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I'm currently trying to estimate the market price of risk (lambda) in the Vasicek Model, and am running into difficulties.

Using the Excel Solver tool and the Maximum Likelihood Estimation method for the other three parameters (mean, reversion speed, volatility) gave me good results but I'm having difficulties with the market price of risk.

Can I just use Excel Solver again (or re-do) with 4 parameters (instead of the initial 3), or is there another way to transform the real world parameters into risk-neutral parameters?

Thank you in advance

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To get "risk-neutral" parameters you must have prices of traded instruments on the interest rate, and not just historical data of (your estimate of) the spot rate, since the risk-neutral measure is inferred from market instruments.

A good paper that might help you is the following: http://www.planchet.net/EXT/ISFA/1226.nsf/d512ad5b22d73cc1c1257052003f1aed/0daceb518d4ed890c12576fe00412e59/$FILE/MPR%20Ahmad-IS27v2.pdf

It requires you to have two interest rate series: your spot rate and a slightly longer rate, in order to infer the market price of risk from the slope of the short end of the yield curve.

Hope that helps.

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  • $\begingroup$ Thank you for the response and the paper. So my historical data consists of U.S. Treasury bills from 1-month to 10-year, won't this work as a way to estimate lambda? $\endgroup$
    – Ryan
    Dec 11 '19 at 14:00
  • $\begingroup$ I would say it is "a way", but 10Y is quite far from the short end of the yield curve ^^ $\endgroup$
    – siou0107
    Dec 11 '19 at 14:06
  • $\begingroup$ But would I be able to use Solver by maximizing all four variables instead of the initial 3? As this incorporates the short rate $\endgroup$
    – Ryan
    Dec 11 '19 at 14:44

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