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3,900
Option Pricing Accuracy for Estimated Heston Models
q-fin.MF
We consider assets for which price $X_t$ and squared volatility $Y_t$ are jointly driven by Heston joint stochastic differential equations (SDEs). When the parameters of these SDEs are estimated from $N$ sub-sampled data $(X_{nT}, Y_{nT})$, estimation errors do impact the classical option pricing PDEs. We estimate thes...
finance
3,901
Modelling the skew and smile of SPX and DAX index options using the Shifted Log-Normal and SABR stochastic models
q-fin.MF
We discuss modelling of SPX and DAX index option prices using the Shifted Log-Normal (SLN) model, (also known as Displaced Diffusion), and the SABR model. We found out that for SPX options, an example of strongly skewed option prices, SLN can produce a quite accurate fit. Moreover, for both types of index options, the ...
finance
3,902
Reconstruction of density functions by sk-splines
q-fin.MF
Reconstruction of density functions and their characteristic functions by radial basis functions with scattered data points is a popular topic in the theory of pricing of basket options. Such functions are usually entire or admit an analytic extension into an appropriate tube and "bell-shaped" with rapidly decaying tai...
finance
3,903
Interest rate models and Whittaker functions
q-fin.MF
I present the technique which can analyse some interest rate models: Constantinides-Ingersoll, CIR-model, geometric CIR and Geometric Brownian Motion. All these models have the unified structure of Whittaker function. The main focus of this text is closed-form solutions of the zero-coupon bond value in these models. In...
finance
3,904
Intensity Process for a Pure Jump Lévy Structural Model with Incomplete Information
q-fin.MF
In this paper we discuss a credit risk model with a pure jump L\'evy process for the asset value and an unobservable random barrier. The default time is the first time when the asset value falls below the barrier. Using the indistinguishability of the intensity process and the likelihood process, we prove the existence...
finance
3,905
Valuation and Hedging of Contracts with Funding Costs and Collateralization
q-fin.MF
The research presented in this work is motivated by recent papers by Brigo et al. (2011), Burgard and Kjaer (2009), Cr\'epey (2012), Fujii and Takahashi (2010), Piterbarg (2010) and Pallavicini et al. (2012). Our goal is to provide a sound theoretical underpinning for some results presented in these papers by developin...
finance
3,906
Explicit investment rules with time-to-build and uncertainty
q-fin.MF
We establish explicit socially optimal rules for an irreversible investment deci- sion with time-to-build and uncertainty. Assuming a price sensitive demand function with a random intercept, we provide comparative statics and economic interpreta- tions for three models of demand (arithmetic Brownian, geometric Brownian...
finance
3,907
Path Diffusion, Part I
q-fin.MF
This paper investigates the position (state) distribution of the single step binomial (multi-nomial) process on a discrete state / time grid under the assumption that the velocity process rather than the state process is Markovian. In this model the particle follows a simple multi-step process in velocity space which a...
finance
3,908
Option Pricing in an Imperfect World
q-fin.MF
In a model with no given probability measure, we consider asset pricing in the presence of frictions and other imperfections and characterize the property of coherent pricing, a notion related to (but much weaker than) the no arbitrage property. We show that prices are coherent if and only if the set of pricing measure...
finance
3,909
Robust pricing and hedging under trading restrictions and the emergence of local martingale models
q-fin.MF
We consider the pricing of derivatives in a setting with trading restrictions, but without any probabilistic assumptions on the underlying model, in discrete and continuous time. In particular, we assume that European put or call options are traded at certain maturities, and the forward price implied by these option pr...
finance
3,910
Optimal Hybrid Dividend Strategy Under The Markovian Regime-Switching Economy
q-fin.MF
In this paper, we consider the optimal dividend problem for a company. We describe the surplus process of the company by a diffusion model with regime switching. The aim of the company is to choose a dividend policy to maximize the expected total discounted payments until ruin. In this article, we consider a hybrid div...
finance
3,911
Utility indifference pricing and hedging for structured contracts in energy markets
q-fin.MF
In this paper we study the pricing and hedging of structured products in energy markets, such as swing and virtual gas storage, using the exponential utility indifference pricing approach in a general incomplete multivariate market model driven by finitely many stochastic factors. The buyer of such contracts is allowed...
finance
3,912
Long Term Optimal Investment in Matrix Valued Factor Models
q-fin.MF
Long term optimal investment problems are studied in a factor model with matrix valued state variables. Explicit parameter restrictions are obtained under which, for an isoelastic investor, the finite horizon value function and optimal strategy converge to their long-run counterparts as the investment horizon approache...
finance
3,913
On Correlated Defaults and Incomplete Information
q-fin.MF
In this paper, we study a continuous time structural asset value model for two correlated firms using a two-dimensional Brownian motion. We consider the situation of incomplete information, where the information set available to the market participants includes the default time of each firm and the periodic asset value...
finance
3,914
Distance to the line in the Heston model
q-fin.MF
The main object of study in the paper is the distance from a point to a line in the Riemannian manifold associated with the Heston model. We reduce the problem of computing such a distance to certain minimization problems for functions of one variable over finite intervals. One of the main ideas in this paper is to use...
finance
3,915
Option pricing in constant elasticity of variance model with liquidity costs
q-fin.MF
Paper is based on "The cost of illiquidity and its effects on hedging", L. C. G. Rogers and Surbjeet Singh, 2010. We generalize its thesis to constant elasticity model, which own previously used Black-Schoels model as a special case. The Goal of this article is to find optimal hedging strategy of European call/put opti...
finance
3,916
Multi-asset consumption-investment problems with infinite transaction costs
q-fin.MF
The subject of this paper is an optimal consumption/optimal portfolio problem with transaction costs and with multiple risky assets. In our model the transaction costs take a special form in that transaction costs on purchases of one of the risky assets (the endowed asset) are infinite, and transaction costs involvin...
finance
3,917
Generalized Dynkin game of switching type representation for defaultable claims in presence of contingent CSA
q-fin.MF
We study the solution's existence for a generalized Dynkin game of switching type which is shown to be the natural representation for general defaultable OTC contract with contingent CSA. This is a theoretical counterparty risk mitigation mechanism that allows the counterparty of a general OTC contract to switch from z...
finance
3,918
Rationality parameter for exercising American put
q-fin.MF
The main result of this paper is a probabilistic proof of the penalty method for approximating the price of an American put in the Black-Scholes market. The method gives a parametrized family of partial differential equations, and by varying the parameter the corresponding solutions converge to the price of an American...
finance
3,919
Ross Recovery with Recurrent and Transient Processes
q-fin.MF
Recently, Ross showed that it is possible to recover an objective measure from a risk-neutral measure. His model assumes that there is a finite-state Markov process X that drives the economy in discrete time. Many authors extended his model to a continuous-time setting with a Markov diffusion process X with state space...
finance
3,920
Arbitrage theory without a numéraire
q-fin.MF
This note develops an arbitrage theory for a discrete-time market model without the assumption of the existence of a num\'eraire asset. Fundamental theorems of asset pricing are stated and proven in this context. The distinction between the notions of investment-consumption arbitrage and pure-investment arbitrage provi...
finance
3,921
Banach geometry of arbitrage free markets
q-fin.MF
The article presents a description of geometry of Banach structures forming mathematical base of markets arbitrage absence type phenomena. In this connection the role of reflexive subspaces (replacing classically considered finite-dimensional subspaces) and plasterable cones is uncovered.
finance
3,922
Visualisation of financial time series by linear principal component analysis and nonlinear principal component analysis
q-fin.MF
In this dissertation, the main goal is visualisation of financial time series. We expect that visualisation of financial time series will be a useful auxiliary for technical analysis. Firstly, we review the technical analysis methods and test our trading rules, which are built by the essential concepts of technical ana...
finance
3,923
Positive Eigenfunctions of Markovian Pricing Operators: Hansen-Scheinkman Factorization, Ross Recovery and Long-Term Pricing
q-fin.MF
This paper develops a spectral theory of Markovian asset pricing models where the underlying economic uncertainty follows a continuous-time Markov process X with a general state space (Borel right process (BRP)) and the stochastic discount factor (SDF) is a positive semimartingale multiplicative functional of X. A key ...
finance
3,924
Incorporating Views on Market Dynamics in Options Hedging
q-fin.MF
We examine the possibility of incorporating information or views of market movements during the holding period of a portfolio, in the hedging of European options with respect to the underlying. Given a fixed holding period interval, we explore whether it is possible to adjust the number of shares needed to effectively ...
finance
3,925
The Intrinsic Bounds on the Risk Premium of Markovian Pricing Kernels
q-fin.MF
The risk premium is one of main concepts in mathematical finance. It is a measure of the trade-offs investors make between return and risk and is defined by the excess return relative to the risk-free interest rate that is earned from an asset per one unit of risk. The purpose of this article is to determine upper and ...
finance
3,926
Dynamic Defaultable Term Structure Modelling beyond the Intensity Paradigm
q-fin.MF
The two main approaches in credit risk are the structural approach pioneered in Merton (1974) and the reduced-form framework proposed in Jarrow & Turnbull (1995) and in Artzner & Delbaen (1995). The goal of this article is to provide a unified view on both approaches. This is achieved by studying reduced-form approache...
finance
3,927
Optimal Starting-Stopping and Switching of a CIR Process with Fixed Costs
q-fin.MF
This paper analyzes the problem of starting and stopping a Cox-Ingersoll-Ross (CIR) process with fixed costs. In addition, we also study a related optimal switching problem that involves an infinite sequence of starts and stops. We establish the conditions under which the starting-stopping and switching problems admit ...
finance
3,928
Asymptotic behaviour of the fractional Heston model
q-fin.MF
We consider the fractional Heston model originally proposed by Comte, Coutin and Renault. Inspired by recent ground-breaking work on rough volatility, which showed that models with volatility driven by fractional Brownian motion with short memory allows for better calibration of the volatility surface and more robust e...
finance
3,929
Existence and Uniqueness of a Steady State for an OTC Market with Several Assets
q-fin.MF
We introduce and study a class of over-the-counter market models specified by systems of Ordinary Differential Equations (ODE's), in the spirit of Duffie- G^arleanu-Pedersen [6]. The key innovation is allowing for multiple assets. We show the existence and uniqueness of a steady state for these ODE's.
finance
3,930
Reserve-Dependent Surrender
q-fin.MF
We study the modelling and valuation of surrender and other behavioural options in life insurance and pension. We place ourselves in between the two extremes of completely arbitrary intervention and optimal intervention by the policyholder. We present a method that is based on differential equations and that can be use...
finance
3,931
A BSDE approach to fair bilateral pricing under endogenous collateralization
q-fin.MF
Our previous results are extended to the case of the margin account, which may depend on the contract's value for the hedger and/or the counterparty. The present work generalizes also the papers by Bergman (1995), Mercurio (2013) and Piterbarg (2010). Using the comparison theorems for BSDEs, we derive inequalities for ...
finance
3,932
Indifference prices and implied volatilities
q-fin.MF
We consider a general local-stochastic volatility model and an investor with exponential utility. For a European-style contingent claim, whose payoff may depend on either a traded or non-traded asset, we derive an explicit approximation for both the buyer's and seller's indifference price. For European calls on a trade...
finance
3,933
Fundamental theorem of asset pricing: a strengthened version and $p$-summable markets
q-fin.MF
In the article a strenthened version of the 'Fundamental Theorem of asset Pricing' for one-period market model is proven. The principal role in this result play total and nonanihilating cones.
finance
3,934
Optimal switching for pairs trading rule: a viscosity solutions approach
q-fin.MF
This paper studies the problem of determining the optimal cut-off for pairs trading rules. We consider two correlated assets whose spread is modelled by a mean-reverting process with stochastic volatility, and the optimal pair trading rule is formulated as an optimal switching problem between three regimes: flat positi...
finance
3,935
On financial applications of the two-parameter Poisson-Dirichlet distribution
q-fin.MF
Capital distribution curve is defined as log-log plot of normalized stock capitalizations ranked in descending order. The curve displays remarkable stability over periods of time. Theory of exchangeable distributions on set partitions, developed for purposes of mathematical genetics and recently applied in non-parame...
finance
3,936
Non-concave utility maximisation on the positive real axis in discrete time
q-fin.MF
We treat a discrete-time asset allocation problem in an arbitrage-free, generically incomplete financial market, where the investor has a possibly non-concave utility function and wealth is restricted to remain non-negative. Under easily verifiable conditions, we establish the existence of optimal portfolios.
finance
3,937
Effect of Volatility Clustering on Indifference Pricing of Options by Convex Risk Measures
q-fin.MF
In this article, we look at the effect of volatility clustering on the risk indifference price of options described by Sircar and Sturm in their paper (Sircar, R., & Sturm, S. (2012). From smile asymptotics to market risk measures. Mathematical Finance. Advance online publication. doi:10.1111/mafi.12015). The indiffere...
finance
3,938
Short-time at-the-money skew and rough fractional volatility
q-fin.MF
The Black-Scholes implied volatility skew at the money of SPX options is known to obey a power law with respect to the time-to-maturity. We construct a model of the underlying asset price process which is dynamically consistent to the power law. The volatility process of the model is driven by a fractional Brownian mot...
finance
3,939
Convex duality with transaction costs
q-fin.MF
Convex duality for two two different super--replication problems in a continuous time financial market with proportional transaction cost is proved. In this market, static hedging in a finite number of options, in addition to usual dynamic hedging with the underlying stock, are allowed. The first one the problems consi...
finance
3,940
Archimedean-based Marshall-Olkin Distributions and Related Copula Functions
q-fin.MF
A new class of bivariate distributions is introduced that extends the Generalized Marshall-Olkin distributions of Li and Pellerey (2011). Their dependence structure is studied through the analysis of the copula functions that they induce. These copulas, that include as special cases the Generalized Marshall-Olkin copul...
finance
3,941
The pricing of lookback options and binomial approximation
q-fin.MF
Refining a discrete model of Cheuk and Vorst we obtain a closed formula for the price of a European lookback option at any time between emission and maturity. We derive an asymptotic expansion of the price as the number of periods tends to infinity, thereby solving a problem posed by Lin and Palmer. We prove, in partic...
finance
3,942
Consistent Recalibration of Yield Curve Models
q-fin.MF
The analytical tractability of affine (short rate) models, such as the Vasicek and the Cox-Ingersoll-Ross models, has made them a popular choice for modelling the dynamics of interest rates. However, in order to account properly for the dynamics of real data, these models need to exhibit time-dependent or even stochast...
finance
3,943
Extreme-Strike Asymptotics for General Gaussian Stochastic Volatility Models
q-fin.MF
We consider a stochastic volatility asset price model in which the volatility is the absolute value of a continuous Gaussian process with arbitrary prescribed mean and covariance. By exhibiting a Karhunen-Lo\`{e}ve expansion for the integrated variance, and using sharp estimates of the density of a general second-chaos...
finance
3,944
Rational Multi-Curve Models with Counterparty-Risk Valuation Adjustments
q-fin.MF
We develop a multi-curve term structure setup in which the modelling ingredients are expressed by rational functionals of Markov processes. We calibrate to LIBOR swaptions data and show that a rational two-factor lognormal multi-curve model is sufficient to match market data with accuracy. We elucidate the relationship...
finance
3,945
Some new results on Dufffie-type OTC markets
q-fin.MF
The extended Wild sums considered in this article generalize the classi- cal Wild sums of statistical physics. We first show how to obtain explicit solutions for the evolution equation of a large system where the interactions are given by a single, but general, interacting kernel which involves m components, for a fixe...
finance
3,946
Profitable forecast of prices of stock options on real market data via the solution of an ill-posed problem for the Black-Scholes equation
q-fin.MF
A new mathematical model for the Black-Scholes equation is proposed to forecast option prices. This model includes new interval for the price of the underlying stock as well as new initial and boundary conditions. Conventional notions of maturity time and strike prices are not used. The Black-Scholes equation is solved...
finance
3,947
About the decomposition of pricing formulas under stochastic volatility models
q-fin.MF
We obtain a decomposition of the call option price for a very general stochastic volatility diffusion model extending the decomposition obtained by E. Al\`os in [2] for the Heston model. We realize that a new term arises when the stock price does not follow an exponential model. The techniques used are non anticipative...
finance
3,948
Dynkin Game of Convertible Bonds and Their Optimal Strategy
q-fin.MF
This paper studies the valuation and optimal strategy of convertible bonds as a Dynkin game by using the reflected backward stochastic differential equation method and the variational inequality method. We first reduce such a Dynkin game to an optimal stopping time problem with state constraint, and then in a Markovian...
finance
3,949
Indifference Pricing and Hedging in a Multiple-Priors Model with Trading Constraints
q-fin.MF
This paper considers utility indifference valuation of derivatives under model uncertainty and trading constraints, where the utility is formulated as an additive stochastic differential utility of both intertemporal consumption and terminal wealth, and the uncertain prospects are ranked according to a multiple-priors ...
finance
3,950
Asymptotic analysis of forward performance processes in incomplete markets and their ill-posed HJB equations
q-fin.MF
We consider the problem of optimal portfolio selection under forward investment performance criteria in an incomplete market. The dynamics of the prices of the traded assets depend on a pair of stochastic factors, namely, a slow factor (e.g. a macroeconomic indicator) and a fast factor (e.g. stochastic volatility). We ...
finance
3,951
Polynomial term structure models
q-fin.MF
In this article, we explore a class of tractable interest rate models that have the property that the price of a zero-coupon bond can be expressed as a polynomial of a state diffusion process. Our results include a classification of all such time-homogeneous single-factor models in the spirit of Filipovic's maximal deg...
finance
3,952
A Posteriori Error Estimator for a Front-Fixing Finite Difference Scheme for American Options
q-fin.MF
For the numerical solution of the American option valuation problem, we provide a script written in MATLAB implementing an explicit finite difference scheme. Our main contribute is the definition of a posteriori error estimator for the American options pricing which is based on Richardson's extrapolation theory. This e...
finance
3,953
Network Structure and Counterparty Credit Risk
q-fin.MF
In this paper we offer a novel type of network model which can capture the precise structure of a financial market based, for example, on empirical findings. With the attached stochastic framework it is further possible to study how an arbitrary network structure and its expected counterparty credit risk are analytical...
finance
3,954
On statistical indistinguishability of complete and incomplete discrete time market models
q-fin.MF
We investigate the possibility of statistical evaluation of the market completeness for discrete time stock market models. It is known that the market completeness is not a robust property: small random deviations of the coefficients convert a complete market model into a incomplete one. The paper shows that market inc...
finance
3,955
Non-Arbitrage Under Additional Information for Thin Semimartingale Models
q-fin.MF
This paper completes the two studies undertaken in \cite{aksamit/choulli/deng/jeanblanc2} and \cite{aksamit/choulli/deng/jeanblanc3}, where the authors quantify the impact of a random time on the No-Unbounded-Risk-with-Bounded-Profit concept (called NUPBR hereafter) when the stock price processes are quasi-left-continu...
finance
3,956
Approximate hedging problem with transaction costs in stochastic volatility markets
q-fin.MF
This paper studies the problem of option replication in general stochastic volatility markets with transaction costs, using a new specification for the volatility adjustment in Leland's algorithm \cite{Leland}. We prove several limit theorems for the normalized replication error of Leland's strategy, as well as that of...
finance
3,957
Approximate hedging with proportional transaction costs in stochastic volatility models with jumps
q-fin.MF
We study the problem of option replication under constant proportional transaction costs in models where stochastic volatility and jumps are combined to capture the market's important features. Assuming some mild condition on the jump size distribution we show that transaction costs can be approximately compensated by ...
finance
3,958
Hedging of defaultable claims in a structural model using a locally risk-minimizing approach
q-fin.MF
In the context of a locally risk-minimizing approach, the problem of hedging defaultable claims and their Follmer-Schweizer decompositions are discussed in a structural model. This is done when the underlying process is a finite variation Levy process and the claims pay a predetermined payout at maturity, contingent on...
finance
3,959
Small-time asymptotics for Gaussian self-similar stochastic volatility models
q-fin.MF
We consider the class of self-similar Gaussian stochastic volatility models, and compute the small-time (near-maturity) asymptotics for the corresponding asset price density, the call and put pricing functions, and the implied volatilities. Unlike the well-known model-free behavior for extreme-strike asymptotics, small...
finance
3,960
An analytic recursive method for optimal multiple stopping: Canadization and phase-type fitting
q-fin.MF
We study an optimal multiple stopping problem for call-type payoff driven by a spectrally negative Levy process. The stopping times are separated by constant refraction times, and the discount rate can be positive or negative. The computation involves a distribution of the Levy process at a constant horizon and hence t...
finance
3,961
Good deal bounds with convex constraints
q-fin.MF
We investigate the structure of good deal bounds, which are subintervals of a no-arbitrage pricing bound, for financial market models with convex constraints as an extension of Arai and Fukasawa (2014). The upper and lower bounds of a good deal bound are naturally described by a convex risk measure. We call such a risk...
finance
3,962
An Empirical Approach to Financial Crisis Indicators Based on Random Matrices
q-fin.MF
The aim of this work is to build financial crisis indicators based on spectral properties of the dynamics of market data. After choosing an optimal size for a rolling window, the historical market data in this window is seen every trading day as a random matrix from which a covariance and a correlation matrix are obtai...
finance
3,963
No-Arbitrage Prices of Cash Flows and Forward Contracts as Choquet Representations
q-fin.MF
In a market of deterministic cash flows, given as an additive, symmetric relation of exchangeability on the finite signed Borel measures on the non-negative real time axis, it is shown that the only arbitrage-free price functional that fulfills some additional mild requirements is the integral of the unit zero-coupon b...
finance
3,964
Optimal Static Quadratic Hedging
q-fin.MF
We propose a flexible framework for hedging a contingent claim by holding static positions in vanilla European calls, puts, bonds, and forwards. A model-free expression is derived for the optimal static hedging strategy that minimizes the expected squared hedging error subject to a cost constraint. The optimal hedge in...
finance
3,965
Model-free Superhedging Duality
q-fin.MF
In a model free discrete time financial market, we prove the superhedging duality theorem, where trading is allowed with dynamic and semi-static strategies. We also show that the initial cost of the cheapest portfolio that dominates a contingent claim on every possible path $\omega \in \Omega$, might be strictly greate...
finance
3,966
Market shape formation, statistical equilibrium and neutral evolution theory
q-fin.MF
Mathematical methods of population genetics and framework of exchangeability provide a Markov chain model for analysis and interpretation of stochastic behaviour of equity markets, explaining, in particular, market shape formation, statistical equilibrium and temporal stability of market weights.
finance
3,967
Itô's formula for finite variation Lévy processes: The case of non-smooth functions
q-fin.MF
Extending It\^o's formula to non-smooth functions is important both in theory and applications. One of the fairly general extensions of the formula, known as Meyer-It\^o, applies to one dimensional semimartingales and convex functions. There are also satisfactory generalizations of It\^o's formula for diffusion process...
finance
3,968
Radner equilibrium in incomplete Levy models
q-fin.MF
We construct continuous-time equilibrium models based on a finite number of exponential utility investors. The investors' income rates as well as the stock's dividend rate are governed by discontinuous Levy processes. Our main result provides the equilibrium (i.e., bond and stock price dynamics) in closed-form. As an a...
finance
3,969
Muckenhoupt's $(A_p)$ condition and the existence of the optimal martingale measure
q-fin.MF
In the problem of optimal investment with utility function defined on $(0,\infty)$, we formulate sufficient conditions for the dual optimizer to be a uniformly integrable martingale. Our key requirement consists of the existence of a martingale measure whose density process satisfies the probabilistic Muckenhoupt $(A_p...
finance
3,970
A risk analysis for a system stabilized by a central agent
q-fin.MF
We formulate and analyze a multi-agent model for the evolution of individual and systemic risk in which the local agents interact with each other through a central agent who, in turn, is influenced by the mean field of the local agents. The central agent is stabilized by a bistable potential, the only stabilizing force...
finance
3,971
Robust replication of barrier-style claims on price and volatility
q-fin.MF
We show how to price and replicate a variety of barrier-style claims written on the $\log$ price $X$ and quadratic variation $\langle X \rangle$ of a risky asset. Our framework assumes no arbitrage, frictionless markets and zero interest rates. We model the risky asset as a strictly positive continuous semimartingale w...
finance
3,972
Optimal liquidation of an asset under drift uncertainty
q-fin.MF
We study a problem of finding an optimal stopping strategy to liquidate an asset with unknown drift. Taking a Bayesian approach, we model the initial beliefs of an individual about the drift parameter by allowing an arbitrary probability distribution to characterise the uncertainty about the drift parameter. Filtering ...
finance
3,973
Correction to Black-Scholes formula due to fractional stochastic volatility
q-fin.MF
Empirical studies show that the volatility may exhibit correlations that decay as a fractional power of the time offset. The paper presents a rigorous analysis for the case when the stationary stochastic volatility model is constructed in terms of a fractional Ornstein Uhlenbeck process to have such correlations. It is...
finance
3,974
Can You hear the Shape of a Market? Geometric Arbitrage and Spectral Theory
q-fin.MF
Geometric Arbitrage Theory reformulates a generic asset model possibly allowing for arbitrage by packaging all assets and their forwards dynamics into a stochastic principal fibre bundle, with a connection whose parallel transport encodes discounting and portfolio rebalancing, and whose curvature measures, in this geom...
finance
3,975
Optimal Insurance with Rank-Dependent Utility and Increasing Indemnities
q-fin.MF
Bernard et al. (2015) study an optimal insurance design problem where an individual's preference is of the rank-dependent utility (RDU) type, and show that in general an optimal contract covers both large and small losses. However, their contracts suffer from a problem of moral hazard for paying more compensation for a...
finance
3,976
On the no-arbitrage market and continuity in the Hurst parameter
q-fin.MF
We consider a market with fractional Brownian motion with stochastic integrals generated by the Riemann sums. We found that this market is arbitrage free if admissible strategies that are using observations with an arbitrarily small delay. Moreover, we found that this approach eliminates the discontinuity of the stocha...
finance
3,977
An example of short-term relative arbitrage
q-fin.MF
Long-term relative arbitrage exists in markets where the excess growth rate of the market portfolio is bounded away from zero. Here it is shown that under a time-homogeneity hypothesis this condition will also imply the existence of relative arbitrage over arbitrarily short intervals.
finance
3,978
On the Solution of the Multi-asset Black-Scholes model: Correlations, Eigenvalues and Geometry
q-fin.MF
In this paper, we study the multi-asset Black-Scholes model in terms of the importance that the correlation parameter space (equivalent to an $N$ dimensional hypercube) has in the solution of the pricing problem. We show that inside of this hypercube there is a surface, called the Kummer surface $\Sigma_K$, where the d...
finance
3,979
Regularity properties in a state-constrained expected utility maximization problem
q-fin.MF
We consider a stochastic optimal control problem in a market model with temporary and permanent price impact, which is related to an expected utility maximization problem under finite fuel constraint. We establish the initial condition fulfilled by the corresponding value function and show its first regularity property...
finance
3,980
Hedging with Temporary Price Impact
q-fin.MF
We consider the problem of hedging a European contingent claim in a Bachelier model with transient price impact as proposed by Almgren and Chriss. Following the approach of Rogers and Singh and Naujokat and Westray, the hedging problem can be regarded as a cost optimal tracking problem of the frictionless hedging strat...
finance
3,981
Viscosity properties with singularities in a state-constrained expected utility maximization problem
q-fin.MF
We consider the value function originating from an expected utility maximization problem with finite fuel constraint and show its close relation to a nonlinear parabolic degenerated Hamilton-Jacobi-Bellman (HJB) equation with singularity. On one hand, we give a so-called verification argument based on the dynamic progr...
finance
3,982
Trajectory based models. Evaluation of minmax pricing bounds
q-fin.MF
The paper studies sub and super-replication price bounds for contingent claims defined on general trajectory based market models. No prior probabilistic or topological assumptions are placed on the trajectory space, trading is assumed to take place at a finite number of occasions but not bounded in number nor necessari...
finance
3,983
Foundations for Wash Sales
q-fin.MF
Consider an ephemeral sale-and-repurchase of a security resulting in the same position before the sale and after the repurchase. A sale-and-repurchase is a wash sale if these transactions result in a loss within $\pm 30$ calendar days. Since a portfolio is essentially the same after a wash sale, any tax advantage from ...
finance
3,984
Sensitivity Analysis of Long-Term Cash Flows
q-fin.MF
In this article, a sensitivity analysis of long-term cash flows with respect to perturbations in the underlying process is presented. For this purpose, we employ the martingale extraction through which a pricing operator is transformed into what is easier to address. The method of Fournie et al. will be combined with t...
finance
3,985
Representation of homothetic forward performance processes in stochastic factor models via ergodic and infinite horizon BSDE
q-fin.MF
In an incomplete market, with incompleteness stemming from stochastic factors imperfectly correlated with the underlying stocks, we derive representations of homothetic (power, exponential and logarithmic) forward performance processes in factor-form using ergodic BSDE. We also develop a connection between the forward ...
finance
3,986
Integration with respect to model-free price paths with jumps
q-fin.MF
For every adapted, c\`agl\`ad process (strategy) $G$ and typical c\`adl\`ag price paths whose jumps satisfy some mild growth condition we define integral $G\cdot S$ as a limit of simple integrals.
finance
3,987
On the Existence of Martingale Measures in Jump Diffusion Market Models
q-fin.MF
In the context of jump-diffusion market models we construct examples that satisfy the weaker no-arbitrage condition of NA1 (NUPBR), but not NFLVR. We show that in these examples the only candidate for the density process of an equivalent local martingale measure is a supermartingale that is not a martingale, not even a...
finance
3,988
A Framework for Analyzing Stochastic Jumps in Finance based on Belief and Knowledge
q-fin.MF
We introduce a formal language IE that is a variant of the language PAL developed in [van Benthem 2011] by adding a belief operator and a common belief operator,specializing to stochastic analysis. A constant symbol in the language denotes a stochastic process so that we can represent several financial events as formul...
finance
3,989
Arbitrage and Hedging in model-independent markets with frictions
q-fin.MF
We provide a Fundamental Theorem of Asset Pricing and a Superhedging Theorem for a model independent discrete time financial market with proportional transaction costs. We consider a probability-free version of the Robust No Arbitrage condition introduced in Schachermayer ['04] and show that this is equivalent to the e...
finance
3,990
Purely pathwise probability-free Ito integral
q-fin.MF
This paper gives several simple constructions of the pathwise Ito integral $\int_0^t\phi d\omega$ for an integrand $\phi$ and a price path $\omega$ as integrator, with $\phi$ and $\omega$ satisfying various topological and analytical conditions. The definitions are purely pathwise in that neither $\phi$ nor $\omega$ ar...
finance
3,991
Variations on an example of Karatzas and Ruf
q-fin.MF
Markets composed of stocks with capitalization processes represented by positive continuous semimartingales are studied under the condition that the market excess growth rate is bounded away from zero. The following examples of these markets are given: i) a market with a singular covariance matrix and instantaneous rel...
finance
3,992
A generalized intensity based framework for single-name credit risk
q-fin.MF
The intensity of a default time is obtained by assuming that the default indicator process has an absolutely continuous compensator. Here we drop the assumption of absolute continuity with respect to the Lebesgue measure and only assume that the compensator is absolutely continuous with respect to a general $\sigma$-fi...
finance
3,993
Calibration and simulation of arbitrage effects in a non-equilibrium quantum Black-Scholes model by using semiclassical methods
q-fin.MF
An interacting Black-Scholes model for option pricing, where the usual constant interest rate r is replaced by a stochastic time dependent rate r(t) of the form r(t)=r+f(t) dW/dt, accounting for market imperfections and prices non-alignment, was developed in [1]. The white noise amplitude f(t), called arbitrage bubble,...
finance
3,994
Approximation of forward curve models in commodity markets with arbitrage-free finite dimensional models
q-fin.MF
In this paper we show how to approximate a Heath-Jarrow-Morton dynamics for the forward prices in commodity markets with arbitrage-free models which have a finite dimensional state space. Moreover, we recover a closed form representation of the forward price dynamics in the approximation models and derive the rate of c...
finance
3,995
Symmetry reduction and exact solutions of the non-linear Black--Scholes equation
q-fin.MF
In this paper, we investigate the non-linear Black--Scholes equation: $$u_t+ax^2u_{xx}+bx^3u_{xx}^2+c(xu_x-u)=0,\quad a,b>0,\ c\geq0.$$ and show that the one can be reduced to the equation $$u_t+(u_{xx}+u_x)^2=0$$ by an appropriate point transformation of variables. For the resulting equation, we study the group-theore...
finance
3,996
Consistent Re-Calibration of the Discrete-Time Multifactor Vasiček Model
q-fin.MF
The discrete-time multifactor Vasi\v{c}ek model is a tractable Gaussian spot rate model. Typically, two- or three-factor versions allow one to capture the dependence structure between yields with different times to maturity in an appropriate way. In practice, re-calibration of the model to the prevailing market conditi...
finance
3,997
Uniform bounds for Black--Scholes implied volatility
q-fin.MF
In this note, Black--Scholes implied volatility is expressed in terms of various optimisation problems. From these representations, upper and lower bounds are derived which hold uniformly across moneyness and call price. Various symmetries of the Black--Scholes formula are exploited to derive new bounds from old. These...
finance
3,998
Speculative Futures Trading under Mean Reversion
q-fin.MF
This paper studies the problem of trading futures with transaction costs when the underlying spot price is mean-reverting. Specifically, we model the spot dynamics by the Ornstein-Uhlenbeck (OU), Cox-Ingersoll-Ross (CIR), or exponential Ornstein-Uhlenbeck (XOU) model. The futures term structure is derived and its conne...
finance
3,999
CoCos under short-term uncertainty
q-fin.MF
In this paper we analyze an extension of the Jeanblanc and Valchev (2005) model by considering a short-term uncertainty model with two noises. It is a combination of the ideas of Duffie and Lando (2001) and Jeanblanc and Valchev (2005): share quotations of the firm are available at the financial market, and these can b...
finance