# Total Return Swap (TRS) on Convertible Bond

Is there any relevant paper/source I can look at for pricing TRS on convertible bond? Specially, how should I evaluate the asset return leg? Let's say I already have an convertible bond pricer that can calcualte the m2m value of the convertible bond $$V_c(0)$$, how should I leverage this pricer to calculate the asset return leg value of the TRS?

From my understanding, there should be three parts of the asset leg: $$V_{asset}(0) = V_{coupon}(0) + V_{price}(0) + V_{recovery}(0)$$

1. The coupon value $$V_{coupon}(0) = \sum_{i=1}^n C_i \cdot DF(t_i)$$
2. The price depreciation: $$V_{price}(0) = [V_c(T_{TRS}) - V_0] \cdot DF(T_{TRS})$$ where $$V_0$$ is some pre-specified value and $$T_{TRS}$$ denotes the TRS swap maturity date.
3. The recovery value if the bond is default: $$V_{recovery}(0) = \sum_{i=1}^n [S(t_{i-1}) - S(t_i)] \cdot R(t_i) \cdot DF(t_i)$$

Where $$DF(t)$$ denotes the discount factor and $$S(t)$$ denotes the survival probability.

I understand how to price the price depreciation and the recovery part as I already have a pricer for convertible bonds, but how should I evaluate the coupon payments part while there are some optionality (i.e. callable/puttable) embedded in the convertible bond?