发表机构
NYU; Baruch College, CUNY（纽约大学; 巴鲁克学院，纽约市立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
基于森林展开和Bergomi-Guyon微笑展开，提出用少量魔法执行价处的隐含总方差对幂收益合约（含方差与伽马合约）进行固定点近似定价，证明各阶存在性，数值验证在Heston和粗糙Bergomi模型下精度良好，并指出波动率合约的微笑无法确定前导修正。
AI 中文摘要
基于Alòs、Gatheral和Radoičić的森林展开以及Bourgey和Gatheral（2026）推导的显式Bergomi-Guyon微笑展开，我们推导了以少量魔法执行价处的隐含总方差表示的固定点近似，用于幂收益合约的公允价值；方差和伽马合约作为该单参数族的端点出现，由单一组公式定价。我们证明了此类近似在每一阶都存在：在n阶，2⌈n/2⌉+1个魔法执行价即足够。在Heston和粗糙Bergomi模型下的数值测试表明，即使对于强偏斜微笑，该方法也具有良好精度，且该方法可直接应用于插值市场微笑，无需执行价反演。对于波动率合约，我们表明到期日T的微笑并不能确定对Rolloos-Arslan近似的前导修正。
英文摘要
Building on the forest expansion of Alòs, Gatheral and Radoičić and on the explicit Bergomi-Guyon smile expansion derived by Bourgey and Gatheral (2026), we derive fixed-point approximations, in terms of the implied total variance at a small number of magic strikes, for the fair values of power payoff contracts; the variance and gamma contracts arise as the endpoints of this one-parameter family, priced by a single set of formulae. We prove that such approximations exist at every order: at order $n$, $2\lceil n/2\rceil+1$ magic strikes suffice. Numerical tests under the Heston and rough Bergomi models demonstrate good accuracy even for strongly skewed smiles, and the method applies directly to interpolated market smiles without strike inversion. For the volatility contract, we show that the maturity-T smile does not determine the leading correction to the Rolloos-Arslan approximation.
