Reading Volatility Smiles and Heston’s Long-Horizon Fit
Summary
The document explains how a market volatility smile can be observed and offers a possible reason that the Heston stochastic volatility model may fit longer-dated options better than short-dated options. A smile is inferred from the implied volatilities of traded options across strikes or maturities: option prices map to implied volatilities, so a collection of market prices reveals the pattern. The discussion does not present a calibration procedure or empirical study; it gives a conceptual explanation in response to questions about plotted model and market volatilities.
The proposed explanation separates relatively unpredictable, abrupt moves associated with recent news from smaller fluctuations that may become more predictable over time. Since Heston assumes volatility mean reversion, that assumption may capture long-run behavior better, while near-term noise can make short-maturity fits harder. This is presented as one possible explanation, not a general result or proof. The document gives no data, parameter estimates, or conditions under which the explanation holds, so fit quality will depend on the market, options, and calibration choices.
Key ideas
- Market implied volatility can be compared across traded option strikes and maturities to reveal a smile or surface.
- Option prices and implied volatilities correspond one to one under a specified pricing framework.
- The proposed explanation is that Heston mean reversion may better represent long-run volatility behavior.
- Short-dated volatility can be harder to model because abrupt news-related moves add near-term uncertainty.
- The explanation is conceptual and is not supported by empirical evidence in the document.
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Full text
# How can we observe volatility smile from the market. Drawbacks of Heston Stochastic Volatility Model
# How can we observe volatility smile from the market. Drawbacks of Heston Stochastic Volatility Model
Here are two questions related to implied volatilities.
a) The set up here is for an European option. We can get its implied volatility smile from calibration, the question is why could we also observe 'volatility smile' in the market?
b) The second question is for the Heston stochastic volatility model. We use the Heston model to calibrate the implied volatilities of an European option for short term and long term maturities. The results shows clearly it is better fit with long maturity. Why? (Here the Heston model implied volatilities are plotted against the market implied volatilities)
The full answer is not necessarily needed here, some indications or references can also help.
## Answer by Daniel (score 2)
https://quant.stackexchange.com/a/60501
- The option price and the implied volatility is a one-to-one relationship. At one time, there are many options trading in the market, with varying strike $K$ and time to maturity. If you can try to find the relationship between volatility smiled and $K$ or $t_{maturity}$, you will find the smile.
- There is no correct answer to this, and there is one possible explanation. Stocks volatility can be decomposed into small daily fluctuations and big sudden movements. The big sudden movements usually comes from fresh news recently, which are very unpredictable. The small daily fluctuations are relatively predictable, especially accumulated in the long run. That said, it is generally much harder to predict near term volatility than long term volatility. On the other hand, heston model assumes a mean-reverting process for the volatility. In the long run, this could be good model because we do find the volatility to be mean-reverting, but in the short run, the noises are just too big.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.