Non-linear Gaussian sovereign CDS pricing models

Prior literature indicates that quadratic models and the Black–Karasinski model are very promising for CDS pricing. This paper extends these models and the Black [J. Finance 1995, 50, 1371–1376] model for pricing sovereign CDS’s. For all 10 sovereigns in the sample quadratic models best fit CDS spreads in-sample, and a four factor quadratic model can account for the joint effects on CDS spreads of default risk, default loss risk and liquidity risk with no restriction to factors correlation. Liquidity risk appears to affect sovereign CDS spreads. However, quadratic models tend to over-fit some CDS maturities at the expense of other maturities, while the BK model is particularly immune from this tendency. The Black model seems preferable because its out-of-sample performance in the time series dimension is the best.     

Discounting earnings with stochastic discount rates

This paper presents new equity valuation formulae in closed form that extend the abnormal earnings growth (AEG) valuation of Ohlson [2005. “On Accounting-Based Valuation Formulae.” Review of Accounting Studies 10: 323–347] to the cases of time-varying or stochastic cost of capital as in Ang and Liu [2004. “How to Discount Cash Flows with Time-Varying Expected Returns.” Journal of Finance 59 (6): 2745–2783] or to cases of stochastic interest rates as in Ang and Liu [2001. “A General Affine Earnings Valuation Model.” Review of Accounting Studies 6: 397–425]. Interest rates are modelled by quadratic term structure models, which are not hindered by restrictions to factors correlation or by other shortcomings of affine term structure models in discounting long-term earnings. This is crucial since valuation can be very sensitive to the correlation between the factors driving earnings and interest rates. Positive correlation reduces price-earnings ratios according to US data. Valuation is also sensitive to the ‘volatility’ of abnormal earnings growth. The residual earnings risk-neutral valuation of Ang and Liu (2001) is adapted to quadratic term structure models.     

Valuation of the Firm's Liabilities When Equity Holders Are Also Creditors

Abstract:  This paper presents a tractable structural model whereby controlling equity holders are also among the creditors of the firm. As the firm approaches distress, equity holders can drain the assets of the firm and expropriate other creditors by repaying their credit before bankruptcy. The right of the bankruptcy court to revoke such repayment protects arm's length creditors, reduces the cost of borrowing and induces equity holders to anticipate repayment of their credit. Equity holders decide repayment neither too early nor too late, so as to reduce the risk of repayment revocation by the bankruptcy court. Similar conclusions apply to the preferential repayment of bank loans personally guaranteed by equity holders. The analysis also suggests that callable bearer bonds may be more valuable to equity holders than to other creditors.     

Quadratic term structure models in discrete time

This paper extends the results on quadratic term structure models in continuous time to the discrete time setting. The continuous time setting can be seen as a special case of the discrete time one. Discrete time quadratic models have advantages over their continuous time counterparts as well as over discrete time affine models. Recursive closed form solutions for zero coupon bonds are provided even in the presence of multiple correlated underlying factors, time-dependent parameters, regime changes and “jumps” in the underlying factors. In particular regime changes and “jumps” cannot so easily be accommodated in continuous time quadratic models. Pricing bond options requires simple integration and model estimation does not require a restrictive choice of the market price of risk.     

Gaussian models for Euro high grade government yields

This paper tests affine, quadratic and Black-type Gaussian models on Euro area triple A Government bond yields for maturities up to 30 years. Quadratic Gaussian models beat affine Gaussian models both in-sample and out-of-sample. A Black-type model best fits the shortest maturities and the extremely low yields since 2013, but worst fits the longest maturities. Even for quadratic models we can infer the latent factors from some yields observed without errors, which makes quasi-maximum likelihood (QML) estimation feasible. New specifications of quadratic models fit the longest maturities better than does the ‘classic’ specification of Ahn et al. [2002. ‘Quadratic Term Structure Models: Theory and Evidence.’ The Review of Financial Studies 15 (1): 243–288], but the opposite is true for the shortest maturities. These new specifications are more suitable to QML estimation. Overall quadratic models seem preferable to affine Gaussian models, because of superior empirical performance, and to Black-type models, because of superior tractability. This paper also proposes the vertical method of lines (MOL) to solve numerically partial differential equations (PDEs) for pricing bonds under multiple non-independent stochastic factors. ‘Splitting’ the PDE drastically reduces computations. Vertical MOL can be considerably faster and more accurate than finite difference methods.     

After‐tax Valuation of Convertible Bonds and Participation Exemption

This paper studies the after‐tax valuation of convertible bonds in the light of Europe's participation exemption (PEX) rules and International Financial Reporting Standards (IFRS). The focus is on Italy's representative case. PEX rules exempt from company taxation capital gains realized by companies selling stocks. PEX rules raise the value of convertibles as investor companies can strategically convert the bond into stock to enjoy PEX. Historical cost‐based national accounting standards imply taxation upon realization and valuable tax timing options (TTOs). ‘Fair value’ based IFRS entail mark‐to‐market taxation, which ‘kills’ TTOs, but investor companies can convert the bond early in order to enjoy PEX. Early conversion can be valuable.     

Pricing the Credit Risk of Secured Debt and Financial Leasing

Abstract:  This paper presents closed form solutions to price secured bank loans and financial leases subject to default risk. Secured debt fair credit spreads always increase in the debtor's default probability, whereas financial leasing fair credit spreads may well decrease in the lessee's default probability and even be negative. The reason is that the lessor, unlike the secured lender, can gain from the lessee's default, especially when the leasing contract envisages initial prepayments or the lessee's terminal options to either purchase the leased asset or to extend the lease maturity. This result, which critically depends on contractual and bankruptcy code provisions, can explain some of the empirical evidence and the use of financial leases as an alternative to secured bank lending to finance small, risky and relatively opaque firms.