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Inverting the Markovian projection, with an application to local stochastic volatility modelsMay 15 2019We study two-dimensional stochastic differential equations (SDEs) of McKean--Vlasov type in which the conditional distribution of the second component of the solution given the first enters the equation for the first component of the solution. Such SDEs ... More
Asset Pricing with Heterogeneous Beliefs and IlliquidityMay 14 2019This 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 ... More
A Solvable Two-dimensional Optimal Stopping Problem in the Presence of AmbiguityMay 14 2019According to conventional wisdom, ambiguity accelerates optimal timing by decreasing the value of waiting in comparison with the unambiguous benchmark case. We study this mechanism in a multidimensional setting and show that in a multifactor model ambiguity ... More
On the consistency of jump-diffusion dynamics for FX rates under inversionMay 13 2019In this note we investigate the consistency under inversion of jump diffusion processes in the Foreign Exchange (FX) market. In other terms, if the EUR/USD FX rate follows a given type of dynamics, under which conditions will USD/EUR follow the same type ... More
Asset Pricing with General Transaction Costs: Theory and NumericsMay 13 2019We 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, the equilibrium returns mean-revert around their frictionless counterparts -- ... More
A Stock Selection Method Based on Earning Yield Forecast Using Sequence Prediction ModelsMay 13 2019Long-term investors, different from short-term traders, focus on examining the underlying forces that affect the well-being of a company. They rely on fundamental analysis which attempts to measure the intrinsic value an equity. Quantitative investment ... More
Repo convexityMay 08 2019There is an observed basis between repo discounting, implied from market repo rates, and bond discounting, stripped from the market prices of the underlying bonds. Here, this basis is explained as a convexity effect arising from the decorrelation between ... More
A class of recursive optimal stopping problems with applications to stock tradingMay 07 2019In this paper we introduce and solve a class of optimal stopping problems of recursive type. In particular, the stopping payoff depends directly on the value function of the problem itself. In a multi-dimensional Markovian setting we show that the problem ... More
A Binomial Asset Pricing Model in a Categorical SettingMay 06 2019Adachi and Ryu introduced a category Prob of probability spaces whose objects are all probability spaces and whose arrows correspond to measurable functions satisfying an absolutely continuous requirement in [Adachi and Ryu, 2019]. In this paper, we develop ... More
Fundamental Theorem of Asset Pricing under fixed and proportional transaction costsMay 06 2019We show that the lack of arbitrage in a model with both fixed and proportional transaction costs is equivalent to the existence of a family of absolutely continuous single-step probability measures together with an adapted process between the bid-ask ... More
Fundamental Theorem of Asset Pricing under fixed and proportional transaction costsMay 06 2019May 08 2019We show that the lack of arbitrage in a model with both fixed and proportional transaction costs is equivalent to the existence of a family of absolutely continuous single-step probability measures, together with an adapted process with values between ... More
Model-free pricing and hedging in discrete time using rough path signaturesMay 05 2019We make use of a family of primitive securities, in the spirit of Arrow-Debreu, to price and hedge in a model-free way path-dependent exotic derivatives in discrete time. These primitive securities are called signature payoffs. First, we show that cash ... More
Efficient Computation of Various Valuation Adjustments Under Local Lévy ModelsMay 05 2019Various valuation adjustments, or XVAs, can be written in terms of non-linear PIDEs equivalent to FBSDEs. In this paper we develop a Fourier-based method for solving FBSDEs in order to efficiently and accurately price Bermudan derivatives, including options ... More
Nonparametric pricing and hedging of exotic derivativesMay 02 2019In the spirit of Arrow-Debreu, we introduce a family of financial derivatives that act as primitive securities in that exotic derivatives can be approximated by their linear combinations. We call these financial derivatives signature payoffs. We show ... More
Risk measures and progressive enlargement of filtration: a BSDE approachApr 30 2019We consider dynamic risk measures induced by Backward Stochastic Differential Equations (BSDE) in enlargement of filtration setting. On a fixed probability space, we are given a standard Brownian motion and a pair of random variables $(\tau, \zeta) \in ... More
Pricing and hedging of VIX options for Barndorff-Nielsen and Shephard modelsApr 28 2019The VIX call options for the Barndorff-Nielsen and Shephard models will be discussed. Derivatives written on the VIX, which is the most popular volatility measurement, have been traded actively very much. In this paper, we give representations of the ... More
Risk-neutral pricing for APTApr 25 2019We consider the problem of super-replication (hedging without risk) for the Arbitrage Pricing Theory. The dual characterization of super-replication cost is provided. It is shown that the reservation prices of investors converge to this cost as their ... More
A neural network-based framework for financial model calibrationApr 23 2019A data-driven approach called CaNN (Calibration Neural Network) is proposed to calibrate financial asset price models using an Artificial Neural Network (ANN). Determining optimal values of the model parameters is formulated as training hidden neurons ... More
Optimal valuation of American callable credit default swaps under drawdownApr 22 2019This paper discusses the valuation of credit default swaps, where default is announced when the reference asset price has gone below certain level from the last record maximum, also known as the high-water mark or drawdown. We assume that the protection ... More
Certainty Equivalent and Utility Indifference Pricing for Incomplete Preferences via Convex Vector OptimizationApr 20 2019For incomplete preference relations that are represented by multiple priors and/or multiple -- possibly multivariate -- utility functions, we define a certainty equivalent as well as the utility buy and sell prices and indifference price bounds as set-valued ... More
Horizon-unbiased Investment with AmbiguityApr 20 2019In the presence of ambiguity on the driving force of market randomness, we consider the dynamic portfolio choice without any predetermined investment horizon. The investment criteria is formulated as a robust forward performance process, reflecting an ... More
ADOL - Markovian approximation of rough lognormal modelApr 19 2019In this paper we apply Markovian approximation of the fractional Brownian motion (BM), known as the Dobric-Ojeda (DO) process, to the fractional stochastic volatility model where the instantaneous variance is modelled by a lognormal process with drift ... More
No-arbitrage with multiple-priors in discrete timeApr 18 2019We investigate different notions of arbitrage in a multiple-priors setting in discrete time. We revisit the so-called quasi-sure no-arbitrage condition and prove a geometric and a quantitative version of it. We also study three alternative notions and ... More
Averaging plus Learning in financial marketsApr 17 2019This paper develops original models to study interacting agents in financial markets. The key feature of these models is how interactions are formulated and analysed. Agents learn from their observations and learning ability to interpret news or private ... More
Optimal loss-carry-forward taxation for Lévy risk processes stopped at general draw-down timeApr 17 2019Motivated by Kyprianou and Zhou (2009), Wang and Hu (2012), Avram et al. (2017), Li et al. (2017) and Wang and Zhou (2018), we consider in this paper the problem of maximizing the expected accumulated discounted tax payments of an insurance company, whose ... More
From multi-dimensional black scholes to Hamilton jacobiApr 16 2019The first widely used financial model is linked to dynamical Hamilton jacobi model
Behaving Optimally in Solar Renewable Energy Certificate MarketsApr 12 2019Solar Renewable Energy Certificate Markets (SREC) markets are a relatively novel market-based system to incentivize the production of energy from solar means. A regulator imposes a floor on the amount of energy each regulated firm must generate from solar ... More
Deep-learning based numerical BSDE method for barrier optionsApr 11 2019As is known, an option price is a solution to a certain partial differential equation (PDE) with terminal conditions (payoff functions). There is a close association between the solution of PDE and the solution of a backward stochastic differential equation ... More
Theory of Cryptocurrency Interest RatesApr 10 2019A term structure model in which the short rate is zero is developed as a candidate for a theory of cryptocurrency interest rates. The price processes of crypto discount bonds are worked out, along with expressions for the instantaneous forward rates and ... More
Theory of Cryptocurrency Interest RatesApr 10 2019May 10 2019A term structure model in which the short rate is zero is developed as a candidate for a theory of cryptocurrency interest rates. The price processes of crypto discount bonds are worked out, along with expressions for the instantaneous forward rates and ... More
Optimal excess-of-loss reinsurance for stochastic factor risk modelsApr 10 2019We study the optimal excess-of-loss reinsurance problem when both the intensity of the claims arrival process and the claim size distribution are influenced by an exogenous stochastic factor. We assume that the insurer's surplus is governed by a marked ... More
Martingale Optimal Transport DualityApr 09 2019We obtain a dual representation of the Kantorovich functional defined for functions on the Skorokhod space using quotient sets. Our representation takes the form of a Choquet capacity generated by martingale measures satisfying additional constraints ... More
A new median-based formula for the Black-Scholes-Merton TheoryApr 09 2019The Black-Scholes-Merton (BSM) theory for price variation has been well established in mathematical financial engineering. However, it has been recognized that long-term outcomes in practice may divert from the Black-Scholes formula, which is the expected ... More
Stability of martingale optimal transport and weak optimal transportApr 08 2019Under mild regularity assumptions, the transport problem is stable in the following sense: if a sequence of optimal transport plans $\pi_1, \pi_2, \ldots$ converges weakly to a transport plan $\pi$, then $\pi$ is also optimal (between its marginals). ... More
Term Structure Modeling under Volatility Uncertainty: A Forward Rate Model driven by G-Brownian MotionApr 05 2019We show how to set up a forward rate model in the presence of volatility uncertainty by using the theory of G-Brownian motion. In order to formulate the model, we extend the G-framework to integration with respect to two integrators and prove a version ... More
Forward Rank-Dependent Performance Criteria: Time-Consistent Investment Under Probability DistortionApr 03 2019We introduce the concept of forward rank-dependent performance processes, 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 ... More
Game of Variable Contributions to the Common Good under UncertaintyMar 31 2019We consider a stochastic game of contribution to the common good in which the players have continuous control over the degree of contribution, and we examine the gradualism arising from the free rider effect. This game belongs to the class of variable ... More
Price equations with symmetric supply/demand; implications for fat tailsMar 30 2019Implementing a set of microeconomic criteria, we develop price dynamics equations using a function of demand/supply with key symmetry properties. The function of demand/supply can be linear or nonlinear. The type of function determines the nature of the ... More
Optimal stopping for the exponential of a Brownian bridgeMar 29 2019In this paper we study the problem of stopping a Brownian bridge $X$ in order to maximise the expected value of an exponential gain function. In particular, we solve the stopping problem $$\sup_{0\le \tau\le 1}\E[\mathrm{e}^{X_\tau}]$$ which was posed ... More
Optimal Reinsurance and Investment in a Diffusion ModelMar 29 2019We consider a diffusion approximation to an insurance risk model where an external driver models a stochastic environment. The insurer can buy reinsurance. Moreover, investment in a financial market is possible. The financial market is also driven by ... More
Short Selling with Margin Risk and Recall RiskMar 28 2019Short sales are regarded as negative purchases in textbook asset pricing theory. In reality, however, the symmetry between purchases and short sales is broken by a variety of costs and risks peculiar to the latter. We formulate an optimal stopping model ... More
Modern Asset Theory: A Framework for Successful Active ManagementMar 22 2019Active management is a term that has many meanings and we have found the defining characteristics needed for success as an "active manager" elusive within the literature. In this paper we offer a set of criteria that defines an active manager and his ... More
Epstein-Zin Utility Maximization on Random HorizonsMar 21 2019This paper solves the consumption-investment problem with Epstein-Zin utility on a random horizon. In an incomplete market, we take the random horizon to be a stopping time adapted to the market filtration, generated by all observable, but not necessarily ... More
Computation of systemic risk measures: a mixed-integer linear programming approachMar 20 2019Systemic risk is concerned with the instability of a financial system whose members are interdependent in the sense that the failure of a few institutions may trigger a chain of defaults throughout the system. Recently, several systemic risk measures ... More
A fast method for pricing American options under the variance gamma modelMar 18 2019We investigate methods for pricing American options under the variance gamma model. The variance gamma process is a pure jump process which is constructed by replacing the calendar time by the gamma time in a Brownian motion with drift, which makes it ... More
Semimartingale theory of monotone mean--variance portfolio allocationMar 16 2019We 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, Li, Wang and Zhu (2012, MAFI) and fully characterize the circumstances ... More
A lending scheme for a system of interconnected banks with probabilistic constraints of failureMar 14 2019We derive a closed form solution for an optimal control of interbank lending subject to terminal probability constraints on the failure of a bank. The solution can be applied to a network of banks providing a general solution when aforementioned probability ... More
Derivative of a Conic Problem with a Unique SolutionMar 13 2019We view a conic optimization problem that has a unique solution as a map from its data to its solution. If sufficient regularity conditions hold at a solution point, namely that the implicit function theorem applies to the normalized residual function ... More
Derivative of a Conic Problem with a Unique SolutionMar 13 2019Mar 15 2019We view a conic optimization problem that has a unique solution as a map from its data to its solution. If sufficient regularity conditions hold at a solution point, namely that the implicit function theorem applies to the normalized residual function ... More
Derivative of a Conic Problem with a Unique SolutionMar 13 2019Mar 27 2019We view a conic optimization problem that has a unique solution as a map from its data to its solution. If sufficient regularity conditions hold at a solution point, namely that the implicit function theorem applies to the normalized residual function ... More
The fractional and mixed-fractional CEV modelMar 13 2019The continuous observation of the financial markets has identified some 'stylized facts' which challenge the conventional assumptions, promoting the born of new approaches. On one hand, the long range dependence has been faced replacing the traditional ... More
Optimal Information Acquisition and Consumption Under Habit Formation PreferenceMar 11 2019We consider a model of two-stage optimal decision making involving pure information learning beforehand and dynamic consumption afterwards: in stage-1 from initial time to a chosen stopping time, the individual investor has access to full market information ... More
Affine term structure models : a time-changed approach with perfect fit to market curvesMar 11 2019We address the so-called calibration problem which consists of fitting in a tractable way a given model to a specified term structure like, e.g., yield or default probability curves. Time-homogeneous jump-diffusions like Vasicek or Cox-Ingersoll-Ross ... More
Affine term structure models : a time-changed approach with perfect fit to market curvesMar 11 2019Mar 18 2019We address the so-called calibration problem which consists of fitting in a tractable way a given model to a specified term structure like, e.g., yield or default probability curves. Time-homogeneous jump-diffusions like Vasicek or Cox-Ingersoll-Ross ... More
Fine Properties of the Optimal Skorokhod Embedding ProblemMar 09 2019We study the problem of stopping a Brownian motion at a given distribution $\nu$ while optimizing a reward function that depends on the (possibly randomized) stopping time and the Brownian motion. Our first result establishes that the set $\mathcal{T}(\nu)$ ... More
Asymptotics for volatility derivatives in multi-factor rough volatility modelsMar 07 2019We present small-time implied volatility asymptotics for Realised Variance (RV) and VIX options for a number of (rough) stochastic volatility models via large deviations principle. We provide numerical results along with efficient and robust numerical ... More
Asymptotics for volatility derivatives in multi-factor rough volatility modelsMar 07 2019Mar 22 2019We present small-time implied volatility asymptotics for Realised Variance (RV) and VIX options for a number of (rough) stochastic volatility models via large deviations principle. We provide numerical results along with efficient and robust numerical ... More
Strict Local Martingales and the Khasminskii test for ExplosionsMar 06 2019We exhibit sufficient conditions such that components of a multidimensional SDE giving rise to a local martingale $M$ are strict local martingales or martingales. We assume that the equations have diffusion coefficients of the form $\sigma(M_t,v_t),$ ... More
Cover's Rebalancing Option With Discrete Hindsight OptimizationMar 03 2019We study T. Cover's rebalancing option (Ordentlich and Cover 1998) under discrete hindsight optimization in continuous time. The payoff in question is equal to the final wealth that would have accrued to a $\$1$ deposit into the best of some finite set ... More
Non-Parametric Robust Model Risk Measurement with Path-Dependent Loss FunctionsMar 02 2019Understanding and measuring model risk is important to financial practitioners. However, there lacks a non-parametric approach to model risk quantification in a dynamic setting and with path-dependent losses. We propose a complete theory generalizing ... More
A convex duality approach for pricing contingent claims under partial information and short selling constraintsFeb 27 2019We consider the pricing problem facing a seller of a contingent claim. We assume that this seller has some general level of partial information, and that he is not allowed to sell short in certain assets. This pricing problem, which is our primal problem, ... More
Fair Capital Risk AllocationFeb 26 2019In this paper we develop a novel methodology for estimation of risk capital allocation. The methodology is rooted in the theory of risk measures. We work within a general, but tractable class of law-invariant coherent risk measures, with a particular ... More
Multiscale Asymptotic Analysis for Portfolio Optimization under Stochastic EnvironmentFeb 19 2019Empirical studies indicate the presence of multi-scales in the volatility of underlying assets: a fast-scale on the order of days and a slow-scale on the order of months. In our previous works, we have studied the portfolio optimization problem in a Markovian ... More
Elicitability of Range Value at RiskFeb 12 2019The predictive performance of point forecasts for a statistical functional, such as the mean, a quantile, or a certain risk measure, is commonly assessed in terms of scoring (or loss) functions. A scoring functions should be (strictly) consistent for ... More
Elicitability of Range Value at RiskFeb 12 2019Mar 26 2019The predictive performance of point forecasts for a statistical functional, such as the mean, a quantile, or a certain risk measure, is commonly assessed in terms of scoring (or loss) functions. A scoring function should be (strictly) consistent for the ... More
Implementation of a Port-graph Model for FinanceFeb 06 2019In this paper we examine the process involved in the design and implementation of a port-graph model to be used for the analysis of an agent-based rational negligence model. Rational negligence describes the phenomenon that occurred during the financial ... More
Foundations of a pathwise volatility framework with explicit fast reversion limitsFeb 05 2019Our first main results are the existence and uniqueness of solutions to a `generalised CIR initial-value problem', which originates from the classical Cox-Ingersoll-Ross (CIR) stochastic differential equation after a time-change. These results hold on ... More
Strong convergence rates for Markovian representations of fractional Brownian motionFeb 04 2019Feb 15 2019Fractional Brownian motion can be represented as an integral over a family of Ornstein-Uhlenbeck processes. This representation naturally lends itself to numerical discretizations, which are shown in this paper to have strong convergence rates of arbitrarily ... More
Strong convergence rates for numerical approximations of fractional Brownian motionFeb 04 2019Fractional Brownian motion can be represented as an integral over a family of Ornstein-Uhlenbeck processes. This representation naturally lends itself to numerical discretizations, which are shown in this paper to have strong convergence rates of arbitrarily ... More
Optimal market making under partial information with general intensitiesFeb 04 2019Starting from the Avellaneda--Stoikov framework, we consider a market maker who wants to optimally set bid/ask quotes over a finite time interval, to maximize her expected utility. The intensities of the orders she receives depend not only on the spreads ... More
The Applications of Graph Theory to InvestingFeb 02 2019How can graph theory be applied to investing in the stock market? The answer may help investors realize the true risks of their investments, help prevent recessions like that of 2008, and increase financial literacy amongst students. Using several original ... More
Deep Learning VolatilityJan 28 2019We present a consistent neural network based calibration method for a number of volatility models -- including the rough volatility family -- that performs the calibration task within a few milliseconds for the full implied volatility surface. The aim ... More
Stochastic control in high-dimensional statistical arbitrage under an Ornstein-Uhlenbeck processJan 27 2019The present paper aims to provide the first systematic study of high-dimensional statistical arbitrage using both factor models and tools from stochastic control theory, obtaining closed-form optimal strategies in most cases and extending in multiple ... More
Erratum: Higher Order Elicitability and Osband's PrincipleJan 25 2019This note corrects conditions in Proposition 3.4 and Theorem 5.2(ii) and comments on imprecisions in Propositions 4.2 and 4.4 in Fissler and Ziegel (2016).
Lattice investment projects support process model with corruptionJan 25 2019Lattice investment projects support process model with corruption is formulated and analyzed. The model is based on the Ising lattice model of ferromagnetic but takes deal with the social phenomenon. Set of corruption agents is considered. It is supposed ... More
Adapted Wasserstein Distances and Stability in Mathematical FinanceJan 22 2019Assume that an agent models a financial asset through a measure Q with the goal to price / hedge some derivative or optimize some expected utility. Even if the model Q is chosen in the most skilful and sophisticated way, she is left with the possibility ... More
Option Pricing in Illiquid Markets with JumpsJan 19 2019The classical linear Black--Scholes model for pricing derivative securities is a popular model in financial industry. It relies on several restrictive assumptions such as completeness, and frictionless of the market as well as the assumption on the underlying ... More
Conditional Optimal Stopping: A Time-Inconsistent OptimizationJan 17 2019Inspired by recent work of P.-L. Lions on conditional optimal control, we introduce a problem of optimal stopping under bounded rationality: the objective is the expected payoff at the time of stopping, conditioned on another event. For instance, an agent ... More
Instantaneous Arbitrage and the CAPMJan 16 2019This paper studies the concept of instantaneous arbitrage in continuous time and its relation to the instantaneous CAPM. Absence of instantaneous arbitrage is equivalent to the existence of a trading strategy which satisfies the CAPM beta pricing relation ... More
Acquisition of Project-Specific Assets with Bayesian UpdatingJan 14 2019We study the impact of learning on the optimal policy and the time-to-decision in an infinite-horizon Bayesian sequential decision model with two irreversible alternatives, exit and expansion. In our model, a firm undertakes a small-scale pilot project ... More
A Risk-Sharing Framework of Bilateral ContractsJan 12 2019We propose a risk-sharing framework for bilateral contracts to find the optimal pair, initial price and amount of collateral, with presence of default risks, collateral, and funding spreads. The derived optimal collateral can be used for contracts between ... More
On the bail-out dividend problem for spectrally negative Markov additive modelsJan 10 2019Jan 31 2019This paper studies the bail-out optimal dividend problem with regime switching under the constraint that the cumulative dividend strategy is absolutely continuous. We confirm the optimality of the regime-modulated refraction-reflection strategy when the ... More
Jump-telegraph models for the short rate: pricing and convexity adjustments of zero coupon bondsJan 10 2019In this article, we consider a Markov-modulated model with jumps for short rate dynamics. We obtain closed formulas for the term structure and forward rates using the properties of the jump-telegraph process and the expectation hypothesis. The results ... More
A dynamic dual representation of the buyer's price of American options in nonlinear incomplete marketsJan 08 2019In this paper we study the problem of nonlinear pricing of an American option with a right-continuous left-limited (RCLL) payoff process in an incomplete market with default, from the buyer's point of view. We show that the buyer's price process can be ... More
A Conjecture Involving Positive Solutions of a Simple Scalar Linear Time-Varying State Equation with DelayJan 08 2019A simple conjecture is presented concerning positive solutions of a scalar, time-varying, linear state equation with delay. Although the equation arises in the context of stock trading, no knowledge of finance is needed in the analysis to follow. Starting ... More
Evaluating betting odds and free coupons using desirabilityJan 07 2019In the UK betting market, bookmakers often offer a free coupon to new customers. These free coupons allow the customer to place extra bets, at lower risk, in combination with the usual betting odds. We are interested in whether a customer can exploit ... More
Invest or Exit? Optimal Decisions in the Face of a Declining Profit StreamJan 06 2019Even in the face of deteriorating and highly volatile demand, firms often invest in, rather than discard, aging technologies. In order to study this phenomenon, we model the firm's profit stream as a Brownian motion with negative drift. At each point ... More
Optimal execution with dynamic risk adjustmentJan 03 2019This paper considers the problem of optimal liquidation of a position in a risky security in a financial market, where price evolution are risky and trades have an impact on price as well as uncertainty in the filling orders. The problem is formulated ... More
Optimal execution with dynamic risk adjustmentJan 03 2019May 03 2019This paper considers the problem of optimal liquidation of a position in a risky security in a financial market, where price evolution are risky and trades have an impact on price as well as uncertainty in the filling orders. The problem is formulated ... More
Consumption, Investment, and Healthcare with AgingJan 02 2019Jan 07 2019This paper solves the problem of optimal dynamic consumption, investment, and healthcare spending with isoelastic utility, when natural mortality grows exponentially to reflect Gompertz' law and investment opportunities are constant. Healthcare slows ... More
Equilibrium price and optimal insider trading strategy under stochastic liquidity with long memoryJan 02 2019Jan 07 2019In this paper, the Kyle model of insider trading is extended by characterizing the trading volume with long memory and allowing the noise trading volatility to follow a general stochastic process. Under this newly revised model, the equilibrium conditions ... More
The robust superreplication problem: a dynamic approachDec 28 2018Feb 15 2019In the frictionless discrete time financial market of Bouchard et al.(2015) we consider a trader who, due to regulatory requirements or internal risk management reasons, is required to hedge a claim $\xi$ in a risk-conservative way relative to a family ... More
The robust superreplication problem: a dynamic approachDec 28 2018In the frictionless discrete time financial market of Bouchard et al.(2015) we consider a trader who, due to regulatory requirements or internal risk management reasons, is required to hedge a claim $\xi$ in a risk-conservative way relative to a family ... More
Predicting the Stock Price of Frontier Markets Using Modified Black-Scholes Option Pricing Model and Machine LearningDec 27 2018The Black-Scholes Option pricing model (BSOPM) has long been in use for valuation of equity options to find the prices of stocks. In this work, using BSOPM, we have come up with a comparative analytical approach and numerical technique to find the price ... More
Characterization of the Ito IntegralDec 23 2018This paper provides an existence-and-uniqueness theorem characterizing the stochastic integral with respect to a Wiener process. The integral is represented as a mapping from the space of measurable and adapted pathwise locally integrable processes to ... More
Affine Rough ModelsDec 20 2018The goal of this survey article is to explain and elucidate the affine structure of recent models appearing in the rough volatility literature, and show how it leads to exponential-affine transform formulas.
Closed-form expansions for option prices with respect to the mixing solutionDec 19 2018Feb 14 2019We consider closed-form expansions for European put option prices within several stochastic volatility frameworks with time-dependent parameters. Our methodology involves writing the put option price as an expectation of a Black-Scholes formula and performing ... More
Closed-form expansions for option prices with respect to the mixing solutionDec 19 2018We consider closed-form expansions for European put option prices within several stochastic volatility frameworks with time-dependent parameters. Our methodology involves writing the put option price as an expectation of a Black-Scholes formula and performing ... More
Network Effects and Default Clustering for Large PortfoliosDec 18 2018We consider a large collection of dynamically interacting components defined on a weighted directed graph determining the impact of default of one component to another one. We prove a law of large numbers for the empirical measure capturing the evolution ... More
Path Dependent Optimal Transport and Model Calibration on Exotic DerivativesDec 09 2018In this paper, we introduce and develop the theory of semimartingale optimal transport in a path dependent setting. Instead of the classical constraints on marginal distributions, we consider a general framework of path dependent constraints. Duality ... More