactions are supposed to be conducted over the life of the contract, but the sequence of independent portfolios will reduce risk to zero asymptotically. This property is illustrated in the experimental section using a dataset of daily stock prices of 18 leading Australian companies for the period of 3 years.

A New Approach to Model Free Option Pricing

Hauser, Raphael; Shahverdyan, Sergey
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 15/01/2015 Português
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In this paper we introduce a new approach to model-free path-dependent option pricing. We first introduce a general duality result for linear optimisation problems over signed measures introduced in [3] and show how the the problem of model-free option pricing can be formulated in the new framework. We then introduce a model to solve the problem numerically when the only information provided is the market data of vanilla call or put option prices. Compared to the common approaches in the literature, e.g. [4], the model does not require the marginal distributions of the stock price for different maturities. Though the experiments are carried out for simple path-dependent options on a single stock, the model is easy to generalise for multi-asset framework.

Theory of Information Pricing

Brody, Dorje C.; Law, Yan Tai
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
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In financial markets valuable information is rarely circulated homogeneously, because of time required for information to spread. However, advances in communication technology means that the 'lifetime' of important information is typically short. Hence, viewed as a tradable asset, information shares the characteristics of a perishable commodity: while it can be stored and transmitted freely, its worth diminishes rapidly in time. In view of recent developments where internet search engines and other information providers are offering information to financial institutions, the problem of pricing information is becoming increasingly important. With this in mind, a new formulation of utility-indifference argument is introduced and used as a basis for pricing information. Specifically, we regard information as a quantity that converts a prior distribution into a posterior distribution. The amount of information can then be quantified by relative entropy. The key to our utility indifference argument is to equate the maximised a posterior utility, after paying certain cost for the information, with the a posterior expectation of the utility based on the a priori optimal strategy. This formulation leads to one price for a given quantity of upside information; and another price for a given quantity of downside information. The ideas are illustrated by means of simple examples.; Comment: 13 pages...

Pricing Step Options under the CEV and other Solvable Diffusion Models

Campolieti, Giuseppe; Makarov, Roman N.; Wouterloot, Karl
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 15/02/2013 Português
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We consider a special family of occupation-time derivatives, namely proportional step options introduced by Linetsky in [Math. Finance, 9, 55--96 (1999)]. We develop new closed-form spectral expansions for pricing such options under a class of nonlinear volatility diffusion processes which includes the constant-elasticity-of-variance (CEV) model as an example. In particular, we derive a general analytically exact expression for the resolvent kernel (i.e. Green's function) of such processes with killing at an exponential stopping time (independent of the process) of occupation above or below a fixed level. Moreover, we succeed in Laplace inverting the resolvent kernel and thereby derive newly closed-form spectral expansion formulae for the transition probability density of such processes with killing. The spectral expansion formulae are rapidly convergent and easy-to-implement as they are based simply on knowledge of a pair of fundamental solutions for an underlying solvable diffusion process. We apply the spectral expansion formulae to the pricing of proportional step options for four specific families of solvable nonlinear diffusion asset price models that include the CEV diffusion model and three other multi-parameter state-dependent local volatility confluent hypergeometric diffusion processes.; 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

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

Multi-Moments Method for Portfolio Management: Generalized Capital Asset Pricing Model in Homogeneous and Heterogeneous markets

Malevergne, Y.; Sornette, D.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 19/07/2002 Português
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We introduce a new set of consistent measures of risks, in terms of the semi-invariants of pdf's, such that the centered moments and the cumulants of the portfolio distribution of returns that put more emphasis on the tail the distributions. We derive generalized efficient frontiers, based on these novel measures of risks and present the generalized CAPM, both in the cases of homogeneous and heterogeneous markets. Then, using a family of modified Weibull distributions, encompassing both sub-exponentials and super-exponentials, to parameterize the marginal distributions of asset returns and their natural multivariate generalizations, we offer exact formulas for the moments and cumulants of the distribution of returns of a portfolio made of an arbitrary composition of these assets. Using combinatorial and hypergeometric functions, we are in particular able to extend previous results to the case where the exponents of the Weibull distributions are different from asset to asset and in the presence of dependence between assets. In this parameterization, we treat in details the problem of risk minimization using the cumulants as measures of risks for a portfolio made of two assets and compare the theoretical predictions with direct empirical data. Our extended formulas enable us to determine analytically the conditions under which it is possible to ``have your cake and eat it too''...

Pricing with coherent risk

Cherny, Alexander S.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 02/05/2006 Português
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This paper deals with applications of coherent risk measures to pricing in incomplete markets. Namely, we study the No Good Deals pricing technique based on coherent risk. Two forms of this technique are presented: one defines a good deal as a trade with negative risk; the other one defines a good deal as a trade with unusually high RAROC. For each technique, the fundamental theorem of asset pricing and the form of the fair price interval are presented. The model considered includes static as well as dynamic models, models with an infinite number of assets, models with transaction costs, and models with portfolio constraints. In particular, we prove that in a model with proportional transaction costs the fair price interval converges to the fair price interval in a frictionless model as the coefficient of transaction costs tends to zero. Moreover, we study some problems in the ``pure'' theory of risk measures: we present a simple geometric solution of the capital allocation problem and apply it to define the coherent risk contribution. The mathematical tools employed are probability theory, functional analysis, and finite-dimensional convex analysis.; Comment: 4 figures

G-Doob-Meyer Decomposition and its Application in Bid-Ask Pricing for American Contingent Claim Under Knightian Uncertainty

Chen, Wei
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 31/12/2013 Português
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The target of this paper is to establish the bid-ask pricing frame work for the American contingent claims against risky assets with G-asset price systems (see \cite{Chen2013b}) on the financial market under Knight uncertainty. First, we prove G-Dooby-Meyer decomposition for G-supermartingale. Furthermore, we consider bid-ask pricing American contingent claims under Knight uncertain, by using G-Dooby-Meyer decomposition, we construct dynamic superhedge stragies for the optimal stopping problem, and prove that the value functions of the optimal stopping problems are the bid and ask prices of the American contingent claims under Knight uncertain. Finally, we consider a free boundary problem, prove the strong solution existence of the free boundary problem, and derive that the value function of the optimal stopping problem is equivalent to the strong solution to the free boundary problem.; Comment: 21 pages

Application of simplest random walk algorithms for pricing barrier options

Krivko, M.; Tretyakov, M. V.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 24/11/2012 Português
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We demonstrate effectiveness of the first-order algorithm from [Milstein, Tretyakov. Theory Prob. Appl. 47 (2002), 53-68] in application to barrier option pricing. The algorithm uses the weak Euler approximation far from barriers and a special construction motivated by linear interpolation of the price near barriers. It is easy to implement and is universal: it can be applied to various structures of the contracts including derivatives on multi-asset correlated underlyings and can deal with various type of barriers. In contrast to the Brownian bridge techniques currently commonly used for pricing barrier options, the algorithm tested here does not require knowledge of trigger probabilities nor their estimates. We illustrate this algorithm via pricing a barrier caplet, barrier trigger swap and barrier swaption.; Comment: It's a pre-publication which final version will appear as a chapter in Recent Developments in Computational Finance (Eds. T. Gerstner and P.E. Kloeden), 2013. [it has one picture and 22 pages]

Fast Numerical Method for Pricing of Variable Annuities with Guaranteed Minimum Withdrawal Benefit under Optimal Withdrawal Strategy

Luo, Xiaolin; Shevchenko, Pavel
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 30/10/2014 Português
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A variable annuity contract with Guaranteed Minimum Withdrawal Benefit (GMWB) promises to return the entire initial investment through cash withdrawals during the policy life plus the remaining account balance at maturity, regardless of the portfolio performance. Under the optimal withdrawal strategy of a policyholder, the pricing of variable annuities with GMWB becomes an optimal stochastic control problem. So far in the literature these contracts have only been evaluated by solving partial differential equations (PDE) using the finite difference method. The well-known Least-Squares or similar Monte Carlo methods cannot be applied to pricing these contracts because the paths of the underlying wealth process are affected by optimal cash withdrawals (control variables) and thus cannot be simulated forward in time. In this paper we present a very efficient new algorithm for pricing these contracts in the case when transition density of the underlying asset between withdrawal dates or its moments are known. This algorithm relies on computing the expected contract value through a high order Gauss-Hermite quadrature applied on a cubic spline interpolation. Numerical results from the new algorithm for a series of GMWB contract are then presented...

Efficient Pricing of CPPI using Markov Operators

Paulot, Louis; Lacroze, Xavier
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 09/01/2009 Português
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Constant Proportion Portfolio Insurance (CPPI) is a strategy designed to give participation in a risky asset while protecting the invested capital. Some gap risk due to extreme events is often kept by the issuer of the product: a put option on the CPPI strategy is included in the product. In this paper we present a new method for the pricing of CPPIs and options on CPPIs, which is much faster and more accurate than the usual Monte-Carlo method. Provided the underlying follows a homogeneous process, the path-dependent CPPI strategy is reformulated into a Markov process in one variable, which allows to use efficient linear algebra techniques. Tail events, which are crucial in the pricing are handled smoothly. We incorporate in this framework linear thresholds, profit lock-in, performance coupons... The American exercise of open-ended CPPIs is handled naturally through backward propagation. Finally we use our pricing scheme to study the influence of various features on the gap risk of CPPI strategies.; Comment: 40 pages

Option Pricing in Multivariate Stochastic Volatility Models of OU Type

Muhle-Karbe, Johannes; Pfaffel, Oliver; Stelzer, Robert
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
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We present a multivariate stochastic volatility model with leverage, which is flexible enough to recapture the individual dynamics as well as the interdependencies between several assets while still being highly analytically tractable. First we derive the characteristic function and give conditions that ensure its analyticity and absolute integrability in some open complex strip around zero. Therefore we can use Fourier methods to compute the prices of multi-asset options efficiently. To show the applicability of our results, we propose a concrete specification, the OU-Wishart model, where the dynamics of each individual asset coincide with the popular Gamma-OU BNS model. This model can be well calibrated to market prices, which we illustrate with an example using options on the exchange rates of some major currencies. Finally, we show that covariance swaps can also be priced in closed form.; Comment: 28 pages, 5 figures, to appear in SIAM Journal on Financial Mathematics

High-Frequency Financial Volatility and the Pricing of Volatility Risk

Sizova, Natalia
Fonte: Universidade Duke Publicador: Universidade Duke
Tipo: Dissertação Formato: 1625594 bytes; application/pdf
Publicado em //2009 Português
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The idea that integrates parts of this dissertation is that high-frequency data allow for more precise and robust methods for forecasting financial volatility and elucidating the role of volatility in forming asset prices. Thus, the first two chapters compare the performance of model-free forecasts specifically designed to employ high-frequency data with the performance of "classical" forecasts developed for daily data. The final chapter of the dissertation incorporates high-frequency data to verify the predictions of asset pricing models about the risk-return relationships at the very shortest horizons. The results are arranged in the following order.

Chapter 1 presents the analytical comparison of feasible reduced-form forecasts designed to employ high-frequency data and model-based forecasts updated to use high-frequency data. The prediction errors of both forecast groups are calculated using the ESV-representation of Meddahi (2003), which allows one to generalize the statements from this analysis to a wider class of volatility processes. The results show that reduced-form forecasts outperform model-based forecasts at longer horizons and perform just as well for day-ahead forecasts.

Chapter 2 expands the conclusions from Chapter 1 to economic measures of forecast performance. These performance measures are constructed within a microeconomic framework that mimics the decision making process of a variance trader who uses volatility forecasts to predict the future profitability of a trade. The results support the theoretical predictions of Chapter 1.

Chapter 3 is co-authored with Professor Tim Bollerslev and Professor George Tauchen. It extends the "long-run risk" model of Bansal and Yaron(2004) to consistently price volatility risks and to be applicable to high-frequency data. The hypothesis at the outset is that while financial volatility is a long-memory process (it exhibits long-range dependence)...