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.     

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).     

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.     

Option pricing under non-normality: a comparative analysis

This paper carries out a comparative analysis of the calibration and performance of a variety of options pricing models. These include Black and Scholes (J Polit Econ 81:637–659, 1973), the Gram–Charlier (GC) approach of Backus et al. (1997), the stochastic volatility (HS) model of Heston (Rev Financ Stud 6:327–343, 1993), the closed-form GARCH process of Heston and Nandi (Rev Financ Stud 13:585–625, 2000) and a variety of Lévy processes including the Variance Gamma (VG), Normal Inverse Gaussian (NIG), and, CGMY and Kou (Manag Sci 48:1086–1101, 2002) jump-diffusion models. Unlike most studies of option pricing, we compare these models using a common point-in-time data which reflects the perspective of a new investor who wishes to choose between models using only the most minimal recent data set. For each of these models, we also examine the accuracy of delta and delta-gamma approximations to the valuation of both individual options and an illustrative option portfolio.     

Tobin meets Oates: solidarity and the optimal fiscal federal structure

We explore the implications for the optimal degree of fiscal decentralization when people’s preferences for goods and services—which classic treatments of fiscal federalism (Oates in Fiscal federalism, 1972) place in the purview of local governments—exhibit specific egalitarianism (Tobin in J. Law Econ. 13(2): 263–277, 1970), or solidarity. We find that a system in which the central government provides a common minimum level of the publicly provided good, and local governments are allowed to use their own resources to provide an even higher local level, performs better from an efficiency perspective relative to all other systems analyzed for a relevant range of preferences over solidarity.     

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.     

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).     

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.     

Portfolio allocation using multivariate variance gamma models

In this paper, we investigate empirically the effect of using higher moments in portfolio allocation when parametric and nonparametric models are used. The nonparametric model considered in this paper is the sample approach; the parametric model is constructed assuming multivariate variance gamma (MVG) joint distribution for asset returns.We consider the MVG models proposed by Madan and Seneta (1990), Semeraro (2008) and Wang (2009). We perform an out-of-sample analysis comparing the optimal portfolios obtained using the MVG models and the sample approach. Our portfolio is composed of 18 assets selected from the S&P500 Index and the dataset consists of daily returns observed from 01/04/2000 to 01/09/2011.     

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.     

Analytical bounds for Treasury bond futures prices

The pricing of delivery options, particularly timing options, in Treasury bond futures is prohibitively expensive. Recursive use of the lattice model is unavoidable for valuing such options, as Boyle in J Finance 14(1):101?C113, (1989) demonstrates. As a result, the main purpose of this study is to derive upper bounds and lower bounds for Treasury bond futures prices. This study first shows that the popular preference-free, closed form cost of carry model is an upper bound for the Treasury bond futures price. Then, the next step is to derive analytical lower bounds for the futures price under one and two-factor Cox-Ingersoll-Ross models of the term structure. The bound under the two-factor Cox-Ingersoll-Ross model is then tested empirically using weekly futures prices from January 1987 to December 2000.     

A comparative study of two models SV with MCMC algorithm

This paper examines two asymmetric stochastic volatility models used to describe the volatility dependencies found in most financial returns. The first is the autoregressive stochastic volatility model with Student??s t-distribution (ARSV-t), and the second is the basic SVOL of Jacquier et al. (J Bus Econ Stat 14:429?C434, 1994). In order to estimate these models, our analysis is based on the Markov Chain Monte-Carlo (MCMC) method. Therefore, the technique used is a Metropolishastings (Hastings in Biometrika 57:97?C109, 1970), and the Gibbs sampler (Casella and George in The Am Stat 46:167?C174, 1992; Gelfand and smith in J Am Stat Assoc 85:398?C409, 1990; Gilks and Wild in 41:337?C348, 1992). The empirical results concerned on the Standard and Poor??s 500 composite Index (S&P), CAC40, Nasdaq, Nikkei and DowJones stock price indexes reveal that the ARSV-t model provides a better performance than the SVOL model on the MSE and the maximum Likelihood function.     

Duality and convergence for binomial markets with friction

We prove limit theorems for the super-replication cost of European options in a binomial model with friction. Examples covered are markets with proportional transaction costs and illiquid markets. A dual representation for the super-replication cost in these models is obtained and used to prove the limit theorems. In particular, the existence of a liquidity premium for the continuous-time limit of the model proposed in Çetin et al. (Finance Stoch. 8:311–341, 2004) is proved. Hence, this paper extends the previous convergence result of Gökay and Soner (Math Finance 22:250–276, 2012) to the general non-Markovian case. Moreover, the special case of small transaction costs yields, in the continuous limit, the G-expectation of Peng as earlier proved by Kusuoka (Ann. Appl. Probab. 5:198–221, 1995).     

Semi-Static Hedging Based on a Generalized Reflection Principle on a Multi Dimensional Brownian Motion

On a multi-assets Black-Scholes economy, we introduce a class of barrier options, where the knock-out boundary is a cone. In this model we apply a generalized reflection principle in a context of the finite reflection group acting on a Euclidean space to give a valuation formula and the semi-static hedge. The result is a multi-dimensional generalization of the put-call symmetry by Bowie and Carr (Risk (7):45–49, 1994), Carr and Chou (Risk 10(9):139–145, 1997), etc. The important implication of our result is that with a given volatility matrix structure of the multi-assets, one can design a multi-barrier option and a system of plain options, with the latter the former is statically hedged.     

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.     

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.     

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).     

A fractional cointegration approach to testing the Ohlson accounting based valuation model

We examine the long-run relationship between market value, book value, and residual income in the Ohlson (Contemp Acc Res 11(2):661–687, 1995) model. In particular, we test if market value is cointegrated with book value and residual income in light of their non-stationary behaviors. We find that cointegration applies to only 51 % of the sample firms, casting doubt that book value and residual income alone are adequate in tracking variations in market value, yet we find that market value is fractional cointegrated with book value and residual income for 89 % of the sample firms. This implies that the long-run relationship follows a slow but mean-reverting process. Our results therefore support the Ohlson model.     

On NIMBY and commuting

The paper highlights that the race-to-top result shown by Wellisch (J. Urban Econ. 37:290–310, 1995) and Kunce and Shogren (J. Environ. Econ. Manage. 50:212–224, 2005a) may be exacerbated by inter-jurisdictional commuting, leading to increased NIMBY behavior (Not-In-My-Back-Yard) among metropolitan jurisdictions. Local governments try to push polluting economic activities to the neighboring jurisdictions, while commuting guarantees their residents’ labor income. Commuting generates a leakage of the local production benefits of pollution as non-resident commuters take the wages to their home jurisdictions. Jurisdictions may thus face a prisoners’ dilemma, in which they all push for pollution levels that are too low (race-to-the-top). Fiercer competition in the common labor market due to a larger number of jurisdictions intensifies this race-to-the-top in environmental regulation; whereas transboundary pollution, local ownership of firms, pollution taxes, and payroll taxes reduce the incentive for overly restrictive pollution policies.     

Forecasting Long-Term Interest Rates with a General-Equilibrium Model of the Euro Area: What Role for Liquidity Services of Bonds?

This paper studies the forecasting performance of a general equilibrium model of bond yields where government bonds provide liquidity services and are, as such, an integral part of the monetary transmission mechanism. The model is estimated with Bayesian methods on Euro area data. I compare the out-of-sample predictive performance of the model against a variety of competing specifications, including that of De Graeve et al. (J Monet Econ 56(4):545–559, 2009). Forecast accuracy is evaluated through both univariate and multivariate measures. I also control the statistical significance of the forecast differences using the tests of Diebold and Mariano (J Bus Econ Stat 13(3):253–263, 1995), Hansen (J Bus Econ Stat 23:365–380, 2005) and White (Econometrica 68(5):1097–1126, 1980). The results indicate that accounting for the liquidity services of bonds contributes to generate superior out-of-sample forecasts for both real variables, such as output, and inflation, and for bond yields.