MONTE CARLO METHODS FOR THE VALUATION OF MULTIPLE-EXERCISE OPTIONS

We discuss Monte Carlo methods for valuing options with multiple-exercise features in discrete time. By extending the recently developed duality ideas for American option pricing, we show how to obtain estimates on the prices of such options using Monte Carlo techniques. We prove convergence of our approach and estimate the error. The methods are applied to options in the energy and interest rate derivative markets.     

ON THE CONSISTENCY OF REGRESSION‐BASED MONTE CARLO METHODS FOR PRICING BERMUDAN OPTIONS IN CASE OF ESTIMATED FINANCIAL MODELS

In many applications of regression‐based Monte Carlo methods for pricing, American options in discrete time parameters of the underlying financial model have to be estimated from observed data. In this paper suitably defined nonparametric regression‐based Monte Carlo methods are applied to paths of financial models where the parameters converge toward true values of the parameters. For various Black–Scholes, GARCH, and Levy models it is shown that in this case the price estimated from the approximate model converges to the true price.     

TRUE UPPER BOUNDS FOR BERMUDAN PRODUCTS VIA NON-NESTED MONTE CARLO

We present a generic non-nested Monte Carlo procedure for computing true upper bounds for Bermudan products, given an approximation of the Snell envelope. The pleonastic true stresses that, by construction, the estimator is biased above the Snell envelope. The key idea is a regression estimator for the Doob martingale part of the approximative Snell envelope, which preserves the martingale property. The so constructed martingale can be employed for computing tight dual upper bounds without nested simulation. In general, this martingale can also be used as a control variate for simulation of conditional expectations. In this context, we develop a variance reduced version of the nested primal-dual estimator. Numerical experiments indicate the efficiency of the proposed algorithms.     

ON THE ERROR IN THE MONTE CARLO PRICING OF SOME FAMILIAR EUROPEAN PATH-DEPENDENT OPTIONS

This paper studies the relative error in the crude Monte Carlo pricing of some familiar European path-dependent multiasset options. For the crude Monte Carlo method it is well known that the convergence rate   O ( n ^−1/2)  , where n is the number of simulations, is independent of the dimension of the integral. This paper also shows that for a large class of pricing problems in the multiasset Black-Scholes market the constant in   O ( n ^−1/2)  is independent of the dimension. To be more specific, the constant is only dependent on the highest volatility among the underlying assets, time to maturity, and degree of confidence interval.     

FAST MONTE CARLO GREEKS FOR FINANCIAL PRODUCTS WITH DISCONTINUOUS PAY‐OFFS

We introduce a new class of numerical schemes for discretizing processes driven by Brownian motions. These allow the rapid computation of sensitivities of discontinuous integrals using pathwise methods even when the underlying densities postdiscretization are singular. The two new methods presented in this paper allow Greeks for financial products with trigger features to be computed in the LIBOR market model with similar speed to that obtained by using the adjoint method for continuous pay‐offs. The methods are generic with the main constraint being that the discontinuities at each step must be determined by a one‐dimensional function: the proxy constraint. They are also generic with the sole interaction between the integrand and the scheme being the specification of this constraint.     

CONVERGENCE OF A LEAST‐SQUARES MONTE CARLO ALGORITHM FOR AMERICAN OPTION PRICING WITH DEPENDENT SAMPLE DATA

We analyze the convergence of the Longstaff–Schwartz algorithm relying on only a single set of independent Monte Carlo sample paths that is repeatedly reused for all exercise time‐steps. We prove new estimates on the stochastic component of the error of this algorithm whenever the approximation architecture is any uniformly bounded set of L² functions of finite Vapnik–Chervonenkis dimension (VC‐dimension), but in particular need not necessarily be either convex or closed. We also establish new overall error estimates, incorporating bounds on the approximation error as well, for certain nonlinear, nonconvex sets of neural networks.     

助学贷款的另一种选择:由社保基金来发放贷款

助学贷款难已经引起了社会的广泛关注,本文讨论了制约助学贷款发放的基本原因,指出深层次的矛盾在于国家助学贷款的政策性实质和作为商业贷款发放的制度性错位.以此为出发点,认为实现与社保基金的结合才是助学贷款的最好出路.社保基金的制度特点也决定了由其发放助学贷款具有得天独厚的优势,并有着切实的可操作性和可行性.     

助学贷款的另一种选择:热由社保基金来发放贷款

助学贷款难已经引起了社会的广泛关注,本文讨论了制约助学贷款发放的基本原因,指出深层次的矛盾在于国家助学贷款的政策性实质和作为商业贷款发放的制度性错位。以此为出发点,认为实现与社保基金的结合才是助学贷款的最好出路。社保基金的制度特点也决定了由其发放助学贷款具有得天独厚的优势,并有着切实的可操作性和可行性。     

EVIDENCE THEORY: A MATHEMATICAL FRAMEWORK FOR UNPREDICTABLE HYPOTHESES

Shafer's evidence theory is a branch of the mathematics of uncertain reasoning that allows for novel possibilities to be conceived by a decision‐maker. Many of its findings exhibit striking similarities with an alternative decision theory put forward by Shackle in the 1950s, before expected utility maximization monopolized the scene. Evidence theory does not attempt to formalize the emergence of novelties, but it is a suitable framework for reconstructing the formation of beliefs when novelties appear. An application to decision‐making in the biotech and pharmaceutical industries illustrates the potentialities of evidence theory, as well as its shortcomings.     

EXCHANGE RATE BANDS OF INACTION AND PLAY‐HYSTERESIS IN GERMAN EXPORTS—SECTORAL EVIDENCE FOR SOME OECD DESTINATIONS

A non‐linear model is applied, where suddenly strong spurts of exports occur when changes of the exchange rate go beyond a zone of inaction, which we call ‘play’ area—analogous to mechanical play. We implement an algorithm describing path‐dependent play‐hysteresis into a regression framework. The hysteretic impact of real exchange rates on German exports is estimated based on the period from 1995Q1 to 2010Q3. Looking at some of the main export partners of Germany outside the euro area and some of the most important tradeable sectors we find significant hysteretic effects for a part of the German exports.     

农产品出口策略研究——以青岛农产品出口为研究样本

农业是关系国计民生的基础产业,也是工业和服务业良性发展的坚实基础,尤其是在我国经济发展到现阶段,"三农"问题已经成为关系到我国经济社会能否实现可持续发展的关键因素.     

CONDITIONAL DEMAND FUNCTIONS,SEPARABILITY, AND THE LENGTH OF RUN: SOME NOTES FOR THE APPLIED RESEARCHER OF HOUSEHOLD BEHAVIOUR1

This paper introduces the concepts of conditional demand functions, the length of run, and separability to consumer and family economists as useful tools for empirical research on household behaviour. The relationships among demand, expenditure, and consumption functions are sketched. Then conditional demand functions are explained, their uses in empirical work addressed, and several applications discussed. The concepts of the length of run and of separability are explained in terms of conditional demand and their implications for and applications to empirical research on household behaviour treated.     

THE 4/2 STOCHASTIC VOLATILITY MODEL: A UNIFIED APPROACH FOR THE HESTON AND THE 3/2 MODEL

We introduce a new stochastic volatility model that includes, as special instances, the Heston (1993) and the 3/2 model of Heston (1997) and Platen (1997). Our model exhibits important features: first, instantaneous volatility can be uniformly bounded away from zero, and second, our model is mathematically and computationally tractable, thereby enabling an efficient pricing procedure. This called for using the Lie symmetries theory for partial differential equations; doing so allowed us to extend known results on Bessel processes. Finally, we provide an exact simulation scheme for the model, which is useful for numerical applications.