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This paper introduces stochastic covariance models in Hilbert spaces with stationary affine instantaneous covariance processes. We explore the applications of these models in the context of forward curve dynamics within fixed-income and commodity markets. The affine instantaneous covariance process is defined on positive self-adjoint Hilbert–Schmidt operators, and we prove the existence of a unique limit distribution for subcritical affine processes, provide convergence rates of the transition kernels in the Wasserstein distance of order p ∈ [ 1 , 2 ] , and give explicit formulas for the first two moments of the limit distribution. Our results allow us to introduce affine stochastic covariance models in the stationary covariance regime and to investigate the behaviour of the implied forward volatility for large forward dates in commodity forward markets. [ABSTRACT FROM AUTHOR]

In this paper, we consider one-dimensional generalized affine processes under the paradigm of Knightian uncertainty (the so-called nonlinear generalized affine models). This extends and generalizes previous results in Fadina et al. (2019) and Lütkebohmert et al. (2022). In particular, we study the case when the payoff is allowed to depend on the path, like it is the case for barrier options or Asian options. To this end, we develop the path-dependent setting for the value function relying on functional Itô calculus. We establish a dynamic programming principle which then leads to a functional nonlinear Kolmogorov equation describing the evolution of the value function. While for Asian options, the valuation can be traced back to PDE methods, this is no longer possible for more complicated payoffs like barrier options. To handle such payoffs in an efficient manner, we approximate the functional derivatives with deep neural networks and show that the numerical valuation under parameter uncertainty is highly tractable. Finally, we consider the application to structural modelling of credit and counterparty risk, where both parameter uncertainty and path-dependence are crucial and the approach proposed here opens the door to efficient numerical methods in this field. [ABSTRACT FROM AUTHOR]

Overnight rates, such as the Secured Overnight Financing Rate (SOFR) in the United States, are central to the current reform of interest rate benchmarks. A striking feature of overnight rates is the presence of jumps and spikes occurring at predetermined dates due to monetary policy interventions and liquidity constraints. This corresponds to stochastic discontinuities (i.e., discontinuities occurring at ex ante known points in time) in their dynamics. In this work, we propose a term structure modeling framework based on overnight rates and characterize absence of arbitrage in a generalized Heath–Jarrow–Morton (HJM) setting. We extend the classical short‐rate approach to accommodate stochastic discontinuities, developing a tractable setup driven by affine semimartingales. In this context, we show that simple specifications allow to capture stylized facts of the jump behavior of overnight rates. In a Gaussian setting, we provide explicit valuation formulas for bonds and caplets. Furthermore, we investigate hedging in the sense of local risk‐minimization when the underlying term structures feature stochastic discontinuities. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a multi-curve model under the historical probability based upon multiplicative relative spreads, inspired by the HJM and affine factor approaches, which implies positive and ordered spreads. In particular, we focus upon δi-XIBOR relative (instantaneous) forward rates and appropriate XIBOR HJM drift constraints, and we describe the dynamics of the different forward rates and spreads under different measure changes (including forward measures).We introduce an explicit model satisfying both the XIBOR HJM drift constraints as well as the property of positive and ordered spreads. We demonstrate the flexibility of this model for derivative pricing by focusing upon the price of a caplet and of options with a payoff based upon XIBOR forward prices with different tenors. We perform on one hand a calibration of the model based upon cap prices. On the other hand, we do an estimation of a spread curve in our proposed model under the historical probability by using a Kalman filter approach. Numerical results are included, and they confirm that the model performs very well. [ABSTRACT FROM AUTHOR]

This paper studies the transition density and exponential ergodicity for affine processes on the canonical state space R≥0m×Rn$\mathbb {R}_{\ge 0}^{m}\times \mathbb {R}^{n}$. Under a Hörmander‐type condition for diffusion components as well as a boundary nonattainment condition, we derive the existence and regularity of the transition densities and then prove the strong Feller property of the associated semigroup. Moreover, we also show that, under an additional subcriticality condition on the drift, the corresponding affine process is exponentially ergodic in the total variation distance. [ABSTRACT FROM AUTHOR]

We study Markov-modulated affine processes (abbreviated MMAPs), a class of Markov processes that are created from affine processes by allowing some of their coefficients to be a function of an exogenous Markov process X. MMAPs largely preserve the tractability of standard affine processes, as their characteristic function has a computationally convenient functional form. Our setup is a substantial generalization of earlier work, since we consider the case where the generator of X is an unbounded operator. We prove existence of MMAPs via a martingale problem approach, we derive the formula for their characteristic function and we study various mathematical properties. [ABSTRACT FROM AUTHOR]

We study pricing and hedging under parameter uncertainty for a class of Markov processes which we call generalized affine processes and which includes the Black–Scholes model as well as the constant elasticity of variance (CEV) model as special cases. Based on a general dynamic programming principle, we are able to link the associated nonlinear expectation to a variational form of the Kolmogorov equation which opens the door for fast numerical pricing in the robust framework. The main novelty of the paper is that we propose a deep hedging approach which efficiently solves the hedging problem under parameter uncertainty. We numerically evaluate this method on simulated and real data and show that the robust deep hedging outperforms existing hedging approaches in highly volatile periods. [ABSTRACT FROM AUTHOR]

The price V of a contingent claim in finance, insurance and economics is defined as an expectation of a stochastic expression. If the underlying uncertainty is modeled as a strong Markov process X, the Feynman–Kac theorem suggests that V is the unique solution of a boundary problem for a parabolic equation. In the case of PDO with constant symbols, simple probabilistic tools explained in this paper can be used to explicitly calculate expectations under very weak conditions on the process and study the regularity of the solution. Assuming that the Feynman–Kac theorem holds, and a more general boundary problem can be localized, the local results can be used to study the existence and regularity of solutions, and derive efficient numerical methods. In the paper, difficulties for the realization of this program are analyzed, several outstanding problems are listed, and several closely efficient methods are outlined. [ABSTRACT FROM AUTHOR]

We propose an affine term structure model that allows for tenor-dependence of yield curves and thus for different risk categories in interbank rates, an important feature of post-crisis interest rate markets. The model has a Nelson–Siegel factor loading structure and thus economically well interpretable parameters. We show that the model is tractable in terms of estimation and provides good in-sample fit and out-of-sample forecasting performance. The proposed model is arbitrage-free across maturities and tenors, and thus perfectly suited for risk management and pricing purposes. We apply our framework to the pricing of caplets in order to illustrate its practical applicability and its suitability for stress testing. [ABSTRACT FROM AUTHOR]

This article provides new developments in characterizing the class of regime-switching exponential affine interest rate processes in the context of pricing a zero-coupon bond. A finite-state Markov chain in continuous time dictates the random switching of time-dependent parameters of such processes. We present exact and approximate bond pricing formulas by solving a system of partial differential equations and minimizing an error functional. The bond price expression exhibits a representation that shows how it is explicitly impacted by the rate matrix and the time-dependent coefficient functions of the short rate models. We validate the bond pricing formulas numerically by examining a regime-switching Vasicek model. [ABSTRACT FROM AUTHOR]

We develop a class of rational term structure models in the framework of the potential approach based upon a family of positive supermartingales that are driven by an affine Markov process. These models generally feature nonnegative interest rates and analytic pricing formulae for zero bonds, caps, swaptions, and European currency options, even in the presence of multiple factors. Moreover, in a model specification, the short rate stays near the zero lower bound for an extended period. [ABSTRACT FROM AUTHOR]

We consider the problem of computing the credit value adjustment (CVA) of a European option in presence of the wrong way risk in a default intensity setting. Namely we model the asset price evolution as solution to a linear equation that might depend on different stochastic factors and we provide an approximate evaluation of the option's price, by exploiting a correlation expansion approach, introduced in Antonelli and Scarlatti (Finance Stoch 13:269–303, 2009). We also extend our theoretical analysis to include some further value adjustments, for instance due to collateralization and funding costs. Finally, in the CVA case, we compare the numerical performance of our method with the one recently proposed by Brigo and Vrins (Eur J Oper Res 269:1154–1164, 2018) and Brigo et al. (Innovations in insurance, risk and asset management, WSPC proceedings, 2018), in the case of a call option driven by a GBM correlated with a CIR default intensity. We additionally compare with the numerical evaluations obtained by other methods. [ABSTRACT FROM AUTHOR]

The price V of a contingent claim in finance, insurance and economics is defined as an expectation of a stochastic expression. If the underlying uncertainty is modeled as a strong Markov process X, the Feynman–Kac theorem suggests that V is the unique solution of a boundary problem for a parabolic equation. In the case of PDO with constant symbols, simple probabilistic tools explained in this paper can be used to explicitly calculate expectations under very weak conditions on the process and study the regularity of the solution. Assuming that the Feynman–Kac theorem holds, and a more general boundary problem can be localized, the local results can be used to study the existence and regularity of solutions, and derive efficient numerical methods. In the paper, difficulties for the realization of this program are analyzed, several outstanding problems are listed, and several closely efficient methods are outlined.

We examine European call options in the jump-diffusion version of the Double Heston stochastic volatility model for the underlying price process to provide a more flexible model for the term structure of volatility. We assume, in addition, that the stochastic interest rate is governed by the Cox-- Ross -- Ingersoll (CIR) dynamics. The instantaneous volatilities are correlated with the dynamics of the stock price process, whereas the short-term rate is assumed to be independent of the dynamics of the price process and its volatility. The main result furnishes a semi-analytical formula for the price of the European call option in the hybrid call option/interest rates model. Numerical results show that the model implied volatilities are comparable for in-sample but outperform out-of-sample implied volatilities compared to the benchmark Heston model[1], and Double Heston volatility model put forward by Christoffersen et al., [2] for calls on the S&P 500 index.

We consider stochastic (partial) differential equations appearing as Markovian lifts of affine Volterra processes with jumps from the point of view of the generalized Feller property which was introduced in, e.g., Dörsek and Teichmann (A semigroup point of view on splitting schemes for stochastic (partial) differential equations, 2010. arXiv:1011.2651). In particular, we provide new existence, uniqueness and approximation results for Markovian lifts of affine rough volatility models of general jump diffusion type. We demonstrate that in this Markovian light the theory of stochastic Volterra processes becomes almost classical. [ABSTRACT FROM AUTHOR]

Let X be a multi-type continuous-state branching process with immigration on state space R + d. Denote by g t , t ≥ 0 , the law of X (t). We provide sufficient conditions under which g t has, for each t > 0 , a density with respect to the Lebesgue measure. Such density has, by construction, some Besov regularity. Our approach is based on a discrete integration by parts formula combined with a precise estimate on the error of the one-step Euler approximations of the process. As an auxiliary result, we also provide a criterion for the existence of densities of solutions to a general stochastic equation driven by Brownian motions and Poisson random measures, whose coefficients are Hölder continuous and might be unbounded. [ABSTRACT FROM AUTHOR]

In this work, we develop polynomial processes where the coefficients of the process may depend on time. A full characterization of this model class is given by means of their semimartingale characteristics. While in the time-homogeneous case, moments can be calculated easily through matrix exponentials, we show that in the inhomogeneous case this is no longer possible. As an alternative we explore a connection to Magnus series for fast numerical approximations. The model class studied in this work extends existing models, for example Sato processes and time-inhomogeneous affine processes. [ABSTRACT FROM AUTHOR]

We introduce the notion of a regime switching affine process. Informally this is a Markov process that behaves conditionally on each regime as an affine process with specific parameters. To facilitate our analysis, specific restrictions are imposed on these parameters. The regime switches are driven by a Markov chain. We prove that the joint process of the Markov chain and the conditionally affine part is a process with an affine structure on an enlarged state space, conditionally on the starting state of the Markov chain. Like for affine processes, the characteristic function can be expressed in a set of ordinary differential equations that can sometimes be solved analytically. This result unifies several semi-analytical solutions found in the literature for pricing derivatives of specific regime switching processes on smaller state spaces. It also provides a unifying theory that allows us to introduce regime switching to the pricing of many derivatives within the broad class of affine processes. Examples include European options and term structure derivatives with stochastic volatility and default. Essentially, whenever there is a pricing solution based on an affine process, we can extend this to a regime switching affine process without sacrificing the analytical tractability of the affine process. [ABSTRACT FROM AUTHOR]

In this paper we propose a method for pricing Asian options in market models with the risky asset dynamics driven by a Hawkes process with exponential kernel. For these processes the couple (λ (t) , X (t)) is affine, this property allows to extend the general methodology introduced by Hubalek et al. (Quant Finance 17:873–888, 2017) for Geometric Asian option pricing to jump-diffusion models with stochastic jump intensity. Although the system of ordinary differential equations providing the characteristic function of the related affine process cannot be solved in closed form, a COS-type algorithm allows to obtain the relevant quantities needed for options valuation. We describe, by means of graphical illustrations, the dependence of Asian options prices by the main parameters of the driving Hawkes process. Finally, by using Geometric Asian options values as control variates, we show that Arithmetic Asian options prices can be computed in a fast and efficient way by a standard Monte Carlo method. [ABSTRACT FROM AUTHOR]

The theory of affine processes has been recently extended to continuous stochastic Volterra equations. These so-called affine Volterra processes overcome modeling shortcomings of affine processes by incorporating path-dependent features and trajectories with regularity different from the paths of Brownian motion. More specifically, singular kernels yield rough affine processes. This paper extends the theory by considering affine stochastic Volterra equations with jumps. This extension is not straightforward because the jump structure and possible singularities of the kernel may induce explosions of the trajectories. This study also provides exponential affine formulas for the conditional Fourier–Laplace transform of marked Hawkes processes. [ABSTRACT FROM AUTHOR]

We consider stochastic partial differential equations appearing as Markovian lifts of matrix-valued (affine) Volterra-type processes from the point of view of the generalized Feller property (see, e.g., Dörsek and Teichmann in A semigroup point of view on splitting schemes for stochastic (partial) differential equations, 2010. arXiv:1011.2651). We introduce in particular Volterra Wishart processes with fractional kernels and values in the cone of positive semidefinite matrices. They are constructed from matrix products of infinite dimensional Ornstein–Uhlenbeck processes whose state space is the set of matrix-valued measures. Parallel to that we also consider positive definite Volterra pure jump processes, giving rise to multivariate Hawkes-type processes. We apply these affine covariance processes for multivariate (rough) volatility modeling and introduce a (rough) multivariate Volterra Heston-type model. [ABSTRACT FROM AUTHOR]

We provide a general and tractable framework under which all multiple yield curve modeling approaches based on affine processes, be it short rate, Libor market, or Heath–Jarrow–Morton modeling, can be consolidated. We model a numéraire process and multiplicative spreads between Libor rates and simply compounded overnight indexed swap rates as functions of an underlying affine process. Besides allowing for ordered spreads and an exact fit to the initially observed term structures, this general framework leads to tractable valuation formulas for caplets and swaptions and embeds all existing multicurve affine models. The proposed approach also gives rise to new developments, such as a short rate type model driven by a Wishart process, for which we derive a closed‐form pricing formula for caplets. The empirical performance of two specifications of our framework is illustrated by calibration to market data. [ABSTRACT FROM AUTHOR]

We study asymptotic properties of conditional least squares estimators for the drift parameters of two-factor affine diffusions based on continuous time observations. We distinguish three cases: subcritical, critical and supercritical. For all the drift parameters, in the subcritical and supercritical cases, asymptotic normality and asymptotic mixed normality is proved, while in the critical case, non-standard asymptotic behavior is described. [ABSTRACT FROM AUTHOR]

We study search and investment in an income ladder setting modeled by a regime-switching affine jump–diffusion income process with transition rates controlled by costly sequential search effort. The agent has exponential utility and can invest in a risky asset possibly correlated with the income process. Optimal policies are characterized explicitly, which allows us to identify the impact of risk aversion, search frictions, investment, and income risk in the agent's decisions. We illustrate our results with numerical examples. In particular, we find that search effort is reduced as the income mean-reversion increases or the hedging opportunities the financial markets offer increase. • We study optimal control of transition rates in a regime-switching income model. • The model admits a wide variety of applications: job search, R&D innovation, etc. • We identify impact of risk aversion, search costs, investment and income risk. • Optimal search is reduced as financial hedging opportunities increase. [ABSTRACT FROM AUTHOR]

Spot option prices, forwards and options on forwards relevant for the commodity markets are computed when the underlying process S is modelled as an exponential of a process ξ with memory as, e.g., a Volterra equation driven by a Lévy process. Moreover, the interest rate and a risk premium ρ representing storage costs, illiquidity, convenience yield or insurance costs, are assumed to be stochastic. When the interest rate is deterministic and the risk premium is explicitly modelled as an Ornstein-Uhlenbeck type of dynamics with a mean level that depends on the same memory term as the commodity, the process ( ξ ; ρ ) has an affine structure under the pricing measure Q and an explicit expression for the option price is derived in terms of the Fourier transform of the payoff function.

The jump threshold framework for credit risk modelling developed by Garreau and Kercheval enjoys the advantages of both structural- and reduced-form models. In their article, the focus is on multidimensional default dependence, under the assumptions that stock prices follow an exponential Lévy process (i.i.d. log returns) and that interest rates and stock volatility are constant. Explicit formulas for default time distributions and basket credit default swap (CDS) prices are obtained when the default threshold is deterministic, but only in terms of expectations when the default threshold is stochastic. In this article, we restrict attention to the one-dimensional, single-name case in order to obtain explicit closed-form solutions for the default time distribution when the default threshold, interest rate and volatility are all stochastic. When the interest rate and volatility processes are affine diffusions and the stochastic default threshold is properly chosen, we provide explicit formulas for the default time distribution, prices of defaultable bonds and CDS premia. The main idea is to make use of the Duffie–Pan–Singleton method of evaluating expectations of exponential integrals of affine diffusions. [ABSTRACT FROM AUTHOR]

We apply a new numerical method, the singular Fourier--Padé (SFP) method invented by Driscoll and Fornberg [Numer. Algorithms, 2001, 26, 77-92; The Gibbs Phenomenon in Various Representations and Applications, 2011], to price European-type options in Lévy and affine processes. The motivation behind this application is to reduce the inefficiency of current Fourier techniques when they are used to approximate piecewise continuous (non-smooth) probability density functions. When techniques such as fast Fourier transforms and Fourier series are applied to price and hedge options with nonsmooth probability density functions, they cause the Gibbs phenomenon; accordingly, the techniques converge slowly for density functions with jumps in value or derivatives. This seriously adversely affects the efficiency and accuracy of these techniques. In this paper, we derive pricing formulae and their option Greeks using the SFP method to resolve the Gibbs phenomenon and restore the global spectral convergence rate. Moreover, we show that our method requires a small number of terms to yield fast error convergence, and it is able to accurately price any European-type option deep in/out of the money and with very long/short maturities. Furthermore, we conduct an error-bound analysis of the SFP method in option pricing. This new method performs favourably in numerical experiments compared with existing techniques. [ABSTRACT FROM AUTHOR]

A characterization of the existence of non-central Wishart distributions (with shape and non-centrality parameter) as well as the existence of solutions to Wishart stochastic differential equations (with initial data and drift parameter) in terms of their exact parameter domains is given. These two families are the natural extensions of the non-central chi-square distributions and the squared Bessel processes to the positive semidefinite matrices. [ABSTRACT FROM AUTHOR]

Abstract: The two main approaches in credit risk are the structural approach pioneered by Merton and the reduced‐form framework proposed by Jarrow and Turnbull and by Artzner and Delbaen. The goal of this paper is to provide a unified view on both approaches. This is achieved by studying reduced‐form approaches under weak assumptions. In particular, we do not assume the global existence of a default intensity and allow default at fixed or predictable times, such as coupon payment dates, with positive probability. In this generalized framework, we study dynamic term structures prone to default risk following the forward‐rate approach proposed by Heath, Jarrow, and Morton. It turns out that previously considered models lead to arbitrage possibilities when default can happen at a predictable time. A suitable generalization of the forward‐rate approach contains an additional stochastic integral with atoms at predictable times and necessary and sufficient conditions for an appropriate no‐arbitrage condition are given. For efficient implementations, we develop a new class of affine models that do not satisfy the standard assumption of stochastic continuity. The chosen approach is intimately related to the theory of enlargement of filtrations, for which we provide an example by means of filtering theory where the Azéma supermartingale contains upward and downward jumps, both at predictable and totally inaccessible stopping times. [ABSTRACT FROM AUTHOR]

Interest rate market models, such as the LIBOR market model, have the advantage that the basic model quantities are directly observable in financial markets. Inflation market models extend this approach to inflation markets, where two types of swaps, zero-coupon and year-on-year inflation-indexed swaps, are the basic observable products. For inflation market models considered so far, closed formulas exist for only one type of swap, but not for both. The model in this paper uses affine processes in such a way that prices for both types of swaps can be calculated explicitly. Furthermore, call and put options on both types of swap rates can be calculated using one-dimensional Fourier inversion formulas. Using the derived formulas, we present an example calibration to market data. [ABSTRACT FROM PUBLISHER]

In this paper, we present some results on Geometric Asian option valuation for affine stochastic volatility models with jumps. We shall provide a general framework into which several different valuation problems based on some average process can be cast, and we shall obtain closed form solutions for some relevant affine model classes. [ABSTRACT FROM AUTHOR]

A model describing the dynamics of a foreign exchange (FX) rate should preserve the same level of analytical tractability when the inverted FX process is considered. We show that affine stochastic volatility models satisfy such a requirement. Such a finding allows us to use affine stochastic volatility models as a building block for FX dynamics that are functionally-invariant with respect to the construction of suitable products/ratios of rates, thus generalizing the model of [A. De Col, A. Gnoatto & M. Grasselli (2013) Smiles all around: FX joint calibration in a multi-Heston model, Journal of Banking and Finance 37 (10), 3799-3818.]. [ABSTRACT FROM AUTHOR]

We consider affine Markov processes taking values in convex cones. In particular, we characterize all affine processes taking values in irreducible symmetric cones in terms of certain Lévy-Khintchine triplets. This is the natural, coordinate-free formulation of the theory of Wishart processes on positive semidefinite matrices, as put forward by Bru (J Theor Probab 4(4):725-751, 1991) and Cuchiero et al. (Ann Appl Probab 21(2):397-463, 2011), in the more general context of symmetric cones, which also allows for simpler, alternative proofs. [ABSTRACT FROM AUTHOR]

The class of affine LIBOR models is appealing since it satisfies three central requirements of interest rate modeling. It is arbitrage-free, interest rates are nonnegative, and caplet and swaption prices can be calculated analytically. In order to guarantee nonnegative interest rates affine LIBOR models are driven by nonnegative affine processes, a restriction that makes it hard to produce volatility smiles. We modify the affine LIBOR models in such a way that real-valued affine processes can be used without destroying the nonnegativity of interest rates. Numerical examples show that in this class of models, pronounced volatility smiles are possible. [ABSTRACT FROM PUBLISHER]

We propose a general framework for modelling multiple yield curves which have emerged after the last financial crisis. In a general semimartingale setting, we provide an HJM approach to model the term structure of multiplicative spreads between FRA rates and simply compounded OIS risk-free forward rates. We derive an HJM drift and consistency condition ensuring absence of arbitrage and, in addition, we show how to construct models such that multiplicative spreads are greater than one and ordered with respect to the tenor's length. When the driving semimartingale is an affine process, we obtain a flexible and tractable Markovian structure. Finally, we show that the proposed framework allows unifying and extending several recent approaches to multiple yield curve modelling. [ABSTRACT FROM AUTHOR]

In this paper, we discuss how to model credit risk under the benchmark approach. Firstly we introduce an affine credit risk model. We then show how to price credit default swaps (CDSs) and introduce credit valuation adjustment (CVA) as an extension of CDSs. In particular, our model can capture right-way-and wrong-way exposure. This means, we capture the dependence structure of the default event and the value of the transaction under consideration. For simple contracts, we provide closed-form solutions. However, due to the fact that we allow for a dependence between the default event and the value of the transaction, closed-form solutions are difficult to obtain in general. Hence we conclude this paper with a reduced form model, which is more tractable. [ABSTRACT FROM AUTHOR]

For a commodity spot price dynamics given by an Ornstein-Uhlenbeck (OU) process with Barndorff-Nielsen and Shephard stochastic volatility, we price forwards using a class of pricing measures that simultaneously allow for change of level and speed in the mean reversion of both the price and the volatility. The risk premium is derived in the case of arithmetic and geometric spot price processes, and it is demonstrated that we can provide flexible shapes that are typically observed in energy markets. In particular, our pricing measure preserves the affine model structure and decomposes into a price and volatility risk premium. In the geometric spot price model, we need to resort to a detailed analysis of a system of Riccati equations, for which we show existence and uniqueness of solution and asymptotic properties that explain the possible risk premium profiles. Among the typical shapes, the risk premium allows for a stochastic change of sign, and can attain positive values in the short end of the forward market and negative in the long end. [ABSTRACT FROM AUTHOR]

We construct an exotic one-parameter semigroup of endomorphisms of a symmetric cone C , whose generator is not the sum of a Lie group generator and an endomorphism of C . The question is motivated by the theory of affine processes on symmetric cones, which plays an important role in mathematical finance. On the other hand, theoretical question that we solve in this paper seems to have been implicitly open even much longer then this motivation suggests. [ABSTRACT FROM AUTHOR]

In this paper, we quantitatively compare the forecasts from four different mortality models. We consider one discrete-time model proposed by Lee and Carter (1992) and three continuous-time models: the Wills and Sherris (2011) model, the Feller process and the Ornstein-Uhlenbeck (OU) process. The first two models estimate the whole surface of mortality simultaneously, while in the latter two, each generation is modelled and calibrated separately. We calibrate the models to UK and Australian population data. We find that all the models show relatively similar absolute total error for a given dataset, except the Lee-Carter model, whose performance differs significantly. To evaluate the forecasting performance we therefore look at two alternative measures: the relative error between the forecasted and the actual mortality rates and the percentage of actual mortality rates which fall within a prediction interval. In terms of the prediction intervals, the results are more divergent since each model implies a different structure for the variance of mortality rates. According to our experiments, the Wills and Sherris model produces superior results in terms of the prediction intervals. However, in terms of the mean absolute error, the OU and the Feller processes perform better. The forecasting performance of the Lee Carter model is mostly dependent on the choice of the dataset.

Over the past few years quadratic Backward Stochastic Differential Equations (BSDEs) have been a popular field of research. However there are only very few examples where explicit solutions for these equations are known. In this paper we consider a class of quadratic BSDEs involving affine processes and show that their solution can be reduced to solving a system of generalized Riccati ordinary differential equations. In other words we introduce a rich and flexible class of quadratic BSDEs which are analytically tractable, i.e. explicit up to the solution of an ODE. Our results also provide analytically tractable solutions to the problem of utility maximization and indifference pricing in multivariate affine stochastic volatility models. This generalizes univariate results of Kallsen and Muhle-Karbe (2010) and some results in the multivariate setting of Leippold and Trojani (2010) by establishing the full picture in the multivariate affine jump-diffusion setting. In particular we calculate the interesting quantity of the power utility indifference value of change of numeraire. Explicit examples in the Heston, Barndorff-Nielsen--Shephard and multivariate Heston setting are calculated. [ABSTRACT FROM AUTHOR]

Abstract: This paper proves the large deviation principle for affine diffusion processes with initial values in the interior of the state space . We approach this problem in two different ways. In the first approach, we first prove the large deviation principle for finite dimensional distributions, and then use it to establish the sample path large deviation principle. For this approach, a more careful examination of the affine transform formula is required. The second approach exploits the exponential martingale method of Donati-Martin et al. for the squares of Ornstein–Uhlenbeck processes. We provide an application to importance sampling of affine diffusion models. [Copyright &y& Elsevier]

This paper presents an approximate formula for pricing average options when the underlying asset price is driven by time-changed Lévy processes. Time-changed Lévy processes are attractive to use for a driving factor of underlying prices because the processes provide a flexible framework for generating jumps, capturing stochastic volatility as the random time change, and introducing the leverage effect. There have been very few studies dealing with pricing problems of exotic derivatives on time-changed Lévy processes in contrast to standard European derivatives. Our pricing formula is based on the Gram-Charlier expansion and the key of the formula is to find analytic treatments for computing the moments of the normalized average asset price. In numerical examples, we demonstrate that our formula give accurate values of average call options when adopting Heston's stochastic volatility model, VG-CIR, and NIG-CIR models. [ABSTRACT FROM AUTHOR]