Can someone expand upon exactly what the market price of risk (q) is. In the context of a single factor interest rate model, I think of it as:q = (mu - r)/sigma^2 i.e. the excess rate of return per unit risk. But I am confused by the some of the literature I am reading. It suggests that q is determined by an investor or is ignored (in the discount bond valuation PDE:dP/dt + (f+gq)dp/dr + 1/2gg(d^2p/dr^2) - rp = 0it then takes about q being derived endogenously in the single factor model (say the Vasicek model). Could someone enlighten me and/or give me an intuitive and practical explanantion for the market price of risk. Many thanks

According to standard utility theory, each investor will have a personal price for risk derived from a utility function. There will be some market-clearing price for risk and each investor will adjust their personal risk until their marginal cost equals the market price.In the equity and commodity markets this is pretty clear, at least in theory. Everyone knows what risk is. But the other markets, including interest rates, are zero-sum. A retired person living off a bond portfolio might regard long-term bonds as safe, and need a premium to invest in shorter-term bonds. A younger investor might regard a long-term bond as having more price risk than a short-term bond, and require a premium to invest long-term. Borrowers fall into the same two groups.In any event, the market will never compensate standard deviation risk, only risk that cannot be eliminated through diversification or hedging.

As far as I know, Peter Carr had a nice discussion on that.