Using SABR Implied Volatility with Black–Scholes for Option Pricing
Summary
The document considers a workflow for pricing a European call: fit a SABR volatility smile to market implied volatilities across strikes, use the fitted model to obtain volatility for the target strike, and insert that volatility into the Black–Scholes formula. This treats SABR as a way to supply strike-specific implied volatility while retaining Black–Scholes for the final price calculation.
The response says calibration generally involves estimating alpha, rho, and nu, while beta is often fixed rather than fitted. Whether the resulting price is close to the market depends on the quality of the SABR fit. With only a few parameters, SABR may fit short-dated equity or equity-index options poorly; the answer describes it as more suitable for foreign-exchange options and interest-rate swaptions. The exchange does not provide calibration data, a fit metric, or a worked price comparison, so accuracy must be assessed for the relevant market and maturity.
Key ideas
- Fit SABR to market implied volatilities across strikes to estimate a volatility smile.
- Use the fitted SABR volatility at the target strike as the volatility input to Black–Scholes.
- The response recommends estimating alpha, rho, and nu while typically fixing beta.
- Price accuracy depends on fit quality, which may be weak for short-maturity equity options.
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# Mixing Black Scholes with SABR
# Mixing Black Scholes with SABR
I am new to the whole concept of stochastic volatility so I am experimenting with option pricing. I think the concept is really difficult to understand / grasp.
I was wondering if the following approach is way of or an appropriate strategy:
At day 0 I want to price a European Call with the underlying asset $S$ option that expires at time $T$. I observe market data for European Call options on $S$ with different strikes. Then I do the following:
- Observe market data (IV for different strikes for an option on $S$) and fit SABR to it to find estimates for $(\alpha,\beta,\rho)$
- Now that I have the SABR parameters: For a given strike ($K1)$ I comute it's volatility: $\hat{\sigma}_{K1} = \sigma_{SABR}(K1;\alpha,\beta,\rho)$
- Then I price the option with strike $K1$ with the naive Black Scholes formula and set volatility to $\hat{\sigma}_{K1}$
Is this a descent aproach for option pricing? Will my Call price with strike $K1$ be close to what is "real" fair value
## Answer by jherek (score 1)
https://quant.stackexchange.com/a/43517
In your first step, you will want to calibrate $\alpha, \rho, \nu$, and probably not $\beta$. See the related question Calibrate a SABR model?
How close your option price is from the market price will depend on the fit quality. SABR has only a few parameters and does not necessarily match well equity or equity index options of short maturities. It is more appropriate for foreign exchange options or interest rate swaptions.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.