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I would like to calculate YTM for every top of the book update on the 10-year note traded on Brokertec. There is no closed form solution so have to use a root finding method like Newton-Rhapson. It will obviously need to be fast. Is NR method the fastest? Are there any other better methods?

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    $\begingroup$ (1) Since you are continuously updating YTM, a good trick is to use the last value as the starting point for the next iteration. (2) NR should be fine. For the absolutely fastest speed you might use table lookup (into a table prepared at the beginning of the day). $\endgroup$ – Alex C Aug 30 '19 at 18:28
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In my old pricing library I used NR to calculate YTM. That was the fastest that I could find.

But, "Alex C" is correct, you can pre-cache. Remember, BT quotes in 64's, so you can easily build up a cacheahead of time. You don't need to worry about non-standard prices.

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Brent https://en.wikipedia.org/wiki/Brent's_method may converge a little faster than NR for price-yield.

Before electronic computers, a "yield book" was a massive paper book where one could find nearest dirty price, days to maturity, and coupon, and then interpolate. Some caching might help you if you keep varying only the price, and look at the same bonds and settlement date.

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