# Swaption pricing: Linear terminal swap rate method

Congratulations on v1.0
I read the analytic coverage pdf in Jim’s announcement. It mentioned linear terminal swap rate method in swaption pricing. I am familiar with the use of terminal swap rate approach in CMS pricing. When you are using in direct swaption pricing is it to handle cash settled swaptions? are there any more details other than reading the code?

Gary,

Yes you are right, we have implemented a pricing of cash-settled swaptions using a linear Terminal Swap Rate method. We are added technical documentation for OG Analytics as we speak.

The method was implemented for an analysis of different pricing approaches to cash-settled swaptions. In particular it was used for the presentation “Cash-settled swaptions: How wrong are we?” at the 7th Fixed Income Conference. The above presentation has just been added (docs.opengamma.com -> Analytics -> Presentations and click on the attachment symbol next to “Presentations”).

I will be adding more details in the “Swaptions” document in the “Quantitative Papers and Working Notes” section (to be pushed in the docs very soon).

ok, got it.
Thanks

The OG Analytics technical documents (swaptions, CMS, bond futures, forex options, smile extrapolation and many more) have now been uploaded.

To answer more specifically to your question on Linear TSR model for cash-settled swaptions, it is described in the section 5.2 of the Swaption Pricing document. The formulas are taken from the chapter 16 of Andersen and Piterbarg book (with adaptations for the multi-curves framework).

hi OpenGamma,
I tried to implement the TSR method for cash-settled swaption using the formula in the OpenGamma research paper “SWAPTION PRICING”. I have several questions since my Pv value seemingly doesn’t make sense.

1. can I fit a flat curve with rate S0 (swap rate at 0) and use this curve to construct the the cash-settled annunity?
I don’t use the formula G(S) = 1/S (1- 1/(1+1/m*s)^n.

2. Do we expect the physical-settled swaption pv has big different with cash-settled swaption if other conditions are the same?

3. The foumula in the paper A0(k(K)*Swpt(S0, K) + integral part). Seems like this formula implies that the cash-settled pv value is larger than physical-settled pv because sometimes A0 is big. Is that right?

Thanks for any information.
George