I studied some bond total return swap valuation. They are very similar but differ in the handling of loss given default and recovery. I feel confused, any have no idea why and what’s the economic concept behind the formula.

(1) According to the discountingbondtrsengine.cpp of ORE( open source risk engine)

TRS=return leg + bond cash flows + recovery amount-funding amount

(2) According to the the paper, Migration plan of Risky Total Return Swap to Bond Return Swap

TRS=return leg + bond cash flows - recovery amount-funding amount

(3)According to the Chapter 7 of the book, Computational Finance using C and C#

TRS=return leg + bond cash flows - (bond notional - recovery amount) -funding amount 

Note:

• a.return leg: the gain or loss due to bond price fluctuation.
• b.bond cash flows : all cash flows of the bond during TRS contract period.
• c.recovery amount :the residual value of the bond given default.
• d.funding amount : basically Libor or Sofr to financing.

I think there should be some linkage between three formula, or there may be some practical assumption behind them.

I studied some bond total return swap valuation. They are very similar but differ in the handling of loss given default and recovery. I feel confused and have no idea why and what’s the economic concept behind the formula.

(1) According to the discountingbondtrsengine.cpp of ORE( open source risk engine)

TRS=return leg + bond cash flows + recovery amount-funding amount

(2) According to the the paper, Migration plan of Risky Total Return Swap to Bond Return Swap

TRS=return leg + bond cash flows - recovery amount-funding amount

(3)According to the Chapter 7 of the book, Computational Finance using C and C#

TRS=return leg + bond cash flows - (bond notional - recovery amount) -funding amount 

Note:

• a.return leg: the gain or loss due to bond price fluctuation.
• b.bond cash flows : all cash flows of the bond during TRS contract period.
• c.recovery amount :the residual value of the bond given default.
• d.funding amount : basically Libor or Sofr to financing.

I think there should be some linkage between three formula, or there may be some practical assumption behind them.

I studied some bond total return swap valuation. They are very similar but differ in the handling of loss given default and recovery. I feel confused, any have no idea why and what’s the economic concept behind the formula.

(1) According to the discountingbondtrsengine.cpp of ORE( open source risk engine)

TRS=return leg + bond cash flows + recovery amount-funding amount

(2) According to the the paper, Migration plan of Risky Total Return Swap to Bond Return Swap

TRS=return leg + bond cash flows - recovery amount-funding amount

(3)According to the Chapter 7 of the book, Computational Finance using C and C#

TRS=return leg + bond cash flows - (bond notional - recovery amount) -funding amount

Note:

• a.return leg: the gain or loss due to bond price fluctuation.
• b.bond cash flows : all cash flows of the bond during TRS contract period.
• c.recovery amount :the residual value of the bond given default.
• d.funding amount : basically Libor or Sofr to financing.

I think there should be some linkage between three formula, or there may be some practical assumption behind them.

I studied some bond total return swap valuation. They are very similar but differ in the handling of loss given default and recovery. I feel confused, any have no idea why and what’s the economic concept behind the formula.

(1) According to the discountingbondtrsengine.cpp of ORE( open source risk engine)

TRS=return leg + bond cash flows + recovery amount-funding amount

(2) According to the the paper, Migration plan of Risky Total Return Swap to Bond Return Swap

TRS=return leg + bond cash flows - recovery amount-funding amount

(3)According to the Chapter 7 of the book, Computational Finance using C and C#

TRS=return leg + bond cash flows - (bond notional - recovery amount) -funding amount 

Note:

• a.return leg: the gain or loss due to bond price fluctuation.
• b.bond cash flows : all cash flows of the bond during TRS contract period.
• c.recovery amount :the residual value of the bond given default.
• d.funding amount : basically Libor or Sofr to financing.

I think there should be some linkage between three formula, or there may be some practical assumption behind them.