AIRO · prepayment optionality · short-rate tree

Prepayment option validation — Bermudan receiver swaption

A fixed-rate bullet loan with a prepayment right = plain loan minus a Bermudan receiver swaption (borrower long, bank short). The swaption is priced on a calibrated short-rate tree by backward induction, exercising when early repayment beats waiting. Figures reconcile to the workbook.

As of 31-Dec-2024

Notional 10,00,000

Maturity 2.00 yrs

dt (γ) 0.25 → 8 steps

Type Fixed bullet

Par coupon 4.1013%

Coupon k 4.1013%

σ (engine) 0.500%

Spread 0.0000%

Valuation result

Plain loan PV (prices at par)

₹10,00,000

Prepayment option (bank short)

−₹3,227.57

Loan value to bank (net)

₹9,96,772.43

Bermudan receiver swaption — exercise / wait map

S(i,j) = MAX( receiver-swap value , discounted expected continuation ). EXERCISE = borrower prepays at that node; blank = wait / not reached.

Bermudan swaption value tree S(i,j)

Validation checks

#	Check	Value	Result

At the calibrated inputs the borrower's prepayment right is worth ₹3,227.57 at the root. Because the bank is short that option, the loan is worth ₹9,96,772.43 to the bank — below par by exactly the option value. The decision map shows prepayment becoming optimal once rates have fallen enough that the borrower can refinance cheaper: the early nodes wait, and exercise switches on across the lower-rate region of the tree. This is the AIRO adjustment that a contractual-cashflow model misses.

Read the optionality methodology → · Cap/floor Black-76 dashboard →

Reproduces the workbook's tree-based Bermudan-swaption valuation of loan prepayment. Illustrative loan; the author's own working, not client data or code.