Bond options

Part 2 put a bond’s quoted and cash prices on one basis, and Part 4 valued a European option by backward induction on a lattice. This part combines them: the underlying of the option is a bond, and the lattice gives the bond values at expiry. The second chapter also uses the survival probability and the recovery of Part 6, because issuer default ends the option.

This part values European options whose underlying is a bond. The first chapter defines a standalone call or put on a bond, puts the strike and the bond value on one cash-price basis, and values the expiry payoffs on an input lattice. The second chapter adds issuer default. Default before exercise extinguishes the option with no rebate, the bond’s recovery stays a separate cash flow of the bond, and each backward step discounts only the survival-weighted option values.

Part 5 of 72 chapters6 numbered equations2 knowledge checks

European bond options
Define a standalone option on a bond, put its prices on one cash-price basis, and value expiry payoffs on an input lattice.
2 equations1 checkdraft
Issuer-default knockout bond options
Value a bond option that is extinguished by issuer default while keeping bond recovery separate.
4 equations1 checkdraft

The argument

A bond option's strike and bond value share one cash-price basis
The lattice gives the bond value at each expiry node
Backward induction values the expiry payoffs
Issuer default before exercise extinguishes the option
Each backward step weights the option value by survival

After this part you can

Interpret a standalone European call or put on a named bond, including exercise time, dirty-versus-clean strike basis, coupon timing, and holder rights.
Calculate a European bond option payoff at expiry and value it by backward induction on an input default-free bond-value lattice.
Interpret an issuer-default knockout bond option as a contract extinguished with zero option rebate if the bond issuer defaults before exercise, separately from any recovery on the bond.
Calculate an issuer-default knockout bond option value on an input joint rate-credit lattice by applying survival to option continuation and zero option payoff on pre-expiry default.