Approaches to Modeling SPX Implied Volatility Surface Dynamics
Summary
The question asks how to model daily SPX implied volatilities across several maturities and moneyness levels, preserving their correlations and incorporating jumps linked to recurring events such as economic releases and dividends. The proposed goal is to calibrate a multivariate process that can simulate future distributions and risk measures.
One answer recommends modeling the volatility surface with a relatively parsimonious stochastic volatility model, using Heston as an example, then fitting parameters over daily or possibly weekly observations and analyzing how those parameters change over time. Another points to a review of surface modeling that covers SVI, rough fractional stochastic volatility, stochastic surface models, and research on volatility risk and premia. The discussion offers starting points rather than a calibrated model or empirical comparison. It does not specify how to encode event-dependent jumps, handle the full cross-sectional dimension, or validate simulations, so those design choices remain open.
Key ideas
- Model the implied volatility surface directly to represent the evolution of its maturities and moneyness levels.
- A parsimonious stochastic volatility model such as Heston is suggested as a manageable starting point.
- Model parameters can be fitted repeatedly and their time series analyzed.
- SVI, rough volatility, and stochastic surface models are cited as alternative modeling approaches.
- The discussion does not provide a tested solution for event-dependent jumps or high-dimensional dependence.
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# Modelling SPX implied volatilities dynamics # Modelling SPX implied volatilities dynamics I'm interested in constructing a model for the daily implied volatilities of the SPX spanning from 2006 to 2024, considering various tenors (1M, 3M, 6M, 9M, 1Y) and moneyness levels (80, 90, 95, 100, 105, 110, 120). Ideally, I aim to develop a multivariate process that captures the correlation among all implied volatilities, while also accommodating jumps dependent on time-to-event variables such as macroeconomic releases, speeches, earnings calendars, and dividend calendars. These time-to-event variables will be calculated cyclically. Any suggestions on where to begin in identifying a process that can be calibrated and enables simulation for computing future distributions and risk metrics? Thank you in advance for your insights! ## Answer by KT8 (score 2, accepted) https://quant.stackexchange.com/a/78420 I would proceed by defining a model for the dynamics of the volatility surface. Otherwise I think this task would be excesivelly complicated and intensive in computing time. I would suggest something like a Heston model for this: a stochastic volatility model can describe better the evolution of the volatility surface dynamics. Moreover, it is simple enough (does not have many parameters) and you can calibrate it easily (as compared to other models). Once you have the dynamics specified, you can try to fit the parameters of your model on that daily basis (or maybe weekly?) and see how these evolve through a time series analysis. I don't know if this answers your question. ## Answer by phdstudent (score 2) https://quant.stackexchange.com/a/78431 One good review paper on the issue is this one: Implied Volatility Surface Construction. In particular section 8 goes in very detail about 4 different modelling approaches: - Stochastic volatility inspired (SVI) - Rough fractional stochastic volatility (RFSV) - Stochastic Models of Implied Volatility Surfaces - Analyzing volatility risk and risk premium in option contracts: A new theory
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