We suggest a methodology for valuing corporate securities that allows the straightforward derivation of closed form solutions for complex scenarios. The tractability of the framework stems from its modularity-we provide a number of intuitive building blocks that are sufficient for valuation in typical situations. A further advantage of our approach is that it makes economic interpretation far easier than what is typically possible with other approaches, such as solving systems of partial differential equations. As examples we consider a corporate coupon bond with discrete payments, and debt subject to strategic debt service.Option Pricing, Barrier Options, Corporate Debt, Credit Risk,
We suggest a methodology for valuing corporate securities that allows the straightforward derivation of closed form solutions for complex capital structure scenarios. The tractability of the approach stems from its modularity-we provide a number of intuitive building blocks that are su¢cient for valuation in most typical situations. A further advantage of our approach is that it makes economic interpretation far easier than what is typically possible with other approaches such as solving partial di¤erential equations. As examples we consider a corporate coupon bond with discrete payments and debt subject to strategic debt service.
W hen option pricing theory was developed some 30 years ago, Black [1985] suggested its most fruitful applications would likely be to the valuation of corporate liabilities. Yet the few attempts to test structural bond pricing models with market prices have not been very successful. Instead, much of the research has shifted focus to the development of reduced-form models, designed to be more empirically tractable. Examples are Jarrow, Lando, and Turnbull [1997], Lando [1998], and Duffie and Singleton [1999].We argue that the perceived advantage of reduced-form models is more a result of the estimation procedure than of model structure. Estimating a structural model in a similar manner, we find that it compares well to previously tested reduced-form models.An important objective for structural as well as reduced-form models is to provide term structure of default probabilities for the valuation of credit-risky securities. 1 Structural models obtain default probabilities from a model of the firm's assets and liabilities, and reduced-form models specify the default process (typically, a hazard rate) directly.While both modeling approaches allow the pricing of bonds, the assets used to estimate the models are different. Structural models are usually estimated using a time series of stock prices, while reduced-form models tend to be estimated using a cross-section of bond prices. All things equal, it is likely that the cross-sec-tion of bond prices provides more information about the issuing firm's term structure of default probabilities than a single time series of its stock. This clearly speaks in favor of reduced-form models.There are two caveats. First, stocks may be more liquid than bonds and thus more informative about a firm's prospects. Second, there may be very few bonds in the cross-section to estimate a model on-in practice, one is often either forced to extend the cross-section to bonds or indexes of the same credit rating, or to include bonds from more than one time, assuming default risk has not changed. See Ronn and Nielsen [1997], Bakshi, Madan, and Zhang [2001], and Elton et al. [2001].The strengths and weaknesses of either approach are evident. Structural models are at an advantage when there are no similar bonds but instead a highly liquid stock price series is available, while reduced-form models are the only alternative when there is no traded equity, but instead there are an appropriate selection of bonds at hand. We aim to combine the advantages of structural models with those of reduced-form models.Incorporating bond price information into the estimation procedure of a structural model provides valuable incremental information. With less upside potential, bond prices are more sensitive than stock prices to financial risk. Moreover, the yield spread of a bond, which has a fixed maturity, provides information about the term structure of default prob-
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.