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How do you calibrate a SABR model using R/Python/Matlab?

Using the data example from: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2725485

1) How does one calibrate the SABR model?

2) How to output and interpret alpha, beta, and rho?

3) How does one interpret the results output?

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1) The paper Explicit SABR Calibration Through Simple Expansions explains how to calibrate the SABR model in practice.

2) The role of alpha, beta and rho is well explained in the original SABR paper Managing Smile Risk. Beta is most often chosen in advance, to represent a specific dynamic. Although one can find references where people calibrate it to option prices, it is in general not a good practice. One reason is that in terms of implied volatility shape, rho and beta have a very similar role. The calibration of both parameters to vanilla option prices leads to an unstable fit. Another reason is that beta controls the backbone dynamic: how the smile moves with the spot price, which is not visible directly from option prices at time t.

3) What do you mean by results output? The output is typically a Black implied volatility, which you use in the Black formula to obtain the price of a European option/swaption.

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  • $\begingroup$ Why is it not a good practice to calibrate beta to option prices? $\endgroup$ – Bob Jansen Jan 8 at 18:30
  • $\begingroup$ 3) As per the output page in the paper, should this be visualised to see the volatility smile? P.s. thank you very much for your help. $\endgroup$ – clairegooner Jan 9 at 14:11
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    $\begingroup$ @BobJansen One reason is that in terms of implied volatility shape, rho and beta have a very similar role. The calibration of both parameters to vanilla option prices leads to an unstable fit. Another reason is that beta controls the backbone dynamic: how the smile moves with the spot price, which is not visible directly from option prices at time t. $\endgroup$ – jherek Jan 9 at 15:24
  • $\begingroup$ @jherek great addition, could you add it to the answer? $\endgroup$ – Bob Jansen Jan 9 at 17:13

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