Introduction: Structure note products provide a way for investors to get customized exposure to various asset classes. These notes can be for instance, providing exposure to emerging markets performance or Crude oil performance etc. Like any financial product, these notes carry market risk. Additionally, they carry issuer risk that is note issuer might default. Hence it becomes imperative to include the issuer risk in the valuation of structured note products.
Issuer Credit Risk: Credit risk of an issuer can be measured in two ways. One way is to imply credit risk from Credit default swaps on the note issuer. Another way to do is to imply credit risk from corporate debt issued by the note issuer. These two methods provide a way to gauge the counterparty risk of the structured note issuer. In practice, corporate debt markets are utilized in determining the issuer credit risk. Mainly because of higher volatility of credit default swap spreads measure of credit risk is prone to wide swings and hence not suitable for incorporating credit risk in structured note valuation.
Issuer Debt: Issuer of structured notes in general issue bullet fixed rate debt in the corporate bond market. These bonds trade at a spread over benchmark treasury security. In determining the value of these corporate bonds investors use Z spread or constant spread over the treasury yield curve. This z spread is excess spread over the treasury rate that is required by the investor to buy the note issued by this issuer. Since treasury rate is considered as risk free rate, this additional spread gives a measure of the credit risk. Once we have decided which bond is used then we need to obtain traded ASK price of this bond. This is very important element. Corporate debt is a liability for the issuer and to retire this debt the issuer has to buy back the bonds and this can happen only at ASK price in the market.
Credit risk using Z-Spreads:
1) Identify the maturity of the bond based on the maturity of the structured note
2) Obtain the ASK price of the bond and the Z spread
3) Shift the Yield curve by the Z spread and discount the cash flows of the note.
Survival probability
1) Identify the maturity of the bond based on the maturity of the structured note
2) Obtain the ASK price of the bond
3) Construct survival probability curve and discount the cash flows of the note.
Modeling Survival Probabilities1.
Survival-based modeling of the Credit Risky bonds follows the assumption of Fractional Recovery of Par. Under this assumption, a bond recovers a given fraction of its face value upon default, regardless of remaining cash flows.
Present value of the Credit Risky bond can be written as sum of Cash flows when there is no default and fraction recovered when default happens.
CF = Cash flow (Principal or Interest)
I{X} = Indicator function for a default event
Zt = Credit Risk Free discount Factor
Et = Expectation under Risk neutral Measure
R = Recovery Rate
Assuming the independence of Default times, Recovery Rates and interest Rates above equation can be translated as
Q (ti) :Survival Probability
Q (t0) = 1 (Survival Probability at current Time)
ZBase : Risk Free Discount rate
Above equation derives the price of the bond based on Survival-probability based approach.
1. Defining, Estimating and Using Credit Term Structures (Lehman Brother Research)
Issuer Credit Risk: Credit risk of an issuer can be measured in two ways. One way is to imply credit risk from Credit default swaps on the note issuer. Another way to do is to imply credit risk from corporate debt issued by the note issuer. These two methods provide a way to gauge the counterparty risk of the structured note issuer. In practice, corporate debt markets are utilized in determining the issuer credit risk. Mainly because of higher volatility of credit default swap spreads measure of credit risk is prone to wide swings and hence not suitable for incorporating credit risk in structured note valuation.
Issuer Debt: Issuer of structured notes in general issue bullet fixed rate debt in the corporate bond market. These bonds trade at a spread over benchmark treasury security. In determining the value of these corporate bonds investors use Z spread or constant spread over the treasury yield curve. This z spread is excess spread over the treasury rate that is required by the investor to buy the note issued by this issuer. Since treasury rate is considered as risk free rate, this additional spread gives a measure of the credit risk. Once we have decided which bond is used then we need to obtain traded ASK price of this bond. This is very important element. Corporate debt is a liability for the issuer and to retire this debt the issuer has to buy back the bonds and this can happen only at ASK price in the market.
Credit risk using Z-Spreads:
1) Identify the maturity of the bond based on the maturity of the structured note
2) Obtain the ASK price of the bond and the Z spread
3) Shift the Yield curve by the Z spread and discount the cash flows of the note.
Survival probability
1) Identify the maturity of the bond based on the maturity of the structured note
2) Obtain the ASK price of the bond
3) Construct survival probability curve and discount the cash flows of the note.
Modeling Survival Probabilities1.
Survival-based modeling of the Credit Risky bonds follows the assumption of Fractional Recovery of Par. Under this assumption, a bond recovers a given fraction of its face value upon default, regardless of remaining cash flows.
Present value of the Credit Risky bond can be written as sum of Cash flows when there is no default and fraction recovered when default happens.
I{X} = Indicator function for a default event
Zt = Credit Risk Free discount Factor
Et = Expectation under Risk neutral Measure
R = Recovery Rate
Assuming the independence of Default times, Recovery Rates and interest Rates above equation can be translated as
Q (ti) :Survival Probability
Q (t0) = 1 (Survival Probability at current Time)
ZBase : Risk Free Discount rate
Above equation derives the price of the bond based on Survival-probability based approach.
1. Defining, Estimating and Using Credit Term Structures (Lehman Brother Research)
