I have to price an american option on a daily basis and I have some questions regarding the CRR binomial tree model:

  1. Is it correct to use implied volatility as an input? Or is it better to use historical vol? If I were to use implied vol, should I calculate one vol per node or just one vol using the time-to-expiry?

  2. Is it correct to use a yield curve to price each node of the tree or should I discount all the nodes just with a single interest rate?

  3. Is there a standard number of steps to build the tree? I'd like to use one step per day, but I don't know if it is correct.

Thanks for your help!


Usually, you would use the volatility from a fitted volatility curve or surface. Those are based on implied volatilities. You can use historical volatility, but then your valuation is likely to be off because the volatility curve/surface is not constant and at historical vol.

You should use a yield curve to present value nodes. This is unlikely to make a big difference in pricing, but you should do it since it is the right thing to do.

The steps will vary with the time to expiry, volatility, etc. You want to have an adaptive number of steps that gives an answer convergent to within some tolerance. That will vary by option and maybe even in other ways. For most exchange-traded options which are most liquid one quarter out, it probably makes sense to have one step per day. Going below one step per day means you may need to consider overnight gap effects.

  • $\begingroup$ When using implied volatility, should I use only the time-to-expiry? Or should I use a different "time-to-expiry" for every single node? $\endgroup$ – DannQ Sep 10 '20 at 15:39
  • $\begingroup$ The implied volatility to use would be for the option time to expiry, not the node time to expiry. $\endgroup$ – kurtosis Sep 10 '20 at 21:37

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