-
The Alpha‐Heston stochastic volatility model Math. Financ. (IF 2.25) Pub Date : 2021-04-05 Ying Jiao, Chunhua Ma, Simone Scotti, Chao Zhou
We introduce an affine extension of the Heston model, called the ‐Heston model, where the instantaneous variance process contains a jump part driven by ‐stable processes with . In this framework, we examine the implied volatility and its asymptotic behavior for both asset and VIX options. Furthermore, we study the jump clustering phenomenon observed on the market. We provide a jump cluster decomposition
-
Liquidity in competitive dealer markets Math. Financ. (IF 2.25) Pub Date : 2021-04-02 Peter Bank, Ibrahim Ekren, Johannes Muhle‐Karbe
We study a continuous‐time version of the intermediation model of Grossman and Miller. To wit, we solve for the competitive equilibrium prices at which liquidity takers' demands are absorbed by dealers with quadratic inventory costs, who can in turn gradually transfer these positions to an exogenous open market with finite liquidity. This endogenously leads to transient price impact in the dealer market
-
Relative arbitrage: Sharp time horizons and motion by curvature Math. Financ. (IF 2.25) Pub Date : 2021-03-31 Martin Larsson, Johannes Ruf
We characterize the minimal time horizon over which any equity market with stocks and sufficient intrinsic volatility admits relative arbitrage with respect to the market portfolio. If , the minimal time horizon can be computed explicitly, its value being zero if and if . If , the minimal time horizon can be characterized via the arrival time function of a geometric flow of the unit simplex in that
-
Simulating risk measures via asymptotic expansions for relative errors Math. Financ. (IF 2.25) Pub Date : 2021-03-30 Wei Jiang, Steven Kou
Risk measures, such as value‐at‐risk and expected shortfall, are widely used in finance. With the necessary sample size being computed using asymptotic expansions for relative errors, we propose a general framework to simulate these risk measures for a wide class of dependent data. The asymptotic expansions are new even for independent and identical data. An extensive numerical study is conducted to
-
Generalized statistical arbitrage concepts and related gain strategies Math. Financ. (IF 2.25) Pub Date : 2021-02-19 Christian Rein, Ludger Rüschendorf, Thorsten Schmidt
The notion of statistical arbitrage introduced in Bondarenko (2003) is generalized to statistical ‐arbitrage corresponding to trading strategies which yield positive gains on average in a class of scenarios described by a ‐algebra . This notion contains classical arbitrage as a special case. Admitting general static payoffs as generalized strategies, as done in Kassberger and Liebmann (2017) in the
-
Asset pricing with general transaction costs: Theory and numerics Math. Financ. (IF 2.25) Pub Date : 2021-02-06 Lukas Gonon, Johannes Muhle‐Karbe, Xiaofei Shi
We study risk‐sharing equilibria with general convex costs on the agents' trading rates. For an infinite‐horizon model with linear state dynamics and exogenous volatilities, we prove that the equilibrium returns mean‐revert around their frictionless counterparts—the deviation has Ornstein‐Uhlenbeck dynamics for quadratic costs whereas it follows a doubly‐reflected Brownian motion if costs are proportional
-
Optimal dynamic risk sharing under the time‐consistent mean‐variance criterion Math. Financ. (IF 2.25) Pub Date : 2021-02-04 Lv Chen, David Landriault, Bin Li, Danping Li
In this paper, we consider a dynamic Pareto optimal risk‐sharing problem under the time‐consistent mean‐variance criterion. A group of n insurers is assumed to share an exogenous risk whose dynamics is modeled by a Lévy process. By solving the extended Hamilton–Jacobi–Bellman equation using the Lagrange multiplier method, an explicit form of the time‐consistent equilibrium risk‐bearing strategy for
-
Forward rank‐dependent performance criteria: Time‐consistent investment under probability distortion Math. Financ. (IF 2.25) Pub Date : 2021-01-21 Xue Dong He, Moris S. Strub, Thaleia Zariphopoulou
We introduce the concept of forward rank‐dependent performance criteria, extending the original notion to forward criteria that incorporate probability distortions. A fundamental challenge is how to reconcile the time‐consistent nature of forward performance criteria with the time‐inconsistency stemming from probability distortions. For this, we first propose two distinct definitions, one based on
-
Double continuation regions for American options under Poisson exercise opportunities Math. Financ. (IF 2.25) Pub Date : 2021-03-15 Zbigniew Palmowski, José Luis Pérez, Kazutoshi Yamazaki
We consider the Lévy model of the perpetual American call and put options with a negative discount rate under Poisson observations. Similar to the continuous observation case, the stopping region that characterizes the optimal stopping time is either a half‐line or an interval. The objective of this paper is to obtain explicit expressions of the stopping and continuation regions and the value function
-
Intra‐Horizon expected shortfall and risk structure in models with jumps Math. Financ. (IF 2.25) Pub Date : 2021-03-21 Walter Farkas, Ludovic Mathys, Nikola Vasiljević
The present article deals with intra‐horizon risk in models with jumps. Our general understanding of intra‐horizon risk is along the lines of the approach taken in Boudoukh et al. (2004); Rossello (2008); Bhattacharyya et al. (2009); Bakshi and Panayotov (2010); and Leippold and Vasiljević (2020). In particular, we believe that quantifying market risk by strictly relying on point‐in‐time measures cannot
-
Sharing the value‐at‐risk under distributional ambiguity Math. Financ. (IF 2.25) Pub Date : 2020-12-23 Zhi Chen, Weijun Xie
This paper considers the problem of risk sharing, where a coalition of homogeneous agents, each bearing a random cost, aggregates their costs, and shares the value‐at‐risk of such a risky position. Due to limited distributional information in practice, the joint distribution of agents' random costs is difficult to acquire. The coalition, being aware of the distributional ambiguity, thus evaluates the
-
Optimal make–take fees for market making regulation Math. Financ. (IF 2.25) Pub Date : 2020-11-10 Omar El Euch, Thibaut Mastrolia, Mathieu Rosenbaum, Nizar Touzi
We address the mechanism design problem of an exchange setting suitable make– take fees to attract liquidity on its platform. Using a principal–agent approach, we provide the optimal compensation scheme of a market maker in quasi‐explicit form. This contract depends essentially on the market maker inventory trajectory and on the volatility of the asset. We also provide the optimal quotes that should
-
Equilibrium concepts for time‐inconsistent stopping problems in continuous time Math. Financ. (IF 2.25) Pub Date : 2020-11-09 Erhan Bayraktar, Jingjie Zhang, Zhou Zhou
A new notion of equilibrium, which we call strong equilibrium, is introduced for time‐inconsistent stopping problems in continuous time. Compared to the existing notions introduced in Huang, Y.‐J., & Nguyen‐Huu, A. (2018, Jan 01). Time‐consistent stopping under decreasing impatience. Finance and Stochastics, 22(1), 69–95 and Christensen, S., & Lindensjö, K. (2018). On finding equilibrium stopping times
-
Markov chains under nonlinear expectation Math. Financ. (IF 2.25) Pub Date : 2020-11-08 Max Nendel
In this paper, we consider continuous‐time Markov chains with a finite state space under nonlinear expectations. We define so‐called Q‐operators as an extension of Q‐matrices or rate matrices to a nonlinear setup, where the nonlinearity is due to model uncertainty. The main result gives a full characterization of convex Q‐operators in terms of a positive maximum principle, a dual representation by
-
Open markets Math. Financ. (IF 2.25) Pub Date : 2020-10-31 Ioannis Karatzas, Donghan Kim
An open market is a subset of a larger equity market, composed of a certain fixed number of top‐capitalization stocks. Though the number of stocks in the open market is fixed, their composition changes over time, as each company's rank by market capitalization fluctuates. When one is allowed to invest also in a money market, an open market resembles the entire “closed” equity market in the sense that
-
Convergence of utility indifference prices to the superreplication price in a multiple‐priors framework Math. Financ. (IF 2.25) Pub Date : 2020-10-16 Romain Blanchard, Laurence Carassus
This paper formulates a utility indifference pricing model for investors trading in a discrete time financial market under nondominated model uncertainty. Investor preferences are described by possibly random utility functions defined on the positive axis. We prove that when the investors's absolute risk aversion tends to infinity, the multiple‐priors utility indifference prices of a contingent claim
-
The asymptotic expansion of the regular discretization error of Itô integrals Math. Financ. (IF 2.25) Pub Date : 2020-10-15 Elisa Alòs, Masaaki Fukasawa
We study an Edgeworth‐type refinement of the central limit theorem for the discretization error of Itô integrals. Toward this end, we introduce a new approach, based on the anticipating Itô formula. This alternative technique allows us to compute explicitly the terms of the corresponding expansion formula. Two applications to finance are given; the asymptotics of discrete hedging error under the Black–Scholes
-
Mean–field moral hazard for optimal energy demand response management Math. Financ. (IF 2.25) Pub Date : 2020-10-13 Romuald Élie, Emma Hubert, Thibaut Mastrolia, Dylan Possamaï
We study the problem of demand response contracts in electricity markets by quantifying the impact of considering a continuum of consumers with mean–field interaction, whose consumption is impacted by a common noise. We formulate the problem as a Principal–Agent problem with moral hazard in which the Principal—she—is an electricity producer who observes continuously the consumption of a continuum of
-
Small‐time, large‐time, and asymptotics for the Rough Heston model Math. Financ. (IF 2.25) Pub Date : 2020-10-06 Martin Forde, Stefan Gerhold, Benjamin Smith
We characterize the behavior of the Rough Heston model introduced by Jaisson and Rosenbaum (2016, Ann. Appl. Probab., 26, 2860–2882) in the small‐time, large‐time, and (i.e., ) limits. We show that the short‐maturity smile scales in qualitatively the same way as a general rough stochastic volatility model , and the rate function is equal to the Fenchel–Legendre transform of a simple transformation
-
Binary funding impacts in derivative valuation Math. Financ. (IF 2.25) Pub Date : 2020-09-14 Junbeom Lee, Chao Zhou
We discuss the binary nature of funding impact in derivative valuation. Under some conditions, funding is either a cost or a benefit, that is, one of the lending/borrowing rates does not play a role in pricing derivatives. When derivatives are priced, considering different lending/borrowing rates leads to semilinear backward stochastic differential equations (BSDEs) and partial differential equation
-
Size matters for OTC market makers: General results and dimensionality reduction techniques Math. Financ. (IF 2.25) Pub Date : 2020-08-23 Philippe Bergault, Olivier Guéant
In most over‐the‐counter (OTC) markets, a small number of market makers provide liquidity to other market participants. More precisely, for a list of assets, they set prices at which they agree to buy and sell. Market makers face therefore an interesting optimization problem: they need to choose bid and ask prices for making money while mitigating the risk associated with holding inventory in a volatile
-
Model risk in credit risk Math. Financ. (IF 2.25) Pub Date : 2020-08-17 Roberto Fontana, Elisa Luciano, Patrizia Semeraro
We provide sharp analytical upper and lower bounds for value‐at‐risk (VaR) and sharp bounds for expected shortfall (ES) of portfolios of any dimension subject to default risk. To do so, the main methodological contribution of the paper consists in analytically finding the convex hull generators for the class of exchangeable Bernoulli variables with given mean and for the class of exchangeable Bernoulli
-
On utility maximization under model uncertainty in discrete‐time markets Math. Financ. (IF 2.25) Pub Date : 2020-07-23 Miklós Rásonyi, Andrea Meireles‐Rodrigues
We study the problem of maximizing terminal utility for an agent facing model uncertainty, in a frictionless discrete‐time market with one safe asset and finitely many risky assets. We show that an optimal investment strategy exists if the utility function, defined either on the positive real line or on the whole real line, is bounded from above. We further find that the boundedness assumption can
-
Asymptotics for small nonlinear price impact: A PDE approach to the multidimensional case Math. Financ. (IF 2.25) Pub Date : 2020-07-20 Erhan Bayraktar, Thomas Cayé, Ibrahim Ekren
We provide an asymptotic expansion of the value function of a multidimensional utility maximization problem from consumption with small nonlinear price impact. In our model, cross‐impacts between assets are allowed. In the limit for small price impact, we determine the asymptotic expansion of the value function around its frictionless version. The leading order correction is characterized by a nonlinear
-
Continuous‐time mean–variance portfolio selection: A reinforcement learning framework Math. Financ. (IF 2.25) Pub Date : 2020-06-23 Haoran Wang, Xun Yu Zhou
We approach the continuous‐time mean–variance portfolio selection with reinforcement learning (RL). The problem is to achieve the best trade‐off between exploration and exploitation, and is formulated as an entropy‐regularized, relaxed stochastic control problem. We prove that the optimal feedback policy for this problem must be Gaussian, with time‐decaying variance. We then prove a policy improvement
-
Optimal investment, derivative demand, and arbitrage under price impact Math. Financ. (IF 2.25) Pub Date : 2020-06-22 Michail Anthropelos, Scott Robertson, Konstantinos Spiliopoulos
This paper studies the optimal investment problem with random endowment in an inventory‐based price impact model with competitive market makers. Our goal is to analyze how price impact affects optimal policies, as well as both pricing rules and demand schedules for contingent claims. For exponential market makers preferences, we establish two effects due to price impact: constrained trading and nonlinear
-
A term structure model for dividends and interest rates Math. Financ. (IF 2.25) Pub Date : 2020-06-16 Damir Filipović, Sander Willems
Over the last decade, dividends have become a standalone asset class instead of a mere side product of an equity investment. We introduce a framework based on polynomial jump‐diffusions to jointly price the term structures of dividends and interest rates. Prices for dividend futures, bonds, and the dividend paying stock are given in closed form. We present an efficient moment based approximation method
-
Convergence of optimal expected utility for a sequence of discrete‐time markets Math. Financ. (IF 2.25) Pub Date : 2020-06-16 David M. Kreps, Walter Schachermayer
We examine Kreps' conjecture that optimal expected utility in the classic Black–Scholes–Merton (BSM) economy is the limit of optimal expected utility for a sequence of discrete‐time economies that “approach” the BSM economy in a natural sense: The nth discrete‐time economy is generated by a scaled n‐step random walk, based on an unscaled random variable ζ with mean 0, variance 1, and bounded support
-
Robust risk aggregation with neural networks Math. Financ. (IF 2.25) Pub Date : 2020-06-13 Stephan Eckstein, Michael Kupper, Mathias Pohl
We consider settings in which the distribution of a multivariate random variable is partly ambiguous. We assume the ambiguity lies on the level of the dependence structure, and that the marginal distributions are known. Furthermore, a current best guess for the distribution, called reference measure, is available. We work with the set of distributions that are both close to the given reference measure
-
When to sell an asset amid anxiety about drawdowns Math. Financ. (IF 2.25) Pub Date : 2020-06-12 Neofytos Rodosthenous, Hongzhong Zhang
We consider risk‐averse investors with different levels of anxiety about asset price drawdowns. The latter is defined as the distance of the current price away from its best performance since inception. These drawdowns can increase either continuously or by jumps, and will contribute toward the investor's overall impatience when breaching the investor's private tolerance level. We investigate the unusual
-
Network valuation in financial systems Math. Financ. (IF 2.25) Pub Date : 2020-06-01 Paolo Barucca, Marco Bardoscia, Fabio Caccioli, Marco D'Errico, Gabriele Visentin, Guido Caldarelli, Stefano Battiston
We introduce a general model for the balance‐sheet consistent valuation of interbank claims within an interconnected financial system. Our model represents an extension of clearing models of interdependent liabilities to account for the presence of uncertainty on banks' external assets. At the same time, it also provides a natural extension of classic structural credit risk models to the case of an
-
Semitractability of optimal stopping problems via a weighted stochastic mesh algorithm Math. Financ. (IF 2.25) Pub Date : 2020-05-27 Denis Belomestny, Maxim Kaledin, John Schoenmakers
In this paper, we propose a Weighted Stochastic Mesh (WSM) algorithm for approximating the value of discrete‐ and continuous‐time optimal stopping problems. In this context, we consider tractability of such problems via a useful notion of semitractability and the introduction of a tractability index for a particular numerical solution algorithm. It is shown that in the discrete‐time case the WSM algorithm
-
Risk functionals with convex level sets Math. Financ. (IF 2.25) Pub Date : 2020-05-27 Ruodu Wang, Yunran Wei
We analyze the “convex level sets” (CxLS) property of risk functionals, which is a necessary condition for the notions of elicitability, identifiability, and backtestability, popular in the recent statistics and risk management literature. We put the CxLS property in the multidimensional setting, with a special focus on signed Choquet integrals, a class of risk functionals that are generally not monotone
-
Azéma martingales for Bessel and CIR processes and the pricing of Parisian zero‐coupon bonds Math. Financ. (IF 2.25) Pub Date : 2020-05-21 Angelos Dassios, Jia Wei Lim, Yan Qu
In this paper, we study the excursions of Bessel and Cox–Ingersoll–Ross (CIR) processes with dimensions . We obtain densities for the last passage times and meanders of the processes. Using these results, we prove a variation of the Azéma martingale for the Bessel and CIR processes based on excursion theory. Furthermore, we study their Parisian excursions, and generalize previous results on the Parisian
-
Self‐similarity in long‐horizon returns Math. Financ. (IF 2.25) Pub Date : 2020-05-05 Dilip B. Madan, Wim Schoutens
Asset returns incorporate new information via the effects of independent and possibly identically distributed random shocks. They may also incorporate long memory effects related to the concept of self‐similarity. The two approaches are here combined. In addition, methods are proposed for estimating the contribution of each component and evidence supporting the presence of both components in both the
-
Asset pricing with heterogeneous beliefs and illiquidity Math. Financ. (IF 2.25) Pub Date : 2020-04-16 Johannes Muhle‐Karbe, Marcel Nutz, Xiaowei Tan
This paper studies the equilibrium price of an asset that is traded in continuous time between N agents who have heterogeneous beliefs about the state process underlying the asset's payoff. We propose a tractable model where agents maximize expected returns under quadratic costs on inventories and trading rates. The unique equilibrium price is characterized by a weakly coupled system of linear parabolic
-
Effective risk aversion in thin risk‐sharing markets Math. Financ. (IF 2.25) Pub Date : 2020-04-12 Michail Anthropelos, Constantinos Kardaras, Georgios Vichos
We consider thin incomplete financial markets, where traders with heterogeneous preferences and risk exposures have motive to behave strategically regarding the demand schedules they submit, thereby impacting prices and allocations. We argue that traders relatively more exposed to the market portfolio tend to behave in a more risk tolerant manner. Noncompetitive equilibrium prices and allocations result
-
Distress and default contagion in financial networks Math. Financ. (IF 2.25) Pub Date : 2020-04-12 Luitgard Anna Maria Veraart
We develop a new model for solvency contagion that can be used to quantify systemic risk in stress tests of financial networks. In contrast to many existing models, it allows for the spread of contagion already before the point of default and hence can account for contagion due to distress and mark‐to‐market losses. We derive general ordering results for outcome measures of stress tests that enable
-
Lifetime investment and consumption with recursive preferences and small transaction costs Math. Financ. (IF 2.25) Pub Date : 2020-04-08 Yaroslav Melnyk, Johannes Muhle‐Karbe, Frank Thomas Seifried
We investigate the effects of small proportional transaction costs on lifetime consumption and portfolio choice. The extant literature has focused on agents with additive utilities. Here, we extend this analysis to the archetype of nonadditive preferences: the isoelastic recursive utilities proposed by Epstein and Zin.
-
A martingale representation theorem and valuation of defaultable securities Math. Financ. (IF 2.25) Pub Date : 2020-04-08 Tahir Choulli, Catherine Daveloose, Michèle Vanmaele
We consider a financial framework with two levels of information: the public information generated by the financial assets, and a larger flow of information that contains additional knowledge about a random time. This random time can represent many economic and financial settings, such as the default time of a firm for credit risk, and the death time of an insured for life insurance. As the random
-
No‐arbitrage implies power‐law market impact and rough volatility Math. Financ. (IF 2.25) Pub Date : 2020-03-24 Paul Jusselin, Mathieu Rosenbaum
Market impact is the link between the volume of a (large) order and the price move during and after the execution of this order. We show that in a quite general framework, under no‐arbitrage assumption, the market impact function can only be of power‐law type. Furthermore, we prove this implies that the macroscopic price is diffusive with rough volatility, with a one‐to‐one correspondence between the
-
Optimal equilibria for time‐inconsistent stopping problems in continuous time Math. Financ. (IF 2.25) Pub Date : 2020-03-04 Yu‐Jui Huang, Zhou Zhou
For an infinite‐horizon continuous‐time optimal stopping problem under nonexponential discounting, we look for an optimal equilibrium, which generates larger values than any other equilibrium does on the entire state space. When the discount function is log sub‐additive and the state process is one‐dimensional, an optimal equilibrium is constructed in a specific form, under appropriate regularity and
-
Cover Image, Volume 30, Issue 2 Math. Financ. (IF 2.25) Pub Date : 2020-03-19
The cover image is based on the Original Article Semistatic and Sparse Variance‐Optimal Hedging by Di Tella et al., https://doi.org/10.1111/mafi.12235.
-
Robust XVA Math. Financ. (IF 2.25) Pub Date : 2020-03-12 Maxim Bichuch, Agostino Capponi, Stephan Sturm
We introduce an arbitrage‐free framework for robust valuation adjustments. An investor trades a credit default swap portfolio with a risky counterparty, and hedges credit risk by taking a position in defaultable bonds. The investor does not know the exact return rate of her counterparty's bond, but she knows it lies within an uncertainty interval. We derive both upper and lower bounds for the XVA process
-
Hedging nontradable risks with transaction costs and price impact Math. Financ. (IF 2.25) Pub Date : 2020-03-12 Álvaro Cartea, Ryan Donnelly, Sebastian Jaimungal
A risk‐averse agent hedges her exposure to a nontradable risk factor U using a correlated traded asset S and accounts for the impact of her trades on both factors. The effect of the agent's trades on U is referred to as cross‐impact. By solving the agent's stochastic control problem, we obtain a closed‐form expression for the optimal strategy when the agent holds a linear position in U. When the exposure
-
Static and semistatic hedging as contrarian or conformist bets Math. Financ. (IF 2.25) Pub Date : 2020-03-12 Svetlana Boyarchenko, Sergei Levendorskiĭ
In this paper, we argue that, once the costs of maintaining the hedging portfolio are properly taken into account, semistatic portfolios should more properly be thought of as separate classes of derivatives, with nontrivial, model‐dependent payoff structures. We derive new integral representations for payoffs of exotic European options in terms of payoffs of vanillas, different from the Carr–Madan
-
Shortfall aversion Math. Financ. (IF 2.25) Pub Date : 2020-03-04 Paolo Guasoni, Gur Huberman, Dan Ren
Shortfall aversion reflects the higher utility loss of spending cuts from a reference than the utility gain from similar spending increases. Inspired by Prospect Theory's loss aversion and the peak‐end rule, this paper posits a model of utility from spending scaled by past peak spending. In contrast to traditional models, which call for spending rates proportional to wealth, the optimal policy in this
-
Dividend policy and capital structure of a defaultable firm Math. Financ. (IF 2.25) Pub Date : 2020-03-04 Alex S. L. Tse
Default risk significantly affects the corporate policies of a firm. We develop a model in which a limited liability entity subject to default at an exponential random time jointly sets its dividend policy and capital structure to maximize the expected lifetime utility from consumption of risk‐averse equity investors. We give a complete characterization of the solution to the singular stochastic control
-
Semimartingale theory of monotone mean–variance portfolio allocation Math. Financ. (IF 2.25) Pub Date : 2020-03-04 Aleš Černý
We study dynamic optimal portfolio allocation for monotone mean–variance preferences in a general semimartingale model. Armed with new results in this area, we revisit the work of Cui et al. and fully characterize the circumstances under which one can set aside a nonnegative cash flow while simultaneously improving the mean–variance efficiency of the left‐over wealth. The paper analyzes, for the first
-
Mean‐field games with differing beliefs for algorithmic trading Math. Financ. (IF 2.25) Pub Date : 2020-02-25 Philippe Casgrain, Sebastian Jaimungal
Even when confronted with the same data, agents often disagree on a model of the real world. Here, we address the question of how interacting heterogeneous agents, who disagree on what model the real world follows, optimize their trading actions. The market has latent factors that drive prices, and agents account for the permanent impact they have on prices. This leads to a large stochastic game, where
-
A regularity structure for rough volatility Math. Financ. (IF 2.25) Pub Date : 2019-11-19 Christian Bayer, Peter K. Friz, Paul Gassiat, Jorg Martin, Benjamin Stemper
A new paradigm has emerged recently in financial modeling: rough (stochastic) volatility. First observed by Gatheral et al. in high‐frequency data, subsequently derived within market microstructure models, rough volatility captures parsimoniously key‐stylized facts of the entire implied volatility surface, including extreme skews (as observed earlier by Alòs et al.) that were thought to be outside
-
Existence of a calibrated regime switching local volatility model Math. Financ. (IF 2.25) Pub Date : 2019-11-18 Benjamin Jourdain, Alexandre Zhou
By Gyöngy's theorem, a local and stochastic volatility model is calibrated to the market prices of all European call options with positive maturities and strikes if its local volatility (LV) function is equal to the ratio of the Dupire LV function over the root conditional mean square of the stochastic volatility factor given the spot value. This leads to a stochastic differential equation (SDE) nonlinear
-
Dynamically consistent alpha‐maxmin expected utility Math. Financ. (IF 2.25) Pub Date : 2019-11-17 Patrick Beissner, Qian Lin, Frank Riedel
The alpha‐maxmin model is a prominent example of preferences under Knightian uncertainty as it allows to distinguish ambiguity and ambiguity attitude. These preferences are dynamically inconsistent for nontrivial versions of alpha. In this paper, we derive a recursive, dynamically consistent version of the alpha‐maxmin model. In the continuous‐time limit, the resulting dynamic utility function can
-
Nonlinear price impact and portfolio choice Math. Financ. (IF 2.25) Pub Date : 2019-11-11 Paolo Guasoni, Marko Hans Weber
In a market with price impact proportional to a power of the order flow, we find optimal trading policies and their implied performance for long‐term investors who have constant relative risk aversion and trade a safe asset and a risky asset following geometric Brownian motion. These quantities admit asymptotic explicit formulas up to a structural constant that depends only on the curvature of the
-
Consistency of option prices under bid-ask spreads. Math. Financ. (IF 2.25) Pub Date : 2019-11-11 Stefan Gerhold,Ismail Cetin Gülüm
Given a finite set of European call option prices on a single underlying, we want to know when there is a market model that 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
-
Semistatic and sparse variance‐optimal hedging Math. Financ. (IF 2.25) Pub Date : 2019-11-11 Paolo Di Tella, Martin Haubold, Martin Keller‐Ressel
We consider the problem of hedging a contingent claim with a “semistatic” strategy composed of a dynamic position in one asset and static (buy‐and‐hold) positions in other assets. We give general representations of the optimal strategy and the hedging error under the criterion of variance optimality and provide tractable formulas using Fourier integration in case of the Heston model. We also consider
-
Optimal equilibria for time‐inconsistent stopping problems in continuous time Math. Financ. (IF 2.25) Pub Date : 2019-11-07 Yu‐Jui Huang, Zhou Zhou
For an infinite‐horizon continuous‐time optimal stopping problem under nonexponential discounting, we look for an optimal equilibrium, which generates larger values than any other equilibrium does on the entire state space. When the discount function is log subadditive and the state process is one‐dimensional, an optimal equilibrium is constructed in a specific form, under appropriate regularity and
-
Pathwise moderate deviations for option pricing Math. Financ. (IF 2.25) Pub Date : 2019-11-07 Antoine Jacquier, Konstantinos Spiliopoulos
We provide a unifying treatment of pathwise moderate deviations for models commonly used in financial applications, and for related integrated functionals. Suitable scaling enables us to transfer these results into small‐time, large‐time, and tail asymptotics for diffusions, as well as for option prices and realized variances. In passing, we highlight some intuitive relationships between moderate deviations
-
Pricing collateralized derivatives with an arbitrary numeraire Math. Financ. (IF 2.25) Pub Date : 2019-11-06 Joanne Kennedy
Since the 2008 crisis collateralized derivatives have become commonplace in the market. There have been many papers in recent years on pricing collateralized derivatives but the topic has been surrounded by confusion with debate focusing on whether or not a risk‐free rate needs to be assumed. In addition, as pointed out by Bielecki and Rutkowski, several authors do not pay enough attention to the pricing
-
Firm capital dynamics in centrally cleared markets Math. Financ. (IF 2.25) Pub Date : 2019-11-06 Agostino Capponi, W. Allen Cheng, Sriram Rajan
We develop a tractable continuous time model of multifirm capital dynamics in a centrally cleared market. Our framework jointly models the strategic interactions between business operations of firms and their trading activities. We show that the endogenous allocation of firm capital between trading and operations can be recovered as the unique fixed point of a system of quadratic equations. Our model
Contents have been reproduced by permission of the publishers.