Estimating ATM Implied Volatility from Sparse Option Quotes

Summary

Implied volatility is inferred from an option’s market price, so without an options market there is no market-implied volatility to observe directly. With sparse but available quotes, the response suggests using the implied volatility of an out-of-the-money option as an input to a pricing model.

The model can then estimate the at-the-money option’s price for the desired maturity and strike. Inverting the Black–Scholes formula on that estimated price gives an implied volatility for the at-the-money option. This is a model-based estimate, not an independently observed market quote. Its reliability depends on the chosen model and on how well the available out-of-the-money prices represent the volatility surface; the brief answer provides no comparison of models or evidence about estimation accuracy.

Key ideas

• Implied volatility is derived from an option’s market price, so it cannot be directly observed when no option market exists.
• Use available out-of-the-money option prices to infer volatility inputs.
• A pricing model can use those inputs to estimate an at-the-money option price.
• Invert the Black–Scholes formula on the estimated price to obtain an at-the-money implied volatility.
• The result depends on the pricing model and sparse market inputs.

Tags

# Measuring implied volatility


# Measuring implied volatility












I'm a new in financial engeneering and trying to understand basic principles of volatility modelling. I wrote many papers and articles about different models (garch, local vol, stoch vol and ect.) and concluded that one of the main parts of that is calibration model parameters to market prices. It's understood and OK.

But I'm concerned about basic thing. Let's suggest that we haven't options market at all or have very illiquid market (1-2 OTM strikes). How can we quote let's say ATM strikes for some maturities? What are the ways of measure implied volatility in that case?

## Answer by siou0107 (score 2)

https://quant.stackexchange.com/a/49960

If there is no market, there can't be any implied volatility since the latter is derived from the market price :)

In your example, you can just extract implied volatility from the OTM option prices. Then, by choosing some pricing model you can get a price for your ATM option, from which you can get the implied volatility by inverting the Black-Scholes formula.

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