Agency MBS / duration / convexity

Process

Start with the mortgage position, measure its duration, offset it with a pay-fixed swap, then test the position under a rate shock. If the rally is large enough, a receiver swaption adds convexity protection back into the book.

  1. Set the MBS position and its starting duration.
  2. Set the swap hedge and the optional swaption overlay.
  3. Move the rate shock and read the resulting duration and P&L.

Definitions

Core terms used in the model.

Duration

The approximate price sensitivity of a bond to a small change in yield.

DV01

The dollar change in market value for a one basis point move in rates.

Convexity

The feature that causes duration to change as rates move. Mortgage securities exhibit negative convexity.

Pay-fixed swap

An interest rate swap used to reduce long duration exposure in a mortgage portfolio.

Receiver swaption

An option that gives the holder the right to receive fixed on a swap at a future date.

Refi wave

A rise in refinancing activity after mortgage rates decline. This shortens MBS duration.

Position setup

Specify the book, the hedge, and the rate shock.

Mortgage position

Interest rate hedge

Rate shock

Selected shock -75 bp
Show calculations

Current DV01

MBS DV01 = market value x duration / 10,000.

Net hedge

Net DV01 = MBS DV01 - swap DV01.

Duration after shock

Stressed duration is a simplified function of the rate shock.

Option overlay

Swaption DV01 is added only after the rally passes the trigger.

Expected P&L

Estimated P&L = current net DV01 x selected shock.

Results

Inspect the resulting duration and DV01 paths.

Duration after shock 0.00 yrs Selected rate move for the scenario calculation.
Swaption protection $0.00 mm / bp Incremental DV01 contributed by the option overlay.
Hedge sign Neutral Indicates whether the resulting book is long or short duration.
Target gap $0.00 mm / bp Difference between the result and a flat duration target.

Duration curve

Estimated duration of the mortgage book across rate shocks.

Starting duration Stressed duration

Net DV01 curve

Net DV01 for the swap hedge alone and for the hedge plus swaption.

Swap only Swap + option

Selected shock stack

Component contribution of the mortgage position, swap hedge, and option overlay.

Scenario ladder

Summary of duration and net DV01 across standard rate shocks.

Shock Duration Net DV01 Classification

The model is intended for instruction. It simplifies prepayments, swap carry, and option pricing.