Interest Risk hedging 1
commercial bank usually has a positive duration gap
when interest go up, due to -Δ*ΔR, asset value go down, to hedge we need to short bond future
when interest go down, asset value go up, we might want to long bond future.
insurance company tend to has a negative duration gap
IF interest go up
asset value go up, long bond future
asset value go down, short bond future.
But banks are not holding a real bond, it has duration albeit synthetic one
so, basis risk exist.
to minimize the basis risk, we need to measure the sensitivity of change in the underlying bond and change in bank equity exposure.
this sensitivity can be termed as br
, same as Beta in CAPM model( certain portfolio relative to market portfolio) , delta in option Greeks(option price relative stock price) or velocity in physics( distance relative to time), they are just one thing: beta in the OLS regression
as using market portfolio to hedge specific stock
using stock to hedge option
we are using future to hedge bank asset
change in equity value = -[(D(A) – D(L)*(L/A)]*A*[ΔR/(1+ R)]
in order to hedge, change in equity must be equal to change in future position:
above = – N*P*Δ(bond)*[ΔR/(1+ R)]
Hedging using bond futures
N = [(D(A) – D(L)*(L/A)]*A/[P*Δ(bond)*br]
N: number of future contract needed to hedge bank equity.
P: price of one bond future contract
Hedging using options
N = [(D(A) – D(L)*(L/A)]*A/[P*Δ(bond)*Δ]