An empirical investigation of asset pricing models under divergent lending and borrowing rates

Asset pricing theory implies that the estimate of the zero-beta rate should fall between divergent lending and borrowing rates. This paper proposes a formal test of this restriction using the difference between the prime loan rate and the 1-month Treasury bill rate as a proxy for the difference between borrowing and lending rates. Based on simulations, this paper shows that in the ordinary least squares case, the Fama and MacBeth (J Pol Econ 81:607–636, 1973) t-statistic has high power against a general alternative, which is not true of the Shanken (Rev Financ Stud 5:1–33, 1992) and Kan et al. (J Financ doi:10.1111/jofi.12035, 2013) t-statistics. In the generalized least squares case, all three t-statistics have high power. The empirical investigation highlights that only the intertemporal capital asset pricing model reasonably prices the zero-beta portfolio. Other models, such as the Fama and French (J Financ Econ 33:3–56, 1993) model, do not assign the correct value to the zero-beta rate.     

A closed-form solution for options with ambiguity about stochastic volatility

We derive a closed-form solution for the price of a European call option in the presence of ambiguity about the stochastic process that determines the variance of the underlying asset’s return. The option pricing formula of Heston (Rev Financ Stud 6(2):327–343, 1993) is a particular case of ours, corresponding to the case in which there is no ambiguity (uncertainty is exclusively risk). In the presence of ambiguity, the variance uncertainty price becomes either a convex or a concave function of the instantaneous variance, depending on whether the variance ambiguity price is negative or positive. We find that if the variance ambiguity price is positive, the option price is decreasing in the level of ambiguity (across all moneyness levels). The opposite happens if the variance ambiguity price is negative. This option pricing model can be used to address various empirical research topics in the future.     

Asymptotic Expansion Formula of Option Price Under Multifactor Heston Model

The stochastic volatility model of Heston (Rev Financ Stud 6(2):327–343, 1993) has found difficulty in describing some of the important features of implied volatility dynamics, leading to a quest for multifactor extensions as well as the incorporation of time-dependent model parameters. In this paper, an asymptotic expansion approach to the multifactor Heston model with time-dependent parameters is developed. The results of Benhamou et al. (SIAM J Financ Math 1(1):289–325, 2010) are extended and it is shown that the extension to the multifactor model involves an extra expansion term that captures the interaction between variance factors. The expansion formula under constant parameters can be explicitly computed and the incorporation of time-dependent parameters is straightforward under the framework. As illustration, a two-factor model is calibrated to data of index options and variance swaps and it is found that it is possible to distinguish a short-term and long-term variance factor from the implied volatility surface and variance swap rates. Moreover, the two-factor model is able to reproduce the shapes of the implied volatility surface during various market scenarios.     

The price of risk and ambiguity in an intertemporal general equilibrium model of asset prices

We consider a version of the intertemporal general equilibrium model of Cox et?al. (Econometrica 53:363–384, 1985) with a single production process and two correlated state variables. It is assumed that only one of them, Y ₂, has shocks correlated with those of the economy’s output rate and, simultaneously, that the representative agent is ambiguous about its stochastic process. This implies that changes in Y ₂ should be hedged and its uncertainty priced, with this price containing risk and ambiguity components. Ambiguity impacts asset pricing through two channels: the price of uncertainty associated with the ambiguous state variable, Y ₂, and the interest rate. With ambiguity, the equilibrium price of uncertainty associated with Y ₂ and the equilibrium interest rate can increase or decrease, depending on: (i) the correlations between the shocks in Y ₂ and those in the output rate and in the other state variable; (ii) the diffusion functions of the stochastic processes for Y ₂ and for the output rate; and (iii) the gradient of the value function with respect to Y ₂. As applications of our generic setting, we deduct the model of Longstaff and Schwartz (J Financ 47:1259–1282, 1992) for interest-rate-sensitive contingent claim pricing and the variance-risk price specification in the option pricing model of Heston (Rev Financ Stud 6:327–343, 1993). Additionally, it is obtained a variance-uncertainty price specification that can be used to obtain a closed-form solution for option pricing with ambiguity about stochastic variance.     

Predicting Recurrent Financial Distresses with Autocorrelation Structure: An Empirical Analysis from an Emerging Market

The dynamic logit model (DLM) with autocorrelation structure (Liang and Zeger Biometrika 73:13–22, 1986) is proposed as a model for predicting recurrent financial distresses. This model has been applied in many examples to analyze repeated binary data due to its simplicity in computation and formulation. We illustrate the proposed model using three different panel datasets of Taiwan industrial firms. These datasets are based on the well-known predictors in Altman (J Financ 23:589–609, 1968), Campbell et al. (J Financ 62:2899–2939, 2008), and Shumway (J Bus 74:101–124, 2001). To account for the correlations among the observations from the same firm, we consider two different autocorrelation structures: exchangeable and first-order autoregressive (AR1). The prediction models including the DLM with independent structure, the DLM with exchangeable structure, and the DLM with AR1 structure are separately applied to each of these datasets. Using an expanding rolling window approach, the empirical results show that for each of the three datasets, the DLM with AR1 structure yields the most accurate firm-by-firm financial-distress probabilities in out-of-sample analysis among the three models. Thus, it is a useful alternative for studying credit losses in portfolios.     

The mixed attribute model in SFAS 133 cash flow hedge accounting: implications for market pricing

In this study, we examine the pricing of cash flow hedge adjustments reported in other comprehensive income (OCICF), under the mixed attribute model in SFAS 133 Accounting for Derivative Instruments and Hedging Activities. Our OCICF pricing investigation integrates empirical research on the derivatives use that gives rise to such mark-to-market adjustments with the accounting information pricing literature. Based on this integration, we generalize mispricing theory for the SFAS 133 mixed attribute model and predict both the direction and magnitude of OCICF pricing. Screening on U.S. multinationals with ex ante exposure to currency risk, we provide evidence of OCICF mispricing in the expected direction, consistent with the notion that SFAS 133 cash flow hedge accounting results in a mixed attribute problem (Gigler et al. in J Account Res 45:257–287, 2007). Moreover, we find that both OCICF gains and losses are inversely related to future cash flows and of the expected magnitude, consistent with our predictions based on valuation theory (for example, Ohlson in Rev Account Stud 4:145–162, 1999). Our results support the Financial Accounting Standards Board’s concern that the SFAS 133 mixed attribute model does not provide the information necessary for investors to understand the net economic effects of derivatives use (FASB in Accounting for financial instruments and revisions to the accounting for derivative instruments and hedging activities. FASB, Norwalk, 2010).     

Correction note for ��The large-maturity smile for the Heston model��

The papers (Forde and Jacquier in Finance Stoch. 15:755?C780, 2011; Forde et al. in Finance Stoch. 15:781?C784, 2011) study large-time behaviour of the price process in the Heston model. This note corrects typos in Forde and Jacquier (Finance Stoch. 15:755?C780, 2011), Forde et al. (Finance Stoch. 15:781?C784, 2011) and clarifies the proof of Forde et al. (Finance Stoch. 15:781?C784, 2011, Proposition 2.3).     

Pricing and hedging volatility smile under multifactor interest rate models

The paper extends Amin and Morton (1994), Zeto (2002), and Kuo and Paxson (2006) by considering jump-diffusion model of Das (1999) with various volatility functions in pricing and hedging Euribor options across strikes and maturities. Adding the jump element into a diffusion model helps capturing volatility smiles in the interest rate options markets, but specifying the mean-reversion volatility function improves the most. A humped volatility function with the additional jump component yields better in-sample and out-of-sample valuation, but level-dependent volatility becomes more crucial for hedging. The specification of volatility function is more crucial than merely adding jumps into any model and the effect of jumps declines as the maturity of options is longer.     

A note on the condition of no unbounded profit with bounded risk

As a corollary to Delbaen and Schachermayer’s fundamental theorem of asset pricing (Delbaen in Math. Ann. 300:463–520, 1994; Stoch. Stoch. Rep. 53:213–226, 1995; Math. Ann. 312:215–250, 1998), we prove, in a general finite-dimensional semimartingale setting, that the no unbounded profit with bounded risk (NUPBR) condition is equivalent to the existence of a strict sigma-martingale density. This generalizes the continuous-path result of Choulli and Stricker (Séminaire de Probabilités XXX, pp. 12–23, 1996) to the càdlàg case and extends the recent one-dimensional result of Kardaras (Finance and Stochastics 16:651–667, 2012) to the multidimensional case. It also refines partially the second main result of Karatzas and Kardaras (Finance Stoch. 11:447–493, 2007) concerning the existence of an equivalent supermartingale deflator. The proof uses the technique of numéraire change.     

Efficiently pricing double barrier derivatives in stochastic volatility models

Imposing a symmetry condition on returns, Carr and Lee (Math Financ 19(4):523–560, 2009) show that (double) barrier derivatives can be replicated by a portfolio of European options and can thus be priced using fast Fourier techniques (FFT). We show that prices of barrier derivatives in stochastic volatility models can alternatively be represented by rapidly converging series, putting forward an idea by Hieber and Scherer (Stat Probab Lett 82(1):165–172, 2012). This representation turns out to be faster and more accurate than FFT. Numerical examples and a toolbox of a large variety of stochastic volatility models illustrate the practical relevance of the results.     

New solvable stochastic volatility models for pricing volatility derivatives

In this paper we discuss a new approach to extend a class of solvable stochastic volatility models (SVM). Usually, classical SVM adopt a CEV process for instantaneous variance where the CEV parameter γ takes just few values: 0—the Ornstein–Uhlenbeck process, 1/2—the Heston (or square root) process, 1—GARCH, and 3/2—the 3/2 model. Some other models, e.g. with γ = 2 were discovered in Henry-Labordére (Analysis, geometry, and modeling in finance: advanced methods in option pricing. Chapman & Hall/CRC Financial Mathematics Series, London, 2009) by making connection between stochastic volatility and solvable diffusion processes in quantum mechanics. In particular, he used to build a bridge between solvable superpotentials (the Natanzon superpotentials, which allow reduction of a Schrödinger equation to a Gauss confluent hypergeometric equation) and existing SVM. Here we propose some new models with ${\gamma \in \mathbb{R}}$ and demonstrate that using Lie’s symmetries they could be priced in closed form in terms of hypergeometric functions. Thus obtained new models could be useful for pricing volatility derivatives (variance and volatility swaps, moment swaps).     

Quantitative error estimates for a least-squares Monte Carlo algorithm for American option pricing

We prove new error estimates for the Longstaff–Schwartz algorithm. We establish an $O(\log^{\frac{1}{2}}(N)N^{-\frac{1}{2}})$ convergence rate for the expected L ² sample error of this algorithm (where N is the number of Monte Carlo sample paths), whenever the approximation architecture of the algorithm is an arbitrary set of L ² functions with finite Vapnik–Chervonenkis dimension. Incorporating bounds on the approximation error as well, we then apply these results to the case of approximation schemes defined by finite-dimensional vector spaces of polynomials as well as that of certain nonlinear sets of neural networks. We obtain corresponding estimates even when the underlying and payoff processes are not necessarily almost surely bounded. These results extend and strengthen those of Egloff (Ann. Appl. Probab. 15, 1396–1432, 2005), Egloff et al. (Ann. Appl. Probab. 17, 1138–1171, 2007), Kohler et al. (Math. Finance 20, 383–410, 2010), Glasserman and Yu (Ann. Appl. Probab. 14, 2090–2119, 2004), Clément et al. (Finance Stoch. 6, 449–471, 2002) as well as others.     

Multi-firm voluntary disclosures for correlated operations

We study the no-arbitrage theory of voluntary disclosure (Dye, J Account Res 23:123–145, 1985, and Ostaszewski and Gietzmann, Rev Quant Financ Account 31: 1–27, 2008), generalized to the setting of $n$ firms, simultaneously and voluntarily, releasing at the interim-report date ‘partial’ information concerning their ‘common operating conditions’. Each of the firms has, as in the Dye model, some (known) probability of observing a signal of their end of period performance, but here this signal includes noise determined by a firm-specific precision parameter. The co-dependency of the firms results entirely from their common operating conditions. Each firm has a disclosure cutoff, which is a best response to the cutoffs employed by the remaining firms. To characterize these equilibrium cutoffs explicitly, we introduce $n$ new hypothetical firms, related to the corresponding actual firms, which are operationally independent, but are assigned refined precision parameters and amended means. This impounds all existing correlations arising from conditioning on the other potentially available sources of information. In the model the actual firms’ equilibrium cutoffs are geometric weighted averages of these hypothetical firms. We uncover two countervailing effects. Firstly, there is a bandwagon effect, whereby the presence of other firms raises each individual cutoff relative to what it would have been in the absence of other firms. Secondly, there is an estimator-quality effect, whereby individual cutoffs are lowered, unless the individual precision is above average.     

Generalized stochastic target problems for pricing and partial hedging under loss constraints��application in optimal book liquidation

We consider a singular version with state constraints of the stochastic target problems studied in Soner and Touzi (SIAM J. Control Optim. 41:404?C424, 2002; J. Eur. Math. Soc. 4:201?C236, 2002) and more recently Bouchard et al. (SIAM J. Control Optim. 48:3123?C3150, 2009), among others. This provides a general framework for the pricing of contingent claims under risk constraints. Our extended version perfectly fits the market models with proportional transaction costs and the order book liquidation issues. Our main result is a direct PDE characterization of the associated pricing function. As an example application, we discuss the valuation of VWAP-guaranteed-type book liquidation contracts, for a general class of risk functions.     

Bottleneck options

In the spirit of Kyprianou and Ott (in Acta Appl. Math., to appear, 2013) and Ott (in Ann. Appl. Probab. 23:2327–2356, 2013) we consider an option whose payoff corresponds to a capped American lookback option with floating strike and solve the associated pricing problem (an optimal stopping problem) in a financial market whose price process is modelled by an exponential spectrally negative Lévy process. Despite the simple interpretation of the cap as a moderation of the payoff, it turns out that the optimal strategy to exercise the option looks very different compared to the situation without a cap. In fact, we show that the continuation region has a feature that resembles a bottleneck and hence the name “bottleneck option”.     

Identifying the Effect of Securitization on Foreclosure and Modification Rates Using Early Payment Defaults

This paper develops and estimates an instrumental variables strategy for identifying the causal effect of securitization on the incidence of mortgage modification and foreclosure based on the early payment default analysis performed by Piskorsi et al. (J Financ Econ 97:360–397, 2010). Estimation results show that securitized mortgages are more likely to be modified and less likely to be foreclosed on by servicers. These results are consistent with the interpretation in Adelino et al. (2009) that low modification rates are not the result of contract frictions inherent in the mortgage securitization process.     

Large Deviations for the Extended Heston Model: The Large-Time Case

We study here the large-time behaviour of all continuous affine stochastic volatility models [in the sense of Keller-Ressel (Math Finan 21(1):73–98, 2011)] and deduce a closed-form formula for the large-maturity implied volatility smile. We concentrate on (rescaled) strikes around the money, which are the most common in practice, and extend the results in Forde and Jacquier (Finan Stoch 15(4):755–780, 2011) and Gatheral and Jacquier (Quant Finan 11(8):1129–1132, 2011).     

An Empirical Comparison of Asset-Pricing Models in the Shanghai A-Share Exchange Market

This paper evaluates and compares the performance of three-asset pricing models—the capital asset pricing model of Sharpe (J Finance 19:425–442, 1964), the three-factor model of Fama and French (J Financ Econ 33:3–56, 1993), and the five-factor model (Fama and French in J Financ Econ 123:1–22, 2015)—in the Shanghai A-share exchange market. Our results do not support the superiority of the five-factor model and show that the three-factor model outperforms the other models. We also verify the redundancy of the book-to-market factor and confirm the findings of Fama and French (2015).     

Discussion of “Are earnings forecasts more accurate when accompanied by cash flow forecasts?”

Call et al. (Rev Account Stud 2009, this issue) demonstrate that, relative to analysts who issue earnings but not cash flow forecasts, analysts who issue both forecasts (i) produce relatively more accurate earnings forecasts, (ii) have a better understanding of the persistence of current earnings, and (iii) are less likely to get fired. In my discussion, I highlight some general challenges facing research on analyst cash flow forecasts, demonstrate the diminishing difference in the relative accuracy over time (including its compete elimination by 2004), and examine the sensitivity of some of the evidence in Call et al. (2009) to the age of the forecast and to the presence of extreme bad-news earnings surprises.