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Price Process (price + process)
Selected AbstractsOn geometric ergodicity of the commodity pricing modelINTERNATIONAL JOURNAL OF ECONOMIC THEORY, Issue 3 2009Kazuo Nishimura C61; C62 We provide a simple proof of geometric ergodicity for Samuelson's (1971) commodity pricing model. The proof yields a rate of convergence to the stationary distribution stated in terms of model primitives. We also provide a rate of convergence for prices to the stationary price process, and for the joint distribution of the state process to the stationary state process. [source] PORTFOLIO OPTIMIZATION WITH JUMPS AND UNOBSERVABLE INTENSITY PROCESSMATHEMATICAL FINANCE, Issue 2 2007Nicole Bäuerle We consider a financial market with one bond and one stock. The dynamics of the stock price process allow jumps which occur according to a Markov-modulated Poisson process. We assume that there is an investor who is only able to observe the stock price process and not the driving Markov chain. The investor's aim is to maximize the expected utility of terminal wealth. Using a classical result from filter theory it is possible to reduce this problem with partial observation to one with complete observation. With the help of a generalized Hamilton,Jacobi,Bellman equation where we replace the derivative by Clarke's generalized gradient, we identify an optimal portfolio strategy. Finally, we discuss some special cases of this model and prove several properties of the optimal portfolio strategy. In particular, we derive bounds and discuss the influence of uncertainty on the optimal portfolio strategy. [source] MODELING LIQUIDITY EFFECTS IN DISCRETE TIMEMATHEMATICAL FINANCE, Issue 1 2007Umut Çetin We study optimal portfolio choices for an agent with the aim of maximizing utility from terminal wealth within a market with liquidity costs. Under some mild conditions, we show the existence of optimal portfolios and that the marginal utility of the optimal terminal wealth serves as a change of measure to turn the marginal price process of the optimal strategy into a martingale. Finally, we illustrate our results numerically in a Cox,Ross,Rubinstein binomial model with liquidity costs and find the reservation ask prices for simple European put options. [source] A MULTINOMIAL APPROXIMATION FOR AMERICAN OPTION PRICES IN LÉVY PROCESS MODELSMATHEMATICAL FINANCE, Issue 4 2006Ross A. Maller This paper gives a tree-based method for pricing American options in models where the stock price follows a general exponential Lévy process. A multinomial model for approximating the stock price process, which can be viewed as generalizing the binomial model of Cox, Ross, and Rubinstein (1979) for geometric Brownian motion, is developed. Under mild conditions, it is proved that the stock price process and the prices of American-type options on the stock, calculated from the multinomial model, converge to the corresponding prices under the continuous time Lévy process model. Explicit illustrations are given for the variance gamma model and the normal inverse Gaussian process when the option is an American put, but the procedure is applicable to a much wider class of derivatives including some path-dependent options. Our approach overcomes some practical difficulties that have previously been encountered when the Lévy process has infinite activity. [source] MORE ON MINIMAL ENTROPY,HELLINGER MARTINGALE MEASUREMATHEMATICAL FINANCE, Issue 1 2006Tahir Choulli This paper extends our recent paper (Choulli and Stricker 2005) to the case when the discounted stock price process may be unbounded and may have predictable jumps. In this very general context, we provide mild necessary conditions for the existence of the minimal entropy,Hellinger local martingale density and we give an explicit description of this extremal martingale density that can be determined by pointwise solution of equations in depending only on the local characteristics of the discounted price process S. The uniform integrability and other integrability properties are investigated for this extremal density, which lead to the conditions of the existence of the minimal entropy,Hellinger martingale measure. Finally, we illustrate the main results of the paper in the case of a discrete-time market model, where the relationship of the obtained optimal martingale measure to a dynamic risk measure is discussed. [source] Nonconvergence in the Variation of the Hedging Strategy of a European Call OptionMATHEMATICAL FINANCE, Issue 4 2003R. Th. In this paper we consider the variation of the hedging strategy of a European call option when the underlying asset follows a binomial tree. In a binomial tree model the hedging strategy of a European call option converges to a continuous process when the number of time points increases so that the price process of the underlying asset converges to a Brownian motion, the Bachelier model. However, the variation of the hedging strategy need not converge to the variation of the limit process. In fact, it is shown that the asymptotic variation of the hedging strategy may be of any order. [source] On the optimal portfolio for the exponential utility maximization: remarks to the six-author paperMATHEMATICAL FINANCE, Issue 2 2002Yuri M. Kabanov This note contains ramifications of results of Delbaen et al. (2002). Assuming that the price process is locally bounded and admits an equivalent local martingale measure with finite entropy, we show, without further assumption, that in the case of exponential utility the optimal portfolio process is a martingale with respect to each local martingale measure with finite entropy. Moreover, the optimal value always can be attained on a sequence of uniformly bounded portfolios. [source] Endogenous Random Asset Prices in Overlapping Generations EconomiesMATHEMATICAL FINANCE, Issue 1 2000Volker Böhm This paper derives a general explicit sequential asset price process for an economy with overlapping generations of consumers. They maximize expected utility with respect to subjective transition probabilities given by Markov kernels. The process is determined primarily by the interaction of exogenous random dividends and the characteristics of consumers, given by arbitrary preferences and expectations, yielding an explicit random dynamical system with expectations feedback. The paper studies asset prices and equity premia for a parametrized class of examples with CARA utilities and exponential distributions. It provides a complete analysis of the role of risk aversion and of subjective as well as rational beliefs. [source] Modeling and Forecasting Realized VolatilityECONOMETRICA, Issue 2 2003Torben G. Andersen We provide a framework for integration of high,frequency intraday data into the measurement, modeling, and forecasting of daily and lower frequency return volatilities and return distributions. Building on the theory of continuous,time arbitrage,free price processes and the theory of quadratic variation, we develop formal links between realized volatility and the conditional covariance matrix. Next, using continuously recorded observations for the Deutschemark/Dollar and Yen/Dollar spot exchange rates, we find that forecasts from a simple long,memory Gaussian vector autoregression for the logarithmic daily realized volatilities perform admirably. Moreover, the vector autoregressive volatility forecast, coupled with a parametric lognormal,normal mixture distribution produces well,calibrated density forecasts of future returns, and correspondingly accurate quantile predictions. Our results hold promise for practical modeling and forecasting of the large covariance matrices relevant in asset pricing, asset allocation, and financial risk management applications. [source] HEDGING BY SEQUENTIAL REGRESSIONS REVISITEDMATHEMATICAL FINANCE, Issue 4 2009Almost 20 years ago Föllmer and Schweizer (1989) suggested a simple and influential scheme for the computation of hedging strategies in an incomplete market. Their approach of,local,risk minimization results in a sequence of one-period least squares regressions running recursively backward in time. In the meantime, there have been significant developments in the,global,risk minimization theory for semimartingale price processes. In this paper we revisit hedging by sequential regression in the context of global risk minimization, in the light of recent results obtained by ,erný and Kallsen (2007). A number of illustrative numerical examples are given. [source] A Fundamental Theorem of Asset Pricing for Large Financial MarketsMATHEMATICAL FINANCE, Issue 4 2000Irene KleinArticle first published online: 25 DEC 200 We formulate the notion of "asymptotic free lunch" which is closely related to the condition "free lunch" of Kreps (1981) and allows us to state and prove a fairly general version of the fundamental theorem of asset pricing in the context of a large financial market as introduced by Kabanov and Kramkov (1994). In a large financial market one considers a sequence (Sn)n=1, of stochastic stock price processes based on a sequence (,n, Fn, (Ftn)t,In, Pn)n=1, of filtered probability spaces. Under the assumption that for all n, N there exists an equivalent sigma-martingale measure for Sn, we prove that there exists a bicontiguous sequence of equivalent sigma-martingale measures if and only if there is no asymptotic free lunch (Theorem 1.1). Moreover we present an example showing that it is not possible to improve Theorem 1.1 by replacing "no asymptotic free lunch" by some weaker condition such as "no asymptotic free lunch with bounded" or "vanishing risk." [source] Multiple Ratings Model of Defaultable Term StructureMATHEMATICAL FINANCE, Issue 2 2000Tomasz R. Bielecki A new approach to modeling credit risk, to valuation of defaultable debt and to pricing of credit derivatives is developed. Our approach, based on the Heath, Jarrow, and Morton (1992) methodology, uses the available information about the credit spreads combined with the available information about the recovery rates to model the intensities of credit migrations between various credit ratings classes. This results in a conditionally Markovian model of credit risk. We then combine our model of credit risk with a model of interest rate risk in order to derive an arbitrage-free model of defaultable bonds. As expected, the market price processes of interest rate risk and credit risk provide a natural connection between the actual and the martingale probabilities. [source] | ||||||||||