粗略-斯特伦局部波动模型

IF 0.5 Q4 BUSINESS, FINANCE

International Journal of Theoretical and Applied Finance Pub Date : 2023-12-27 DOI:10.1142/s0219024923500218

ENRICO DALL’ACQUA, RICCARDO LONGONI, ANDREA PALLAVICINI

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引用次数: 0

摘要

在工业应用中，使用由半马尔马托马尔科夫波动过程驱动的随机波动模型是很常见的。然而，为了精确地拟合市场波动率，这些模型通常通过添加局部波动项来扩展。在此，我们考虑奇异 Volterra 过程的情况，并通过在其马尔可夫提升中添加局部波动项来扩展这些模型，同时保留这些模型在普通期权上隐含的风格化结果。特别是，我们将重点放在粗糙-赫斯顿模型上，分析其隐含的局部波动率函数的小时间渐近线，以便提供一个适当的外推方案用于校准。

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ROUGH-HESTON LOCAL-VOLATILITY MODEL

In industrial applications it is quite common to use stochastic-volatility models driven by semi-martingale Markov volatility processes. However, in order to fit exactly market volatilities, these models are usually extended by adding a local-volatility term. Here, we consider the case of singular Volterra processes, and we extend them by adding a local-volatility term to their Markov lift by preserving the stylized results implied by these models on plain-vanilla options. In particular, we focus on the rough-Heston model, and we analyze the small-time asymptotics of its implied local-volatility function in order to provide a proper extrapolation scheme to be used in calibration.

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来源期刊

International Journal of Theoretical and Applied Finance BUSINESS, FINANCE-

CiteScore

1.10

自引率

20.00%

发文量

期刊介绍： The shift of the financial market towards the general use of advanced mathematical methods has led to the introduction of state-of-the-art quantitative tools into the world of finance. The International Journal of Theoretical and Applied Finance (IJTAF) brings together international experts involved in the mathematical modelling of financial instruments as well as the application of these models to global financial markets. The development of complex financial products has led to new challenges to the regulatory bodies. Financial instruments that have been designed to serve the needs of the mature capitals market need to be adapted for application in the emerging markets.