Insurance ALM

Duration is the weighted average time until cash flows arrive. A cash flow far in the future has a longer duration than a cash flow due next year, and its present value moves more when rates move.

Classroom book: asset duration 6 years, liability duration 12 years. The liabilities wait longer for their cash than the assets do. A parallel rise in rates marks those longer liabilities down by more than the assets. The same rise also changes what cash earns when it is reinvested. If the liability profile may still change, a swap entered today would lock both sides into the remaining nets whether the hedge is still wanted or not.

The book buys a payer swaption struck at 4% and pays a classroom premium of $1.5 million. That premium is spent on both branches. If rates are 5% at the decision, the payer is used and the book can pay fixed at 4% instead of near 5%. If rates are 3%, the option expires and the book can enter a swap near 3% without owing 4%. A swap entered today would have obligated the book in both of those outcomes.

• Rate level is a parallel move in the curve. Curve shape is a twist, such as the 10-year point rising while the 2-year point does not.
• Volatility risk is the swaption’s own vega: the premium changes when the width assumed for the forward swap rate changes, even if the swap rate itself is unchanged.
• Model risk is the chance that the price of that optionality used the wrong smile, the wrong exercise rule, or the wrong curve.
• Basis is the gap between the hedge index and the liability’s index, such as SOFR on the swap and a different credit rate on the liability.
• Liquidity is whether the swaption can be entered or closed at a tight price when the book needs to.
• Counterparty exposure is what the book is owed if the other side of this OTC contract fails before the expiry.
• Exercise timing, on a Bermudan, is the chance of exercising on a date when waiting was worth more, or of waiting past the date when exercise was worth more.