加权方差互换价格的套利界

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摘要翻译：
当有限个共同到期看跌期权的市场价格给定时，我们研究了加权方差互换的鲁棒定价和套期保值。我们假设给定的价格不允许套利，并推导出加权方差互换的无套利边界以及执行这些边界的超复制策略和子复制策略。我们发现，方差互换的市场报价出人意料地接近于我们确定的无模型下限。我们通过将其转化为一个类似的凸收益欧式期权问题来解决这个问题。下界成为半无限线性规划中的一个问题，我们对其进行了详细的求解。上限是显式的。我们在一个模型无关和概率无关的设置中工作。特别地，我们使用并扩展了F“Ollmer的路径随机演算，引入了套利和可容许性的适当概念，从而使我们建立了方差互换和”对数合约“之间的通常套期保值关系以及加权方差互换的类似联系。我们的结果表现为FTAP的形式：我们证明了（弱）套利的不存在等价于一个经典模型的存在，该模型通过风险中性的贴现收益预期再现了观察到的价格。
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英文标题：
《Arbitrage Bounds for Prices of Weighted Variance Swaps》
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作者：
Mark H.A. Davis, Jan Obloj, Vimal Raval
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最新提交年份：
2012
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Pricing of Securities        证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
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英文摘要：
  We develop robust pricing and hedging of a weighted variance swap when market prices for a finite number of co--maturing put options are given. We assume the given prices do not admit arbitrage and deduce no-arbitrage bounds on the weighted variance swap along with super- and sub- replicating strategies which enforce them. We find that market quotes for variance swaps are surprisingly close to the model-free lower bounds we determine. We solve the problem by transforming it into an analogous question for a European option with a convex payoff. The lower bound becomes a problem in semi-infinite linear programming which we solve in detail. The upper bound is explicit.   We work in a model-independent and probability-free setup. In particular we use and extend F\"ollmer's pathwise stochastic calculus. Appropriate notions of arbitrage and admissibility are introduced. This allows us to establish the usual hedging relation between the variance swap and the 'log contract' and similar connections for weighted variance swaps. Our results take form of a FTAP: we show that the absence of (weak) arbitrage is equivalent to the existence of a classical model which reproduces the observed prices via risk-neutral expectations of discounted payoffs.
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PDF链接：
https://arxiv.org/pdf/1001.2678

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关键词：Transforming Quantitative Expectations appropriate derivatives prices 套利 收益 solve 求解