Skip to content

Interest Risk hedging 1

March 9, 2013

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

ELSE

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

summarize:

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)]

then

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]

 

Advertisements

From → Finance

Leave a Comment

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: