Diagnosing Zero Implied Volatility in an Index Call
Summary
The document investigates why an implied volatility calculation for a long-dated S&P 500 index call returns zero. The response checks whether the observed option price is consistent with intrinsic value under the selected interest rate. Using the supplied spot level, rate, and time to maturity, it estimates a forward price and finds that the call quote is below the resulting forward-based intrinsic value. Since a call price below that bound cannot be reconciled by a positive volatility in the assumed framework, a zero implied volatility signals inconsistent inputs or assumptions.
The answer identifies omitted dividends as a likely issue and notes that the risk-free rate alone may not be sufficient for an index option. The document also mentions using the bid-ask midpoint when a last trade is unavailable, but it does not validate that quote choice or provide a full data-cleaning procedure. Its diagnostic is specific to the supplied example; correct dividend and forward inputs are needed before interpreting an implied volatility result.
Key ideas
- A call price below its applicable intrinsic value cannot produce a valid positive implied volatility under the assumed pricing model.
- The response identifies omitted dividends as a likely source of inconsistent index option inputs.
- A risk-free rate and spot price alone may not correctly determine an index option’s forward value.
- Using a bid-ask midpoint when no last trade exists does not by itself ensure that the option data are consistent.
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Full text
# Implied Volatility Calculation
# Implied Volatility Calculation
I want to calculate the implied volatility from the option data that I took from Bloomberg (call Option written on S&P500 index with the maturity of 19-Dec-2009 and strike of 1300), but volatility comes out to be zero. Do you have any ideas how I can calculate the volatility or correct the data?
- As the risk free rate I normally use the 3 month TBill rate.
- As the Last price of the option I use the average of the Bid and Ask Prices (Bloomberg last price is not available for the most of the data points).
Thank you.
```
Date Bid Price Underlying Interest Rate Time to Maturity Ask Price Last Price
22/12/2006 272.5 1411.73999 0.055555 2.989041096 276.5 274.5
26/12/2006 278.5 1417.869995 0.055463 2.978082192 282.5 280.5
27/12/2006 285.8 1427.709961 0.055666 2.975342466 289.8 287.8
28/12/2006 285.1 1425.089966 0.05538 2.97260274 289.1 287.1
```
## Answer by kdragger (score 3)
https://quant.stackexchange.com/a/17205
First, as far as I can tell, you are not taking into account dividends. Second, If you simply take the forward price of the SPX @ $5.5\%$ which is what you are using, you get $1411 \cdot \text{exp}(0.055 \cdot 2.99) = 1663$.
Given a strike of $1300$, the call should have an intrinsic value of $1663-1300= 363$. You have a price of $272$. The price is less than the intrinsic value of the option, therefore no matter what methodology you use, $IV = 0$.
## Answer by Saurabh Bhoomkar (score 1)
https://quant.stackexchange.com/a/18830
See this resource at github , it uses different methods to calculate IV programmaticallyShown 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.