I think I am a bit confused. I intend to estimate the market price of risk the short interest rate, say, under the Hull-White model. I have the following two questions.
Is it correct to state state that the (zero coupon) bond price and the (zero coupon) bond European option price are both valued in the risk-neutral measure, because they are both derivatives of the short rate? If so, the parameters calibrated from these prices would not provide the market price of risk since the latter could only be estimated in the real world measure. Is this correct?
If the answer to the above question is affirmative, how does one estimate the market price of risk (risk premium) of the short interest rate?