Internal-rate-of-return (IRR) settled swaptions are the main interest rate volatility instruments in the European interest rate markets. Industry practice is to use an approximation formula to price IRR swaptions based on Black model, which is not arbitrage-free. We formulate a unified market model to incorporate both swaptions and constant maturity swaps (CMS) pricing under a single, self-consistent framework. We demonstrate that the model is able to calibrate to market quotes well, and is also able to efficiently price both IRR-settled and swap-settled swaptions, along with CMS products. We use the model to illustrate the difference in implied volatilities for IRR-settled payer and receiver swaptions, the pricing of zero-wide collars and in-the-money (ITM) swaptions, the implication on put-call parity, and the issue of negative vega. These findings offer important insights to the ongoing reform in the European swaption market.

中文翻译：

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互换和固定到期互换的统一市场模型

内部收益率（IRR）结算掉期是欧洲利率市场的主要利率波动工具。行业惯例是使用近似公式对基于 Black 模型的 IRR 掉期期权进行定价，这不是无套利的。我们制定了一个统一的市场模型，将掉期期权和固定期限掉期 (CMS) 定价结合在一个单一、自洽的框架下。我们证明该模型能够很好地校准市场报价，并且还能够有效地为 IRR 结算和掉期结算的掉期期权以及 CMS 产品定价。我们使用该模型来说明 IRR 结算的支付方和接收方掉期期权隐含波动率的差异、零宽项圈和价内 (ITM) 掉期期权的定价、对看跌期权平价的影响以及负维加。