{"title":"Watanabe's expansion: A Solution for the convexity conundrum","authors":"David García-Lorite, Raul Merino","doi":"arxiv-2404.01522","DOIUrl":null,"url":null,"abstract":"In this paper, we present a new method for pricing CMS derivatives. We use\nMallaivin's calculus to establish a model-free connection between the price of\na CMS derivative and a quadratic payoff. Then, we apply Watanabe's expansions\nto quadratic payoffs case under local and stochastic local volatility. Our\napproximations are generic. To evaluate their accuracy, we will compare the\napproximations numerically under the normal SABR model against the market\nstandards: Hagan's approximation, and a Monte Carlo simulation.","PeriodicalId":501084,"journal":{"name":"arXiv - QuantFin - Mathematical Finance","volume":"46 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - QuantFin - Mathematical Finance","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2404.01522","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we present a new method for pricing CMS derivatives. We use
Mallaivin's calculus to establish a model-free connection between the price of
a CMS derivative and a quadratic payoff. Then, we apply Watanabe's expansions
to quadratic payoffs case under local and stochastic local volatility. Our
approximations are generic. To evaluate their accuracy, we will compare the
approximations numerically under the normal SABR model against the market
standards: Hagan's approximation, and a Monte Carlo simulation.
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