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Estimating Vasicek Market Price of Risk from Yield Data

Article Quant Q&A · Author: Ryan
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Summary

The document distinguishes estimating Vasicek model parameters from historical short-rate observations from estimating the market price of risk. Maximum likelihood estimation on historical data may estimate real-world parameters such as the long-run mean, reversion speed, and volatility, but those estimates alone do not determine risk-neutral parameters. The reply says risk-neutral values must be inferred from prices of traded interest-rate instruments.

It suggests using both a spot-rate series and a slightly longer-maturity rate to infer the market price of risk from the short-end yield-curve slope. The document points readers to an external paper for further detail, but provides no derivation, equations, or empirical demonstration. Its guidance is therefore conceptual: adding another parameter to a historical-data likelihood fit is not, by itself, a substitute for market pricing information. The method also depends on having suitable rate series or traded-instrument prices; the source does not specify data requirements, estimation steps, or how the approach performs in practice.

Key ideas

  • Historical short-rate data can estimate real-world Vasicek parameters but do not alone identify risk-neutral parameters.
  • Risk-neutral parameters are inferred from prices of traded interest-rate instruments.
  • A spot rate and a slightly longer rate can help infer market price of risk from the yield-curve slope.
  • The document gives no detailed estimation procedure or empirical evidence.

Tags

Fixed incomeStatisticsDerivatives pricing
Full text
# Vasicek Model Parameters Estimation


# Vasicek Model Parameters Estimation












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

## Answer by siou0107 (score 3)

https://quant.stackexchange.com/a/50226

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.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.