Valuing the Asset Return Leg of a Convertible Bond Total Return Swap

Summary

The document asks how to value the asset return leg of a total return swap referencing a convertible bond when a convertible bond mark-to-market pricer is available. It proposes decomposing the leg into coupon cash flows, the change in bond value at swap maturity, and recovery cash flows weighted by default probabilities and discount factors. The specific uncertainty is how to project or value coupons when the convertible includes embedded call or put features that can alter its cash flows or exercise outcomes.

No answer, source, pricing derivation, or worked example is provided, so the proposed decomposition remains the question’s framework rather than a validated methodology. A convertible bond pricer may incorporate embedded optionality in the instrument’s value, but the document does not establish how to reconcile that valuation with coupon, exercise, default, and recovery events over the swap life. Readers would need to specify contract terms, event timing, credit assumptions, and the TRS payment convention before treating the components as a complete valuation.

Key ideas

• The proposed asset leg consists of coupons, bond price change, and recovery components.
• The author has a convertible bond pricer and asks how to use it for the TRS leg.
• Embedded call or put features complicate the treatment of future coupon payments.
• The document supplies no answer or evidence validating the proposed decomposition.

Tags

# Total Return Swap (TRS) on Convertible Bond


# 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: $$ V_{asset}(0) = V_{coupon}(0) + V_{price}(0) + V_{recovery}(0) $$

- The coupon value $V_{coupon}(0) = \sum_{i=1}^n C_i \cdot DF(t_i)$

- 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.

- 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?

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.