Bond valuation

Different methods exist for valuing convertibles. Generally, the most accurate are those employing an embedded option approach, which views the value of each component as being interdependent on the others. Unlike a plain vanilla equity option, the act of exercising the option does not require additional payment. This is why it is not really accurate to call the conversion share price the strike or exercise price. The investor forgoes part or all expected coupon income as the price for holding this option. 

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Bond valuation with real cash flows and yields We currently illustrate the pricing of inflation-linked bonds adopting real cash flows. As noted earlier, according to Fisher s theory, the real yield is given by the following equation ... 

FIGURE 9.13 Convertible bond valuation of BNSIM 2%% 2019, on OVCV screen. (Used with permission of Bloomberg L.P. Copyrights 2014. All rights reserved.)... 

The bond valuation is given by the value of an option-free bond less than the value of the embedded put option (Equation 9.15) ... 

The most important Greek for convertible bond valuation is the delta. Delta measures the sensitivity of the option price to changes in the price of the underlying share price as follows (Equation 9.19) ... 

Brennan, M.J., Schwartz, E.S., 1977. Convertible bonds valuation and optimal strategies for call and conversion. J. Financ. 32 (5), 1699-1715. 

What is worthy then of a further investment of cash to purchase this second edition Hopefully the new chapters on asset swap spread relative value, convertible bonds, callable/putable bonds and floating-rate notes will be sufficient justification additionally we have updated the previous chapters on inflation-linked bonds and risky corporate bonds valuation. We have also included Excel spreadsheets that enable the reader to apply the analysis described in the chapters right away to bonds that he or she selects. 

The intuition for the result reveals a great deal about bond valuation. Why does the present value of the coupon payments fall by more than the present value of the maturity value rises Recall why a coupon... 

In our discussion of bond valuation to this point, we have assumed that the bonds are valued on their coupon payment dates (i.e., the next coupon payment is one year away). 

Bond Valuation from CDS Prices Bloomberg Screen VCDS... 

Bloomberg users can use screen VCDS to obtain a CDS-price implied bond valuation, which can be compared to the actual market-observed asset swap price for a bond. This can then be used as a measure of relative value. 

Vol. 582 J. Andritzky, Sovereign Default Risks Valuation Implications of Debt Crises and Bond Restructurings. 

Ibbotson R. 2006. Stocks, Bonds, Bills, and Inflation (SBBI) Valuation Edition 2006 Yearbook. New York Wiley. 

There is still a consistency problem if we want to price interest rate derivatives on zero bonds, like caplets or floorlets, and on swaps, like swaptions, at the same time within one model. The popular market models concentrate either on the valuation of caps and floors or on swaptions, respectively. Musiela and Rutkowski (2005) put it this way We conclude that lognormal market models of forward LIBORs and forward swap rates are inherently inconsistent with each other. A challenging practical question of the choice of a benchmark model for simultaneous pricing and hedging of LIBOR and swap derivatives thus arises. ... 

James, J., Webber, N., 2000. Interest Rate Modelling. Wiley, Chichester, Chapters 3-5,7-9,15-16. Jamshidian, F., 1991. Bond and option valuation in the Gaussian interest rate model. Res. Finance 9, 131-170. 

Jamshidian, F., 1996. Bond, futures and option valuation in the quadratic interest rate model. Appl. Math. Finance 3, 93-115. 

Cheyette, O., 1992. Term structure dynamics and mortgage valuation. J. Fixed Income 1 (4), 28 1. Das, S., 1997. A Direct Discrete-Time Approach to Poisson-Gaussian Bond Option Pricing in the Heath-Jarrow-Morton Model Working Paper. Harvard Business School, Boston, MA, pp. 1 14. Das, S., Foresi, S., 1996. Exact solutions for bond and option prices with systematic jump risk. Rev. Deriv. Res. 1, 1-24. 

From market observation we know that index-linked bonds can experience considerable volatility in prices, similar to conventional bonds, and therefore, there is an element of volatility in the real yield return of these bonds. Traditional economic theory states that the level of real interest rates is cmistant however, in practice they do vary over time. In addition, there are liquidity and supply and demand factors that affect the market prices of index-linked bonds. In this chapter, we present analytical techniques that can be applied to index-linked bonds, the duration and volatility of index-linked bonds and the concept of the real interest rate term structure. Moreover, we show the valuation of inflation-linked bonds with different cash flow structures and embedded options. 

The price of an inflation-linked bmid is determined as the present value of future coupon payments and principal at maturity. Like a conventional bond, the valuation depends on the cash flow structure. We can have three main cash flow structures of index-linked bonds. 

The Web site associated with this book contains an Excel spreadsheet demonstrating the valuation of inflation-linked bonds, as described in this chapter. The reader may use the spreadsheet to value such bonds using his or her own parameter inputs. 

Considering the example shown in Table A1 of a hypothetical bond with coupons and principal linked to the inflation. We assume a 5-year inflation-linked bond with a 2% annual coupon payment. The expected cash flows, coupons and principal, are discounted with a discount rate of 3%. The valuation is performed by the following steps. 

Therefore, the valuation of corporate bonds needs to consider the put option value in which the payoff at maturity is given by Equation (8.11) ... 

The credit spread is defined as the difference between the risky rate of a defaul-table bond and the risk-free rate of a default-free bond. In this case, with bonds priced at par, between coupon and risk-free rate, the pricing is performed like a valuation of a straight bond, including the default risk adjustment. The price is given by Equation (8.25) ... 

In this chapter we present a discussion on convertible bonds, which have become popular hybrid financial instruments. Convertible bonds are financial instmments that give the bondholders the right, without imposing an obligation, to convert the bond into underlying security, usually common stocks, under conditions illustrate in the indenture at the time of issue. The hybrid characteristic defines the traditional valuation approach as the sum of two components the option-free bond and an embedded option (call option). The option element makes the valuation not easy, above all in pricing term sheets with specific contract clauses as the inclusion of soft calls, put options and reset features. The chapter shows practical examples of valuation in which financial advisors and investment banks adopts in different contexts. 

The proposed methodology determines the theoretical value of convertible bonds as the combination of a straight bond and an embedded call optimi. The valuation is performed in three steps ... 

Craisider a hypothetical situation. Assume that an option-free bond paying a semi-annual coupon 5.5% on par value, with a maturity of 5 years and discount rate of 8.04% (EUR 5-year swap rate of 1.04% plus credit spread of 700 basis points). Therefore, the valuation of a conventional bond is performed as follows (Figure 9.4). 

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