2021/05/13 by Claude Martini, Martini, Claude, Iacopo Raffaelli +1
Economics, Econometrics and Finance · #FOS: Economics and business #Financial Markets and Investment Strategies #Market Dynamics and Volatility #Mathematical Finance (q-fin.MF) #Pricing of Securities (q-fin.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2105.06390
openalex publication_date 2021/05/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Implied volatility is at the very core of modern finance, notwithstanding\nstandard option pricing models continue to derive option prices starting from\nthe joint dynamics of the underlying asset price and the spot volatility. These\nmodels often cause difficulties: no closed formulas for prices, demanding\ncalibration techniques, unclear maps between spot and implied volatility.\nInspired by the practice of using implied volatility as quoting system for\noption prices, models for the joint dynamics of the underlying asset price and\nthe implied volatility have been proposed to replace standard option pricing\nmodels. Starting from Carr and Sun (2014), we develop a framework based on the\nImplied Remaining Variance where minimal conditions for absence of arbitrage\nare identified, and smile bubbles are dealt with. The key concepts arising from\nthe new IRV framework are those of locally consistent dynamics and sandwiched\nmartingale. Within the new IRV framework, the results of Schweizer and Wissel\n(2008b) are reformulated, while those of El Amrani, Jacquier and Martini (2021)\nare independently derived.\n