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5.0

Jun 29, 2018
06/18

by
Damir Filipović; Sander Willems

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We introduce a novel method to estimate the discount curve from market quotes based on the Moore-Penrose pseudoinverse such that 1) the market quotes are exactly replicated, 2) the curve has maximal smoothness, 3) no ad hoc interpolation is needed, and 4) no numerical root-finding algorithms are required. We provide a full theoretical framework as well as practical applications for both single-curve and multi-curve estimation.

Topics: Mathematical Finance, Quantitative Finance

Source: http://arxiv.org/abs/1606.03899

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4.0

Jun 28, 2018
06/18

by
Jacopo Mancin; Wolfgang J. Runggaldier

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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 local martingale. This candidate is given by the supermartingale deflator resulting from the inverse of the discounted growth optimal portfolio. In particular, we con- sider an...

Topics: Mathematical Finance, Quantitative Finance

Source: http://arxiv.org/abs/1511.08349

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7.0

Jun 30, 2018
06/18

by
Alexander M. G. Cox; Zhaoxu Hou; Jan Obloj

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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 prices may be strictly decreasing in time. In discrete time, when call options are traded, the short-selling restrictions ensure no arbitrage, and we show that classical duality...

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1406.0551

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3.0

Jun 29, 2018
06/18

by
José Manuel Corcuera; Arturo Valdivia

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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 be seen as noisy information about the fundamental value, or the firm's asset, from which a low level produces the credit event. We assume there are also reports of the firm,...

Topics: Mathematical Finance, Quantitative Finance

Source: http://arxiv.org/abs/1602.00094

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9.0

Jun 28, 2018
06/18

by
Mourad Lazgham

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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. Moreover, we can prove the existence and uniqueness of optimal strategies under rather mild model assumptions. On the one hand, this result is of independent interest. On the...

Topics: Mathematical Finance, Quantitative Finance

Source: http://arxiv.org/abs/1510.03079

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4.0

Jun 30, 2018
06/18

by
Robert Azencott; Yutheeka Gadhyan; Roland Glowinski

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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 these option pricing errors by combining numerical evaluation of estimation errors for Heston SDEs parameters with the computation of option price partial derivatives with respect to...

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1404.4014

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9.0

Jun 28, 2018
06/18

by
Phillip G. Bradford

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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 such a loss is not allowed. That is, after a wash sale a portfolio is unchanged so any loss captured by the wash sale is deemed to be solely for tax advantage and not investment...

Topics: Mathematical Finance, Quantitative Finance

Source: http://arxiv.org/abs/1511.03704

3
3.0

Jun 28, 2018
06/18

by
Michael R. Tehranchi

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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 bounds are used to reprove asymptotic formulae for implied volatility at extreme strikes and/or maturities.

Topics: Mathematical Finance, Quantitative Finance

Source: http://arxiv.org/abs/1512.06812

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4.0

Jun 29, 2018
06/18

by
N. Serhan Aydin

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We introduce an interactive market setup with sequential auctions where agents receive variegated signals with a known deadline. The effects of differential information and mutual learning on the allocation of overall profit \& loss (P\&L) and the pace of price discovery are analysed. We characterise the signal-based expected P\&L of agents based on explicit formulae for the directional quality of the trading signal, and study the optimal trading pattern using dynamic programming...

Topics: Mathematical Finance, Quantitative Finance

Source: http://arxiv.org/abs/1610.04051

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4.0

Jun 28, 2018
06/18

by
Mauricio Contreras; Alejandro Llanquihuén; Marcelo Villena

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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 determinant of the correlation matrix $\rho$ is zero, so the usual formula for the propagator of the $N$ asset Black-Scholes equation is no longer valid. Worse than that, in some...

Topics: Mathematical Finance, Quantitative Finance

Source: http://arxiv.org/abs/1510.02768

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3.0

Jun 30, 2018
06/18

by
Archil Gulisashvili

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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 a new system of coordinates in the Heston manifold and the level sets associated with this system. In the case of a vertical line, the formulas for the distance to the line are...

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1409.6027

4
4.0

Jun 30, 2018
06/18

by
Scott Robertson; Hao Xing

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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 approaches infinity. This convergence also yields portfolio turnpikes for general utilities. By using results on large time behaviour of semi-linear partial differential equations, our...

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1408.7010

3
3.0

Jun 30, 2018
06/18

by
Frank Gehmlich; Thorsten Schmidt

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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 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 with positive...

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1411.4851

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4.0

Jun 29, 2018
06/18

by
Oliver Janke

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In this article we consider an optimization problem of expected utility maximization of continuous-time trading in a financial market. This trading is constrained by a benchmark for a utility-based shortfall risk measure. The market consists of one asset whose price process is modeled by a Geometric Brownian motion where the market parameters change at a random time. The information flow is modeled by initially and progressively enlarged filtrations which represent the knowledge about the price...

Topics: Mathematical Finance, Quantitative Finance

Source: http://arxiv.org/abs/1610.08644

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6.0

Jun 30, 2018
06/18

by
Vladimir Vovk; Glenn Shafer

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Without probability theory, we define classes of supermartingales, martingales, and semimartingales in idealized financial markets with continuous price paths. This allows us to establish probability-free versions of a number of standard results in martingale theory, including the Dubins-Schwarz theorem, the Girsanov theorem, and results concerning the It\^o integral. We also establish the existence of an equity premium and a CAPM relationship in this probability-free setting.

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1703.08715

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Jun 28, 2018
06/18

by
Mauricio Contreras; Rely Pellicer; Daniel Santiagos; Marcelo Villena

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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, generates a time dependent potential U(t) which changes the usual equilibrium dynamics of the traditional Black-Scholes model. The purpose of this article is to tackle the...

Topics: Mathematical Finance, Quantitative Finance

Source: http://arxiv.org/abs/1512.05377

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5.0

Jun 28, 2018
06/18

by
Sergii Kovalenko; Oleksii Patsiuk

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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 one can be reduced to the equation $$u_t+(u_{xx}+u_x)^2=0$$ by an appropriate point transformation of variables. For the last equation, we study the group-theoretic properties, namely, we find the maximal algebra of invariance of its in Lie sense, carry out the symmetry reduction and seek for a number of exact group-invariant solutions of this...

Topics: Mathematical Finance, Quantitative Finance

Source: http://arxiv.org/abs/1512.06151

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4.0

Jun 30, 2018
06/18

by
Juozas Vaicenavicius

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Optimal liquidation of an asset with unknown constant drift and stochastic regime-switching volatility is studied. The uncertainty about the drift is represented by an arbitrary probability distribution, the stochastic volatility is modelled by $m$-state Markov chain. Using filtering theory, an equivalent reformulation of the original problem as a four-dimensional optimal stopping problem is found and then analysed by constructing approximating sequences of three-dimensional optimal stopping...

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1701.08579

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5.0

Jun 30, 2018
06/18

by
Takanori Adachi; Yoshihiro Ryu

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We generalize the notion of monetary value measures developed with category theory in [Adachi, 2014] by extending their base category from the category \c{hi} to the category of probability spaces Prob introduced in [Adachi and Ryu, 2016].

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1702.01175

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4.0

Jun 30, 2018
06/18

by
Tianran Geng; Thaleia Zariphopoulou

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We present turnpike-type results for the risk tolerance function in an incomplete market setting under time-monotone forward performance criteria. We show that, contrary to the classical case, the temporal and spatial limits do not coincide. We also show that they depend directly on the left- and right-end of the support of an underlying measure, which is used to construct the forward performance criterion. We provide examples with discrete and continuous measures, and discuss the asymptotic...

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1702.05649

5
5.0

Jun 30, 2018
06/18

by
Dmitry Muravey

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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 text I emphasize the specific details of mathematical methods of their determination such as Laplace transform and hypergeometric functions.

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1405.2459

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17

Jun 28, 2018
06/18

by
Sergey Sosnovskiy

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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.

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1506.07163

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10.0

Jun 29, 2018
06/18

by
Romain Blanchard; Laurence Carassus; Miklós Rásonyi

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We consider non-concave and non-smooth random utility functions with do- main of definition equal to the non-negative half-line. We use a dynamic pro- gramming framework together with measurable selection arguments to establish both the no-arbitrage condition characterization and the existence of an optimal portfolio in a (generically incomplete) discrete-time financial market model with finite time horizon. In contrast to the existing literature, we propose to consider a probability space...

Topics: Mathematical Finance, Quantitative Finance

Source: http://arxiv.org/abs/1602.06685

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6.0

Jun 29, 2018
06/18

by
Niushan Gao; Foivos Xanthos

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\begin{abstract} The aim of this paper is to study the spanning power of options in a static financial market that allows non-integrable assets. Our findings extend and unify the results in [8,9,18] for $L_p$-models. We also apply the spanning power properties to the pricing problem. In particular, we show that prices on call and put options of a limited liability asset can be uniquely extended by arbitrage to all marketed contingent claims written on the asset.

Topics: Mathematical Finance, Quantitative Finance

Source: http://arxiv.org/abs/1603.01288

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5.0

Jun 30, 2018
06/18

by
Hyungbin Park

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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 R. Unfortunately, the continuous-time model fails to recover an objective measure from a risk-neutral measure. We determine under which information recovery is possible in the...

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1410.2282

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12

Jun 28, 2018
06/18

by
Josselin Garnier; Knut Solna

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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 shown how the associated implied volatility has a term structure that is a function of maturity to a fractional power.

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1509.01175

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10.0

Jun 30, 2018
06/18

by
Matthieu Mariapragassam; Andrei Cozma; Christoph Reisinger

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We propose a novel and generic calibration technique for four-factor foreign-exchange hybrid local-stochastic volatility models with stochastic short rates. We build upon the particle method introduced by Guyon and Labord\`ere [Nonlinear Option Pricing, Chapter 11, Chapman and Hall, 2013] and combine it with new variance reduction techniques in order to accelerate convergence. We use control variates derived from a calibrated pure local volatility model, a two-factor Heston-type LSV model (both...

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1701.06001

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4.0

Jun 29, 2018
06/18

by
Henry Schellhorn; Ran Zhao

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We consider a dynamic market model where buyers and sellers submit limit orders. If at a given moment in time, the buyer is unable to complete his entire order due to the shortage of sell orders at the required limit price, the unmatched part of the order is recorded in the order book. Subsequently these buy unmatched orders may be matched with new incoming sell orders. The resulting demand curve constitutes the sole input to our model. The clearing price is then mechanically calculated using...

Topics: Mathematical Finance, Quantitative Finance

Source: http://arxiv.org/abs/1608.05900

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21

Jun 27, 2018
06/18

by
Alexander von Felbert

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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 analytically related to each other. This allows us, for the first time, to model the precise structure of an arbitrary financial market and to derive the corresponding expected exposure in...

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1504.06789

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Jun 27, 2018
06/18

by
Alain Bélanger; Gaston Giroux; Ndouné Ndouné

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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 fixed m >= 2. We then show how to retain the explicit formulas for the case of OTC market models where the dynamics is more directly described by two (or more) kernels.

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1503.03006

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7.0

Jun 30, 2018
06/18

by
Saul Jacka; Seb Armstrong; Abdelkarem Berkaoui

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We provide a dual characterisation of the weak$^*$-closure of a finite sum of cones in $L^\infty$ adapted to a discrete time filtration $\mathcal{F}_t$: the $t^{th}$ cone in the sum contains bounded random variables that are $\mathcal{F}_t$-measurable. Hence we obtain a generalisation of Delbaen's m-stability condition for the problem of reserving in a collection of num\'eraires $\mathbf{V}$, called $\mathbf{V}$-m-stability, provided these cones arise from acceptance sets of a dynamic coherent...

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1703.03638

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5.0

Jun 29, 2018
06/18

by
Miles B. Gietzmann; Adam J. Ostaszewski

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Following the approach of standard filtering theory, we analyse investor-valuation of firms, when these are modelled as geometric-Brownian state processes that are privately and partially observed, at random (Poisson) times, by agents. Tasked with disclosing forecast values, agents are able purposefully to withhold their observations; explicit filtering formulas are derived for downgrading the valuations in the absence of disclosures. The analysis is conducted for both a solitary firm and m...

Topics: Mathematical Finance, Quantitative Finance

Source: http://arxiv.org/abs/1606.04039

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4.0

Jun 29, 2018
06/18

by
Peter Bank; Yan Dolinsky

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We study super-replication of contingent claims in markets with fixed transaction costs. The first result in this paper reveals that in reasonable continuous time financial market the super--replication price is prohibitively costly and leads to trivial buy--and--hold strategies. Our second result is derives non trivial scaling limits of super--replication prices in the binomial models with small fixed costs.

Topics: Mathematical Finance, Quantitative Finance

Source: http://arxiv.org/abs/1610.09234

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8.0

Jun 29, 2018
06/18

by
Weston Barger; Matthew Lorig

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We derive asymptotic expansions for the prices of a variety of European and barrier-style claims in a general local-stochastic volatility setting. Our method combines Taylor series expansions of the diffusion coefficients with an expansion in the correlation parameter between the underlying asset and volatility process. Rigorous accuracy results are provided for European-style claims. For barrier-style claims, we include several numerical examples to illustrate the accuracy and versatility of...

Topics: Mathematical Finance, Quantitative Finance

Source: http://arxiv.org/abs/1610.05728

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32

Jun 26, 2018
06/18

by
Sabrina Mulinacci

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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 copulas and the Scale Mixture of Marshall-Olkin copulas (see Li, 2009),are obtained through suitable distortions of bivariate Archimedean copulas: this induces asymmetry, and the...

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1502.01912

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4.0

Jun 29, 2018
06/18

by
Stefan Gerhold; I. Cetin Gülüm

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Given a finite set of European call option prices on a single underlying, we want to know when there is a market model which is consistent with these prices. In contrast to previous studies, we allow models where the underlying trades at a bid-ask spread. The main question then is how large (in terms of a deterministic bound) this spread must be to explain the given prices. We fully solve this problem in the case of a single maturity, and give several partial results for multiple maturities....

Topics: Mathematical Finance, Quantitative Finance

Source: http://arxiv.org/abs/1608.05585

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3.0

Jun 30, 2018
06/18

by
Giovanni Mottola

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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 zero to full/perfect collateralization and switch back whenever she wants until contract maturity paying some switching costs and taking into account the running costs that emerge...

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1410.0594

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4.0

Jun 30, 2018
06/18

by
René Aid; Salvatore Federico; Huyên Pham; Bertrand Villeneuve

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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, and the Cox-Ingersoll-Ross). Committed capacity, that is, the installed capacity plus the in- vestment in the pipeline, must never drop below the best predictor of future...

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1406.0055

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4.0

Jun 28, 2018
06/18

by
Vladimir Vovk

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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 $\omega$ are assumed to be paths of stochastic processes, and the Ito integral exists almost surely in a non-probabilistic financial sense. For example, one of the results shows the...

Topics: Mathematical Finance, Quantitative Finance

Source: http://arxiv.org/abs/1512.01698

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3.0

Jun 28, 2018
06/18

by
Frank Gehmlich; Thorsten Schmidt

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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 $\sigma$-finite measure. This allows for example to incorporate the Merton-model in the generalized intensity based framework. An extension of the Black-Cox model is also considered. We...

Topics: Mathematical Finance, Quantitative Finance

Source: http://arxiv.org/abs/1512.03896

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4.0

Jun 30, 2018
06/18

by
A. Kushpel; J. Levesley

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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 tails. Unfortunately, the domain of such functions is not compact which creates various technical difficulties. We solve interpolation problem on an infinite rectangular...

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1404.5271

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8.0

Jun 29, 2018
06/18

by
Francesca Biagini; Jacopo Mancin; Thilo Meyer Brandis

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In this paper we study mean-variance hedging under the G-expectation framework. Our analysis is carried out by exploiting the G-martingale representation theorem and the related probabilistic tools, in a contin- uous financial market with two assets, where the discounted risky one is modeled as a symmetric G-martingale. By tackling progressively larger classes of contingent claims, we are able to explicitly compute the optimal strategy under general assumptions on the form of the contingent...

Topics: Mathematical Finance, Quantitative Finance

Source: http://arxiv.org/abs/1602.05484

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7.0

Jun 29, 2018
06/18

by
Tanmay S. Patankar

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This project attempts to address the problem of asset pricing in a financial market, where the interest rates and volatilities exhibit regime switching. This is an extension of the Black-Scholes model. Studies of Markov-modulated regime switching models have been well-documented. This project extends that notion to a class of semi-Markov processes known as age-dependent processes. We also allow for time-dependence in volatility within regimes. We show that the problem of option pricing in such...

Topics: Mathematical Finance, Quantitative Finance

Source: http://arxiv.org/abs/1609.04907

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4.0

Jun 30, 2018
06/18

by
Jihun Han; Hyungbin Park

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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 lower bounds on the risk premium of an asset based on the market prices of options. One of the key assumptions to achieve this goal is that the market is Markovian. Under this...

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1411.4606

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Jun 26, 2018
06/18

by
Philipp Harms; David Stefanovits; Josef Teichmann; Mario Wüthrich

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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 stochastic parameters. This in turn breaks their tractability, and modelling and simulating becomes an arduous task. We introduce a new class of Heath-Jarrow-Morton (HJM) models that both...

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1502.02926

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7.0

Jun 29, 2018
06/18

by
Guglielmo D'Amico

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The article presents a general discrete time dividend valuation model when the dividend growth rate is a general continuous variable. The main assumption is that the dividend growth rate follows a discrete time semi-Markov chain with measurable space. The paper furnishes sufficient conditions that assure finiteness of fundamental prices and risks and new equations that describe the first and second order price-dividend ratios. Approximation methods to solve equations are provided and some new...

Topics: Mathematical Finance, Quantitative Finance

Source: http://arxiv.org/abs/1605.02472

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10.0

Jun 29, 2018
06/18

by
Yiran Cui; Sebastian del Bano Rollin; Guido Germano

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Usually, in the Black-Scholes pricing theory the volatility is a positive real parameter. Here we explore what happens if it is allowed to be a complex number. The function for pricing a European option with a complex volatility has essential singularities at zero and infinity. The singularity at zero reflects the put-call parity. Solving for the implied volatility that reproduces a given market price yields not only a real root, but also infinitely many complex roots in a neighbourhood of the...

Topics: Mathematical Finance, Quantitative Finance

Source: http://arxiv.org/abs/1612.01951

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8.0

Jun 30, 2018
06/18

by
Jean-Pierre Fouque; Ruimeng Hu

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Rough stochastic volatility models have attracted a lot of attentions recently, in particular for the linear option pricing problem. In this paper, starting with power utilities, we propose to use a martingale distortion representation of the optimal value function for the nonlinear asset allocation problem in a (non-Markovian) fractional stochastic environment (for all Hurst index $H \in (0,1)$). We rigorously establish a first order approximation of the optimal value, where the return and...

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1703.06969

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Jun 29, 2018
06/18

by
Zuzana Buckova; Beata Stehlikova; Daniel Sevcovic

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In this survey paper we discuss recent advances on short interest rate models which can be formulated in terms of a stochastic differential equation for the instantaneous interest rate (also called short rate) or a system of such equations in case the short rate is assumed to depend also on other stochastic factors. Our focus is on convergence models, which explain the evolution of interest rate in connection with the adoption of Euro currency. Here, the domestic short rate depends on a...

Topics: Mathematical Finance, Quantitative Finance

Source: http://arxiv.org/abs/1607.04968

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3.0

Jun 30, 2018
06/18

by
Tianyang Nie; Marek Rutkowski

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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 the unilateral prices and we give the range for its fair bilateral prices. We also establish results yielding the link to the market model with a single interest rate. In the case...

Topics: Quantitative Finance, Mathematical Finance

Source: http://arxiv.org/abs/1412.2453