Conditions on Option Prices for Absence of Arbitrage and Exact Calibration
Conditions on Option Prices for Absence of Arbitrage and Exact Calibration
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无套利和精确校准的期权价格条件
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
L. Cousot
中科院分区：
文献类型：
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作者：
L. Cousot
在不存在套利的假设下，给定资产的欧式期权报价必须满足著名的不等式，这些不等式在具有里程碑意义的论文Merton（1973）中已有描述。如果我们进一步假设不存在利率波动，标的资产连续支付确定的红利，那么期权的买卖价格也必须满足跨期限不等式，本文证明了当这些不等式满足时，存在一个与期权报价一致的无套利模型.其中一个含义是，所有静态套利策略都是本文所述策略的线性组合，权重为正。我们还刻画了与给定期权报价一致的模型的可容许违约概率。
Under the assumption of absence of arbitrage, European option quotes on a given asset must satisfy well-known inequalities, which have been described in the landmark paper Merton (1973). If we further assume that there is no interest rate volatility and that the underlying asset continuously pays deterministic dividends, cross-maturity inequalities must also be satisfied by the bid and ask option prices.In this paper, we show that there exists an arbitrage-free model, which is consistent with the option quotes, if these inequalities are satisfied. One implication is that all static arbitrage strategies are linear combinations, with positive weights, of those described here. We also characterize admissible default probabilities for models which are consistent with given option quotes.