Deriscope ## The Excel Derivatives Periscope

##### Coverage

BondExt

*BondExt* is a child type of Tradable that represents an extension of Bond that allows for the notional to depend on time and/or the spot value of a specified exchange rate.

The time dependent notional may be specified through an amortization/appreciation schedule supplied as an object of type Amort

In the presence of notional time dependence, the terminal amount paid at maturity is found by multiplying the underlying bond's redemption rate with the notional as of the beginning of the last accrual period.

The exchange rate dependent notional requires the specification of a currency regarded as "foreign" and a respective constant notional amount.

The latter feature is restricted to bonds of type Ibor Rate Bond or CMS Rate Bond with a non-amortizing notional.

A fixed rate leg may still be represented through an *Ibor Rate Bond* that has *Ibor Rate Bond::Gearings* = *0*

More specifically, the domestic notional *Nᵈ(Tᵢ₋₁)* applicable at the beginning of the *iᵗʰ* coupon period *(Tᵢ₋₁,Tᵢ)* should be reset according to the spot value *s(Tᵢ₋₁)* of the fx rate *FOR/DOM* between a foreign currency *FOR* and a domestic currency *DOM* observed at time *Tᵢ₋₁*

When true, the currency *FOR* must be defined in *Reset Currency* and a respective notional amount *Nᶠ* must be given in *Reset Notional* that is regarded denominated in *FOR*

Then the coupon associated with the accrual period *(Tᵢ₋₁,Tᵢ)* will be based on an effective domestic currency notional *Nᵈ(Tᵢ₋₁)* given by:

*Nᵈ(Tᵢ₋₁) = Nᶠs(Tᵢ₋₁)*

Also any change in the effective domestic currency notional will be paid out, just like in the regular amortizing (accreting) notional case.

Concretely, at the beginning of the *iᵗʰ* coupon period *(Tᵢ₋₁,Tᵢ)*, where i > 1, the difference *Nd(Tᵢ₋₁) - Nd(ᵢ₋₂)* will be paid out as an outflow.

The redemption amount at maturity equals the product between the effective domestic currency notional at the beginning of the last period and the redemption factor of the underlying bond.

For example, assume the bond in *Bond* is denominated in JPY and carries a notional of 110M, while the foreign currency is USD with a respective foreign notional of 1M.

Then both the JPY-denominated upfront payment - if existing - and the first coupon will be based on the 110M JPY notional.

If the spot USD/JPY rate at the begining of the second coupon period turns out 112.0, then the effective notional pertaining to the second coupon will be 112.0*1M = 112M JPY.

This higher notional will affect the second coupon and will also cause a cash outflow of 112M - 110M = 2M JPY at the end of the first period.

All remaining coupons will be similarly treated, except of the end of the last coupon period where the respective cash outflow will take into account also the Key Bond::Redemption of the underlying bond.

In particular, if the latter is *R* and the effective notional at the begining of the last coupon period is *N*, the amount received at maturity will be *RN*

Note this product's pricing is carried out by the ORE library.