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Estimating Option Forwards and Implied Volatility from Put–Call Prices

Article Quant Q&A · Author: DomingoBrown
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Summary

The exchange addresses how to obtain the underlying input needed to analyze an options dataset when spot prices are unavailable. It suggests estimating a forward price from put and call quotes at a common maturity: identify the strike where their prices are closest, then adjust that strike using the call–put price difference and the interest rate over the maturity. That forward can be used with the Black model to calculate implied volatility across strikes.

A second reply notes that the options database may not contain underlying security prices and suggests sourcing them separately from CRSP when accessible, linking records through security identifiers. The forward estimate is an alternative when matching put and call quotes are available; the exchange does not discuss quote quality, dividends, or implementation details. It assumes the goal is implied volatility analysis and does not provide empirical validation of either data route.

Key ideas

  • Put and call prices at a shared maturity can be used to estimate a forward price.
  • The strike with the smallest call–put price difference is used as the starting point for that estimate.
  • A forward price can serve as input to the Black formula for implied volatility calculations.
  • Underlying prices may need to be sourced separately and linked to the options data.

Tags

OptionsDerivatives pricingVolatilityEquities
Full text
# IvyDB: St as the only unknown variable in the BS formula


# IvyDB: St as the only unknown variable in the BS formula












Good afternoon.

I have a dataset of options (IvyDB), with the price of the options, and all the information needed to retreive the price from the Black-Scholes formula.

All except the price of the underlying St. I just can't see how to get this info from the BS formula, as the call price,, d1 and d2 all depends on St.

Any tips ?

## Answer by Alex C (score 2)

https://quant.stackexchange.com/a/38864

There is another formula called the Black 1976 formula that is equivalent to the Black Scholes formula but uses the "forward price" $F_t$ instead of the spot price $S_t$.

If you have prices for both Puts and Calls for a given maturity you can estimate $F$ as follows.

- Examine all strikes $K_i$ and select the one where the price difference between calls and puts is as small as possible. Call this strike K.

- Compute the forward as $F=K+e^{rT}(call - put)$

Once you have the forward you can use it, together with the Black formula to find the implied volatilities (which is what I assume you are after) at each strike level.

HTH

## Answer by phdstudent (score 1)

https://quant.stackexchange.com/a/38866

There is no way that from IvDB you can get the prices of the underlying securities. If you are using IvDB I am assuming that you are using OptionMetrics.

If that is the case and if you also have access to WRDS/CRSP then you can download the quotes from CRSP. You will need to link CRSP and OptionMetrics data using Cusips.

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.