Putable bonds

In contrast, for putable bonds, the right to exercise the option is held by the bondholder. In fact, putable bonds allow the bondholder to sell the bond back before maturity. Conversely to callable bonds, this happens when interest rates go up (risk-free rate increases, or the issuer s credit quality decreases). In fact, the bondholders may have the advantage to sell the bond and buy another one with higher coupon payments. 

Putable bonds exhibit a positive convexity, although lower than a conventional bond, above aU with rising interest rates. Figure 11.2 shows the changes of prices according to the interest rate. If the interest rates decrease, option free and putable bonds have the same convexity. If the interest rates rise, putable bonds become more valuable. 

Value of an option free bond Value of a putable bond... 

FIGURE 11.2 The prices of an option free and putable bond. 

The option-adjusted spread (OAS) is the most important measure of risk for bonds with embedded options. It is the average spread required over the yield curve in order to take into account the embedded option element. This is, therefore, the difference between the yield of a bond with embedded option and a government benchmark bond. The spread incorporates the future views of interest rates and it can be determined with an iterative procedure in which the market price obtained by the pricing model is equal to expected cash flow payments (coupons and principal). Also a Monte Carlo simulation may be implemented in order to generate an interest rate path. Note that the option-adjusted spread is influenced by the parameters implemented into the valuation model as the yield curve, but above all by the volatility level assumed. This is referred to volatility dependent. The higher the volatility, the lower the option-adjusted spread for a callable bond and the higher for a putable bond. 

The value of a putable bond is the sum of an option-free bond and an embedded put option. It is attractive for investors because it works as a floor. Thus, greater the value of the option, greater the value of the putable bond. It is given by Formula (11.4) ... 

The pricing of putable bonds is performed with the same methodology exposed before. As introduced, putable bonds give the bondholder the right to seU the bond back before maturity. This is usually done if the interest rates go up. 

To explain the pricing methodology, we suppose a putable bond with the same characteristics of the callable bond. The putable bond can be given back to the issuer with the following put schedule shown in Table 11.4. 

The pricing of the conventional bond is the same than the one exposed for callable bonds in Figure 11.9. Therefore, the option-free bond is always equal to 106.13. The main difference consists in the estimation of the embedded option (put option rather than call option) and pricing of the putable bond. Thus, we illustrate these two steps ... 

Determine the Value of an Embedded Put Option Conversely to a callable bond, the embedded option of a putable bond is a put option. Therefore, the value is estimated as the maximum between 0 and the difference between the strike price and bond s price. The strike price is defined according to the put schedule, while the bond s price is the value of the option-free bond at each node as shown in Figure 11.9. The value at maturity of a putable option if exercised is given by Formula (11.10) ... 

Also for putable bonds, there is the choice of the option holder if exercising the option or wait a further period. Therefore, Formula (11.8) and (11.9) can be used also for putable bonds. 

The Web site associated with this book contains an Excel spreadsheet demonstrating the valuation of callable and putable bonds. The reader may use the spreadsheet to undertake such valuation analysis using his or her own parameter inputs. 

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. 

Bonds with embedded call and put options comprise a relatively small percentage of the European bond market. Exhibit 1.6 shows the percentage of the market value of the Euro Corporate Index and Pan-Euro Corporate Index attributable to bullets (i.e., option-free bonds), callable and putable bonds from the late 1990s through 31 May 2003. Accordingly, our discussion of bonds with embedded options in the remainder of the book will be confined to structured products. 

Callable bonds, putable bonds, mortgage-backed securities, and asset-backed securities are examples of (1). Floating-rate securities and inflation-indexed bonds are examples of (2). Convertible bonds and exchangeable bonds are examples of (3). 

Putable bonds may be redeemed by the bondholder on the dates and at the put price specified in the indenture. Typically, the put price is par value. The advantage to the investor is that if yields rise such that the bond s value falls below the put price, the investor will exercise the put option. If the put price is par value, this means that if market yields rise above the coupon rate, the bond s value will fall below par and the investor will then exercise the put option. 

The value of a putable bond is equal to the value of an option-free bond plus the value of the put option. Thus, the difference between the value of a putable bond and the value of an otherwise comparable option-free bond is the value of the embedded put option. This can be seen in Exhibit 4.19 which shows the price/yield relationship for a putable bond (the curve a-b) and an option-free bond (the curve a-a"). 

At low yield levels (low relative to the issue s coupon rate), the price of the putable bond is basically the same as the price of the option-free bond because the value of the put option is small. As rates rise, the price of the putable bond declines, but the price decline is less than that for an option-free bond. The divergence in the price of the putable bond and an otherwise comparable option-free bond at a given yield level is the value of the put option. When yields rise to a level where the bond s price would fall below the put price, the price at these levels is the put price. 

EXHIBIT 4.19 Price/Yield Relationship for a Putable Bond and an Option-Free Bond... 

For a conventional bond, the value of the option component is zero. For a putable one, the option has a positive value. The portfolio represented by a putable bond contains a long position in a put, which, by acting as a floor on the bond s price, increases the bond s attractiveness to investors. Thus the greater the value of the put, the greater the value of the bond. This is expressed in (11.2). 

It is now possible to complete the price tree for the callable bond. Remember that the option in the case of a callable bond is held by the issuer. Its value, given by the tree in figure 11.11, must therefore be subtracted from the conventional bond price, given by the tree in figure 11.10, to obtain the callable bond value. For instance, the current price of the callable bond is 105.875 — 0.76, or 105.115. FIGURE 11.12 shows the tree that results from this process. A tree constructed in this way, which is programmable into a spreadsheet or as a front-end application, can be used to price either a callable or a putable bond. 

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