Building good deals with arbitrage-free discrete time pricing models

The Spanish Review of Financial Economics Pub Date : 2012-07-01 DOI:10.1016/j.srfe.2012.06.001

Beatriz Balbás , Raquel Balbás

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Abstract

Recent literature has proved that many classical very important pricing models of Financial Economics (Black and Scholes, Heston, etc.) and risk measures (VaR, CVaR, etc.) may lead to “pathological meaningless situations”, since there exist sequences of portfolios whose negative risk and positive expected return are unbounded. Such a sequence of strategies will be called “good deal”.

This paper focuses on a discrete time arbitrage-free and complete pricing model and goes beyond existence properties. It deals with the effective construction of good deals, i.e., sequences $(y_{m})_{m = 1}^{\infty}$ of portfolios such that $(VaR (y_{m}), CVaR (y_{m}), Expected_return (y_{m}))$ tends to (− ∞ , − ∞ , + ∞). Under quite general conditions the explicit expression of a good deal is given, and practical algorithms are provided. The sensitivity of our results with respect to measurement errors or dynamic changes of the parameters is analyzed, and numerical experiments are presented with the binomial model.

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利用无套利离散时间定价模型构建良好交易

最近的文献已经证明，金融经济学的许多经典的非常重要的定价模型（Black and Scholes，Heston等）和风险度量（VaR，CVaR等）可能会导致“病理性的无意义情况”，因为存在负风险和正预期回报是无限的投资组合序列。这样的一系列策略被称为“好交易”。本文重点研究了一个离散时间无套利完全定价模型，并超越了存在性。它处理了好交易的有效构造，即投资组合的序列（ym）m=1∞，使得（VaR（ym。在相当一般的条件下，给出了一个良好条件的显式表达式，并给出了实用的算法。分析了我们的结果对测量误差或参数动态变化的敏感性，并用二项式模型进行了数值实验。

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The Spanish Review of Financial Economics

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