Affine forward variance models

We introduce the class of affine forward variance (AFV) models of which both the conventional Heston model and the rough Heston model are special cases. We show that AFV models can be characterised by the affine form of their cumulant-generating function, which can be obtained as solution of a convolution Riccati equation. We further introduce the class of affine forward order flow intensity (AFI) models, which are structurally similar to AFV models, but driven by jump processes, and which include Hawkes-type models. We show that the cumulant-generating function of an AFI model satisfies a generalised convolution Riccati equation and that a high-frequency limit of AFI models converges in distribution to an AFV model.

     

Model-free hedge ratios and scale-invariant models

A price process is scale-invariant if and only if the returns distribution is independent of the price measurement scale. We show that most stochastic processes used for pricing options on financial assets have this property and that many models not previously recognised as scale-invariant are indeed so. We also prove that price hedge ratios for a wide class of contingent claims under a wide class of pricing models are model-free. In particular, previous results on model-free price hedge ratios of vanilla options based on scale-invariant models are extended to any contingent claim with homogeneous pay-off, including complex, path-dependent options. However, model-free hedge ratios only have the minimum variance property in scale-invariant stochastic volatility models when price–volatility correlation is zero. In other stochastic volatility models and in scale-invariant local volatility models, model-free hedge ratios are not minimum variance ratios and our empirical results demonstrate that they are less efficient than minimum variance hedge ratios.     

Term Premia and Interest Rate Forecasts in Affine Models

The standard class of affine models produces poor forecasts of future Treasury yields. Better forecasts are generated by assuming that yields follow random walks. The failure of these models is driven by one of their key features: Compensation for risk is a multiple of the variance of the risk. Thus risk compensation cannot vary independently of interest rate volatility. I also describe a broader class of models. These "essentially affine" models retain the tractability of standard models, but allow compensation for interest rate risk to vary independently of interest rate volatility. This additional flexibility proves useful in forecasting future yields.     

Business cycle measurement with some theory

A method to evaluate cyclical models not requiring knowledge of the DGP and the exact specification of the aggregate decision rules is proposed. We derive robust restrictions in a class of models; use some to identify structural shocks in the data and others to evaluate the class or contrast sub-models. The approach has good properties, even in small samples, and when the class of models is misspecified. The method is used to sort out the relevance of a certain friction (the presence of rule-of-thumb consumers) in a standard class of models.     

Optional projection under equivalent local martingale measures

We study optional projections of \({\mathbb{G}}\)-adapted strict local martingales on a smaller filtration \({\mathbb{F}}\) under changes of equivalent martingale measures. General results are provided as well as a detailed analysis of two specific examples given by the inverse Bessel process and a class of stochastic volatility models. This analysis contributes to clarify the absence of arbitrage opportunities of market models under restricted information.

     

A Class of Jump-Diffusion Bond Pricing Models within the HJM Framework

This paper considers a class of term structure models that is a parameterisation of the Shirakawa (1991) extension of the Heath et al. (1992) model to the case of jump-diffusions. We consider specific forward rate volatility structures that incorporate state dependent Wiener volatility functions and time dependent Poisson volatility functions. Within this framework, we discuss the Markovianisation issue, and obtain the corresponding affine term structure of interest rates. As a result we are able to obtain a broad tractable class of jump-diffusion term structure models. We relate our approach to the existing class of jump-diffusion term structure models whose starting point is a jump-diffusion process for the spot rate. In particular we obtain natural jump-diffusion versions of the Hull and White (1990, 1994) one-factor and two-factor models and the Ritchken and Sankarasubramanian (1995) model within the HJM framework. We also give some numerical simulations to gauge the effect of the jump-component on yield curves and the implications of various volatility specifications for the spot rate distribution.     

A multivariate stochastic volatility model with applications in the foreign exchange market

The main objective of this paper is to study the behavior of a daily calibration of a multivariate stochastic volatility model, namely the principal component stochastic volatility (PCSV) model, to market data of plain vanilla options on foreign exchange rates. To this end, a general setting describing a foreign exchange market is introduced. Two adequate models—PCSV and a simpler multivariate Heston model—are adjusted to suit the foreign exchange setting. For both models, characteristic functions are found which allow for an almost instantaneous calculation of option prices using Fourier techniques. After presenting the general calibration procedure, both the multivariate Heston and the PCSV models are calibrated to a time series of option data on three exchange rates—USD-SEK, EUR-SEK, and EUR-USD—spanning more than 11 years. Finally, the benefits of the PCSV model which we find to be superior to the multivariate extension of the Heston model in replicating the dynamics of these options are highlighted.     

An evaluation of volatility forecasting techniques

The existing literature contains conflicting evidence regarding the relative quality of stock market volatility forecasts. Evidence can be found supporting the superiority of relatively complex models (including ARCH class models), while there is also evidence supporting the superiority of more simple alternatives. These inconsistencies are of particular concern because of the use of, and reliance on, volatility forecasts in key economic decision-making and analysis, and in asset/option pricing. This paper employs daily Australian data to examine this issue. The results suggest that the ARCH class of models and a simple regression model provide superior forecasts of volatility. However, the various model rankings are shown to be sensitive to the error statistic used to assess the accuracy of the forecasts. Nevertheless, a clear message is that volatility forecasting is a notoriously difficult task.     

Polynomial processes and their applications to mathematical finance

We introduce a class of Markov processes, called m-polynomial, for which the calculation of (mixed) moments up to order m only requires the computation of matrix exponentials. This class contains affine processes, processes with quadratic diffusion coefficients, as well as Lévy-driven SDEs with affine vector fields. Thus, many popular models such as exponential Lévy models or affine models are covered by this setting. The applications range from statistical GMM estimation procedures to new techniques for option pricing and hedging. For instance, the efficient and easy computation of moments can be used for variance reduction techniques in Monte Carlo methods.     

Irish credit unions: Differential regulation based on business model complexity

This study examines the business model complexity of Irish credit unions using a latent class approach to measure structural performance over the period 2002 to 2013. The latent class approach allows the endogenous identification of a multi-class framework for business models based on credit union specific characteristics. The analysis finds a three class system to be appropriate with the multi-class model dependent on three financial viability characteristics. This finding is consistent with the deliberations of the Irish Commission on Credit Unions (2012) which identified complexity and diversity in the business models of Irish credit unions and recommended that such complexity and diversity could not be accommodated within a one size fits all regulatory framework. The analysis also highlights that two of the classes are subject to diseconomies of scale. This may suggest credit unions would benefit from a reduction in scale or perhaps that there is an imbalance in the present change process. Finally, relative performance differences are identified for each class in terms of technical efficiency. This suggests that there is an opportunity for credit unions to improve their performance by using within-class best practice or alternatively by switching to another class.     

Nonparametric identification and estimation of random coefficients in multinomial choice models

We show how to nonparametrically identify the distribution of unobservables, such as random coefficients, that characterizes the heterogeneity among consumers in multinomial choice models. We provide general identification conditions for a class of nonlinear models and then verify these conditions using the primitives of the multinomial choice model. We require that the distribution of unobservables lie in the class of all distributions with finite support, which under our most general assumptions, resembles a product space where some of the product members are function spaces. We show how identification leads to the consistency of a nonparametric estimator.     

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.     

Bond Immunization for Affine Term Structures

This paper generalizes a number of important immunization theorems. We show that the Fisher and Weil immunization, Bierwag and Khang minimax, Redington multiple liability, and Bierwag, Kaufman, and Toevs coverage theorems can be generalized to the class of affine term structures. This class of term structures contains many models that are commonly used in the finance literature.     

Generalized Pareto processes and fund liquidity risk

Motivated by the modelling of liquidity risk in fund management in a dynamic setting, we propose and investigate a class of time series models with generalized Pareto marginals: the autoregressive generalized Pareto process (ARGP), a modified ARGP and a thresholded ARGP. These models are able to capture key data features apparent in fund liquidity data and reflect the underlying phenomena via easily interpreted, low-dimensional model parameters. We establish stationarity and ergodicity, provide a link to the class of shot-noise processes, and determine the associated interarrival distributions for exceedances. Moreover, we provide estimators for all relevant model parameters and establish consistency and asymptotic normality for all estimators (except the threshold parameter, which is to be estimated in advance). Finally, we illustrate our approach using real-world fund redemption data, and we discuss the goodness-of-fit of the estimated models.     

Pricing Surrender Risk in Ratchet Equity-Index Annuities under Regime-Switching Lévy Processes

This article presents a numerical method of pricing the surrender risk in Ratchet equity-index annuities (EIAs). We assume that log-returns of the underlying fund belong to a class of regime-switching models where the parameters are allowed to change randomly according to a hidden Markov chain. The defining feature of these models is the fact that in each regime the characteristic function of log-returns is assumed to have an analytical form. The presented method provides an unified pricing framework within this class and includes the recently developed COS method as a particular case. This aspect of the method is particularly useful when pricing Ratchet options embedded in EIAs, for which the COS method exhibits a low rate of convergence. Our numerical results confirm that for models considered in this article the proposed approach improves convergence of the COS method without increasing the computational burden.     

Are interest rate options important for the assessment of interest rate risk?

Fixed income options contain substantial information on the price of interest rate volatility risk. In this paper, we ask if those options will also provide information related to other moments of the objective distribution of interest rates. Based on dynamic term structure models within the class of affine models, we find that interest rate options are useful for the identification of interest rate quantiles. Two three-factor models are adopted and their adequacy to estimate Value at Risk of zero-coupon bonds is tested. We find significant difference on the quantitative assessment of risk when options are (or not) included in the estimation process of each of these dynamic models. Statistical backtests indicate that bond estimated risk is clearly more adequate when options are adopted, although not yet completely satisfactory.     

A transform approach to compute prices and Greeks of barrier options driven by a class of Lévy processes

In this paper we propose a transform method to compute the prices and Greeks of barrier options driven by a class of Lévy processes. We derive analytical expressions for the Laplace transforms in time of the prices and sensitivities of single barrier options in an exponential Lévy model with hyper-exponential jumps. Inversion of these single Laplace transforms yields rapid, accurate results. These results are employed to construct an approximation of the prices and sensitivities of barrier options in exponential generalized hyper-exponential Lévy models. The latter class includes many of the Lévy models employed in quantitative finance such as the variance gamma (VG), KoBoL, generalized hyperbolic, and the normal inverse Gaussian (NIG) models. Convergence of the approximating prices and sensitivities is proved. To provide a numerical illustration, this transform approach is compared with Monte Carlo simulation in cases where the driving process is a VG and a NIG Lévy process. Parameters are calibrated to Stoxx50E call options.     

Instability of sunspot equilibria in real business cycle models under adaptive learning

We provide conditions under which a general, reduced-form class of real business cycle (RBC) models has rational expectations equilibria that are both indeterminate and stable under adaptive learning. Indeterminacy of equilibrium allows for the possibility that non-fundamental “sunspot” variable realizations can be used to drive the model, and several researchers have offered calibrated structural models where sunspot shocks play such a role. However, we show that the structural restrictions researchers have adopted lead to reduced-form systems that are always unstable under adaptive learning dynamics, thus calling into question the plausibility of these sunspot-driven RBC models.     

Asset allocation using flexible dynamic correlation models with regime switching

The asset allocation decision is often considered as a trade-off between maximizing the expected return of a portfolio and minimizing the portfolio risk. The riskiness is evaluated in terms of variance of the portfolio return, so that it is fundamental to consider correctly the variance of its components and their correlations. The evidence for the heteroskedastic behaviour of the returns and the time-varying relationships among the portfolio components have recently shifted attention to the multivariate GARCH models with time varying correlation. In this work we insert a particular Markov Switching dynamics in some Dynamic Correlation models to consider the abrupt changes in correlations affecting the assets in different ways. This class of models is very general and provides several specifications, constraining some coefficients. The models are applied to solve a sectorial asset allocation problem and are compared with alternative models.