论文标题
没有套利SVI
No arbitrage SVI
论文作者
论文摘要
We fully characterize the absence of Butterfly arbitrage in the SVI formula for implied total variance proposed by Gatheral in 2004. The main ingredient is an intermediary characterization of the necessary condition for no arbitrage obtained for any model by Fukasawa in 2012 that the inverse functions of the -d1 and -d2 of the Black-Scholes formula, viewed as functions of the log-forward moneyness, should be increasing. SVI参数的自然重新缩放和对Durrleman条件的细致分析允许在参数上获得简单的范围条件。这导致在NO套利域上直接实施了最小二乘校准算法，这使我们使用用于测试的市场数据非常适合，并保证在没有蝴蝶套利的情况下产生微笑。
We fully characterize the absence of Butterfly arbitrage in the SVI formula for implied total variance proposed by Gatheral in 2004. The main ingredient is an intermediary characterization of the necessary condition for no arbitrage obtained for any model by Fukasawa in 2012 that the inverse functions of the -d1 and -d2 of the Black-Scholes formula, viewed as functions of the log-forward moneyness, should be increasing. A natural rescaling of the SVI parameters and a meticulous analysis of the Durrleman condition allow then to obtain simple range conditions on the parameters. This leads to a straightforward implementation of a least-squares calibration algorithm on the no arbitrage domain, which yields an excellent fit on the market data we used for our tests, with the guarantee to yield smiles with no Butterfly arbitrage.
