Can we refine the notion interest rate risk. In what units it is measured. I understand that we have interest rate dynamics equation and its solution but than the interest rate risk is still undefined though we talk about hedging and its price.
I try to explain my confusion. Let us look at the paper. It explains market risk and its pricing as following.
"Unlike equities where a model for the ‘underlying’ leads to the Black−Scholes equation, fixed income has a twist. Because the spot rate is not traded it is not possible to eliminate interest-rate risk by dynamic hedging. "
/// a) In theory one can consider that spot rate is a traded asset by assign it a notional principal.
/// b) in equity derivatives we hedge option by a portion of underlings or a share of underlying we hedge by a portion of options. Whether the statement that "Because the spot rate is not traded it is not possible to eliminate interest-rate risk by dynamic hedging" implies the use of derivative contract which has the spot ir u ( r ) by its underlying.
"Contrast this with equity derivatives for which it is theoretically possible to eliminate market risk by delta hedging. If we cannot eliminate risk then we must know how to price it. "
/// In BS theory which admits a risk free portfolio the price of the market risk is a portion of the short stocks in the risk free portfolio.
"This amounts to modelling how much extra expected return is required for a ‘unit’ amount of interest-rate risk. "
/// This statement sounds a little bit indefinably. Is it possible to express it by a formula.
"Once this is specified then we use this same ‘market price of risk’ to price all fixed-income contracts in a consistent way. See Wilmott (2006) for details. We will denote this market price of interest-rate risk by λ"