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Playing with ghosts in a Dynkin gameMay 16 2019We study a class of optimal stopping games (Dynkin games) of preemption type, with uncertainty about the existence of competitors. The set-up is well-suited to model, for example, real options in the context of investors who do not want to publicly reveal ... More

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

Reduced Form Capital OptimizationMay 15 2019We formulate banks' capital optimization problem as a classic mean variance optimization, by leveraging an accurate linear approximation to the Shapely or Constrained Aumann-Shapley (CAS) allocation of max or nested max cost functions. This reduced form ... More

The connection between multiple prices of an Option at a given time with single prices defined at different times: The concept of weak-value in quantum financeMay 14 2019We introduce a new tool for predicting the evolution of an option for the cases where at some specific time, there is a high-degree of uncertainty for identifying its price. We work over the special case where we can predict the evolution of the system ... 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

Approximation of Optimal Transport problems with marginal moments constraintsMay 14 2019Optimal Transport (OT) problems arise in a wide range of applications, from physics to economics. Getting numerical approximate solution of these problems is a challenging issue of practical importance. In this work, we investigate the relaxation of the ... 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

ERRATUM: Stochastic evolution equations for large portfolios of stochastic volatility modelsMay 10 2019In the article "Stochastic evolution equations for large portfolios of Stochastic Volatility models" (Arxiv:1701.05640) there is a mistake in the proof of Theorem 3.1. In this erratum we establish a weaker version of this Theorem and then we redevelop ... 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

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

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

Optimally stopping at a given distance from the ultimate supremum of a spectrally negative Lévy processApr 26 2019We consider the optimal prediction problem of stopping a spectrally negative L\'evy process as close as possible to a given distance $b \geq 0$ from its ultimate supremum, under a squared error penalty function. Under some mild conditions, the solution ... More

Prediction Law of Mixed Gaussian Volterra ProcessesApr 22 2019We study the regular conditional law of mixed Gaussian Volterra processes under the influence of model disturbances. More precisely, we study prediction of Gaussian Volterra processes driven by a Brownian motion in a case where the Brownian motion is ... 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

The Black-Scholes Equation in Presence of ArbitrageApr 17 2019We apply Geometric Arbitrage Theory to obtain results in Mathematical Finance, which do not need stochastic differential geometry in their formulation. First, for a generic market dynamics given by a multidimensional It\^o's process we specify and prove ... 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

Loss-based risk statistics with set-valued analysisApr 16 2019Since the portfolio has become a hot topic, we wii introduce a special risk statistics from the perspective of loss. This new risk statistic can be uesd for the quantification of portfolio risk. Representation results are provided. Finally, examples are ... More

Loss-based risk statistics with scenario analysisApr 16 2019Since the investors and regulators pay more attention to losses rather than gains, we will study a new class of risk statistics, named loss-based risk statistics in this paper. This new class of risk statistics can be considered as a kind of risk extension ... More

Cash sub-additive risk statistics with scenario analysisApr 16 2019Since the money is of time value, we will study a new class of risk statistics, named cash sub-additive risk statistics in this paper. This new class of risk statistics can be considered as a kind of risk extension of risk statistics introduced by Kou, ... More

Tail probabilities of random linear functions of regularly varying random vectorsApr 15 2019We provide a new extension of Breiman's Theorem on computing tail probabilities of a product of random variables to a multivariate setting. In particular, we give a complete characterization of regular variation on cones in $[0,\infty)^d$ under random ... 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

From (Martingale) Schrodinger bridges to a new class of Stochastic Volatility ModelsApr 09 2019Following closely the construction of the Schrodinger bridge, we build a new class of Stochastic Volatility Models exactly calibrated to market instruments such as for example Vanillas, options on realized variance or VIX options. These models differ ... More

A Forward Electricity Contract Price Projection: A Market Equilibrium ApproachApr 08 2019This work presents a methodology for forward electricity contract price projection based on market equilibrium and social welfare optimization. In the methodology supply and demand for forward contracts are produced in such a way that each agent (generator/load/trader) ... More

A Forward Electricity Contract Price Projection: A Market Equilibrium ApproachApr 08 2019Apr 12 2019This work presents a methodology for forward electricity contract price projection based on market equilibrium and social welfare optimization. In the methodology supply and demand for forward contracts are produced in such a way that each agent (generator/load/trader) ... 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

The Leland-Toft optimal capital structure model under Poisson observationsApr 06 2019We revisit the optimal capital structure model with endogenous bankruptcy first studied by Leland \cite{Leland94} and Leland and Toft \cite{Leland96}. Differently from the standard case, where shareholders observe continuously the asset value and bankruptcy ... More

A stochastic PDE model for limit order book dynamicsApr 05 2019We propose an analytically tractable class of models for the dynamics of a limit order book, described as the solution of a stochastic partial differential equation (SPDE) with multiplicative noise. We provide conditions under which the model admits a ... More

Probability-free models in option pricing: statistically indistinguishable dynamics and historical vs implied volatilityApr 03 2019We investigate whether it is possible to formulate option pricing and hedging models without using probability. We present a model that is consistent with two notions of volatility: a historical volatility consistent with statistical analysis, and an ... 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

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

Stacked Monte Carlo for option pricingMar 26 2019We introduce a stacking version of the Monte Carlo algorithm in the context of option pricing. Introduced recently for aeronautic computations, this simple technique, in the spirit of current machine learning ideas, learns control variates by approximating ... More

Non-traded call's volatility smilesMar 19 2019Real life hedging in the Black-Scholes model must be imperfect and if the stock's drift is higher than the risk free rate, leads to a profit on average. Hence the option price is examined as a fair game agreement between the parties, based on expected ... More

Risk and Return models for Equity Markets and Implied Equity Risk PremiumMar 18 2019Equity risk premium is a central component of every risk and return model in finance and a key input to estimate costs of equity and capital in both corporate finance and valuation. An article by Damodaran examines three broad approaches for estimating ... More

Nonlinear expectations of random setsMar 12 2019Sublinear functionals of random variables are known as sublinear expectations; they are convex homogeneous functionals on infinite-dimensional linear spaces. We extend this concept for set-valued functionals defined on measurable set-valued functions ... More

Pricing Formulae of Power Binary and Normal Distribution Standard Options and ApplicationsMar 11 2019In this paper the Buchen's pricing formulae of (higher order) asset and bond binary options are incorporated into the pricing formula of power binary options and a pricing formula of "the normal distribution standard options" with the maturity payoff ... More

Variational inequality for perpetual American option price and convergence to the solution of the difference equationMar 11 2019A variational inequality for pricing the perpetual American option and the corresponding difference equation are considered. First, the maximum principle and uniqueness of the solution to variational inequality for pricing the perpetual American option ... 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

On occupation times in the red of Lévy risk modelsMar 09 2019In this paper, we complement the existing literature on the occupation time in the red (below level $0$) of a spectrally negative L\'evy process, and later extend the analysis to the refracted spectrally negative L\'evy process. For both classes of processes, ... More

Pricing foreign exchange options under stochastic volatility and interest rates using an RBF--FD methodMar 03 2019This paper proposes a numerical method for pricing foreign exchange (FX) options in a model which deals with stochastic interest rates and stochastic volatility of the FX rate. The model considers four stochastic drivers, each represented by an It\^{o}'s ... 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

Mean-field moral hazard for optimal energy demand response managementFeb 27 2019We study the problem of demand response contracts in electricity markets by quantifying the impact of considering a mean-field of consumers, whose consumption is impacted by a common noise. We formulate the problem as a Principal-Agent problem with moral ... More

Mean-field moral hazard for optimal energy demand response managementFeb 27 2019Mar 14 2019We study the problem of demand response contracts in electricity markets by quantifying the impact of considering a mean-field of consumers, whose consumption is impacted by a common noise. We formulate the problem as a Principal-Agent problem with moral ... 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

Closed-End Formula for options linked to Target Volatility StrategiesFeb 23 2019Recent years have seen an emerging class of structured financial products based on options linked to dynamic asset allocation strategies. One of the most chosen approach is the so-called target volatility mechanism. It shifts between risky and riskless ... More

Revising SA-CCRFeb 22 2019Apr 08 2019From SA-CCR to RSA-CCR: making SA-CCR self-consistent and appropriately risk-sensitive by cashflow decomposition in a 3-Factor Gaussian Market Model

From SA-CCR to RSA-CCR: making SA-CCR self-consistent and appropriately risk-sensitive by cashflow decomposition in a 3-Factor Gaussian Market ModelFeb 22 2019SA-CCR has major issues including: lack of self-consistency for linear trades; lack of appropriate risk sensitivity (zero positions can have material add-ons; moneyness is ignored); dependence on economically-equivalent confirmations. We show that SA-CCR ... More

Non-Stationary Dividend-Price RatiosFeb 16 2019Dividend yields have been widely used in previous research to relate stock market valuations to cash flow fundamentals. However, this approach relies on the assumption that dividend yields are stationary. Due to the failure to reject the hypothesis of ... More

Supervised Deep Neural Networks (DNNs) for Pricing/Calibration of Vanilla/Exotic Options Under Various Different ProcessesFeb 15 2019We apply supervised deep neural networks (DNNs) for pricing and calibration of both vanilla and exotic options under both diffusion and pure jump processes with and without stochastic volatility. We train our neural network models under different number ... 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

Equilibrium Asset Pricing with Transaction CostsJan 30 2019We study a risk-sharing equilibrium where heterogenous agents trade subject to quadratic transaction costs. The corresponding equilibrium asset prices and trading strategies are characterised by a system of nonlinear, fully-coupled forward-backward stochastic ... 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

A closed formula for illiquid corporate bonds and an application to the European marketJan 21 2019We deduce a simple closed formula for illiquid corporate coupon bond prices when liquid bonds with similar characteristics (e.g. maturity) are present in the market for the same issuer. The key model parameter is the time-to-liquidate a position, i.e. ... More

Optimal redeeming strategy of stock loans under drift uncertaintyJan 20 2019In practice, one must recognize the inevitable incompleteness of information while making decisions. In this paper, we consider the optimal redeeming problem of stock loans under a state of incomplete information presented by the uncertainty in the (bull ... 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

Pricing path-dependent Bermudan options using Wiener chaos expansion: an embarrassingly parallel approachJan 17 2019In this work, we propose a new policy iteration algorithm for pricing Bermudan options when the payoff process cannot be written as a function of a lifted Markov process. Our approach is based on a modification of the well-known Longstaff Schwartz algorithm, ... 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

Mean-variance portfolio selection under partial information with drift uncertaintyJan 10 2019This paper studies a mean-variance portfolio selection problem under partial information with drift uncertainty. It is proved that all the contingent claims in this model are attainable in the sense of Xiong and Zhou. Further, we propose a numerical scheme ... More

Evaluation of equity-based debt obligationsJan 08 2019We consider a class of participation rights, i.e. obligations issued by a company to investors who are interested in performance-based compensation. Albeit having desirable economic properties equity-based debt obligations (EbDO) pose challenges in accounting ... More

Timing the market: the economic value of price extremesJan 07 2019By decomposing asset returns into potential maximum gain (PMG) and potential maximum loss (PML) with price extremes, this study empirically investigated the relationships between PMG and PML. We found significant asymmetry between PMG and PML. PML significantly ... 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

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.

An optimization approach to adaptive multi-dimensional capital managementDec 20 2018Firms should keep capital to offer sufficient protection against the risks they are facing. In the insurance context methods have been developed to determine the minimum capital level required, but less so in the context of firms with multiple business ... 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

Consistent Inter-Model Specification for Time-Homogeneous SPX Stochastic Volatility and VIX Market ModelsDec 14 2018This paper shows how to recover stochastic volatility models (SVMs) from market models for the VIX futures term structure. Market models have more flexibility for fitting of curves than do SVMs, and therefore they are better-suited for pricing VIX futures ... 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

Uniqueness for contagious McKean--Vlasov systems in the weak feedback regimeNov 29 2018We present a simple uniqueness argument for a collection of McKean-Vlasov problems that have seen recent interest. Our first result shows that, in the weak feedback regime, there is global uniqueness for a very general class of random drivers. By weak ... More

A Game of MartingalesNov 28 2018Dec 04 2018We consider a two player dynamic game played over $T \leq \infty$ periods. In each period each player chooses any probability distribution with support on $[0,1]$ with a given mean, where the mean is the realized value of the draw from the previous period. ... More

Option Pricing in a Regime Switching Jump Diffusion ModelNov 28 2018Feb 05 2019This paper presents the solution to a European option pricing problem by considering a regime-switching jump diffusion model of the underlying financial asset price dynamics. The regimes are assumed to be the results of an observed pure jump process, ... More

Calculating CVaR and bPOE for Common Probability Distributions With Application to Portfolio Optimization and Density EstimationNov 27 2018Feb 17 2019Conditional Value-at-Risk (CVaR) and Value-at-Risk (VaR), also called the superquantile and quantile, are frequently used to characterize the tails of probability distribution's and are popular measures of risk. Buffered Probability of Exceedance (bPOE) ... More

On the martingale property in the rough Bergomi modelNov 27 2018Dec 03 2018We consider a class of fractional stochastic volatility models (including the so-called rough Bergomi model), where the volatility is a superlinear function of a fractional Gaussian process. We show that the stock price is a true martingale if and only ... More

Representation Results for Law Invariant Recursive Dynamic Deviation Measures and Risk SharingNov 22 2018Dec 11 2018In this paper we analyze a dynamic recursive extension of the (static) notion of a deviation measure and its properties. We study distribution invariant deviation measures and show that the only dynamic deviation measure which is law invariant and recursive ... More

Fast mean-reversion asymptotics for large portfolios of stochastic volatility modelsNov 21 2018We consider a large portfolio limit where the asset prices evolve according certain stochastic volatility models with default upon hitting a lower barrier. When the asset prices and the volatilities are correlated via systemic Brownian Motions, that limit ... More

Neural Network for CVA: Learning Future ValuesNov 21 2018A new challenge to quantitative finance after the recent financial crisis is the study of credit valuation adjustment (CVA), which requires modeling of the future values of a portfolio. In this paper, following recent work in [Weinan E(2017), Han(2017)], ... More

Arbitrage Opportunities in CDS Term Structure: Theory and Implications for OTC DerivativesNov 20 2018Dec 16 2018Absence-of-Arbitrage (AoA) is the basic assumption underpinning derivatives pricing theory. As part of the OTC derivatives market, the CDS market not only provides a vehicle for participants to hedge and speculate on the default risks of corporate and ... More

On approximations of Value at Risk and Expected Shortfall involving kurtosisNov 15 2018We derive new approximations for the Value at Risk and the Expected Shortfall at high levels of loss distributions with positive skewness and excess kurtosis, and we describe their precisions for notable ones such as for exponential, Pareto type I, lognormal ... More

Analysis of the problem of intervention control in the economy on the basis of solving the problem of tuningNov 09 2018The paper proposes a new stochastic intervention control model conducted in various commodity and stock markets. The essence of the phenomenon of intervention is described in accordance with current economic theory. A review of papers on intervention ... More

The equivalence of two tax processesNov 05 2018We introduce two models of taxation, the latent and natural tax processes, which have both been used to represent loss-carry-forward taxation on the capital of an insurance company. In the natural tax process, the tax rate is a function of the current ... More

The equivalence of two tax processesNov 05 2018May 11 2019We introduce two models of taxation, the latent and natural tax processes, which have both been used to represent loss-carry-forward taxation on the capital of an insurance company. In the natural tax process, the tax rate is a function of the current ... More

Continuity of Utility Maximization under Weak ConvergenceNov 04 2018Dec 04 2018In this paper we find sufficient conditions for the continuity of the value of the utility maximization problem from terminal wealth with respect to the convergence in distribution of the underlying processes. We provide several examples which illustrate ... More

Continuity of Utility Maximization under Weak ConvergenceNov 04 2018May 03 2019In this paper we find tight sufficient conditions for the continuity of the value of the utility maximization problem from terminal wealth with respect to the convergence in distribution of the underlying processes. We also establish a weak convergence ... More

A martingale concept for non-monotone information in a jump process frameworkNov 02 2018Dec 07 2018The classical concept of martingales and compensators bases on the monotony of filtrations. This paper looks at the situation where innovations can have an expiry date such that the information dynamics becomes non-monotone. By focussing on the properties ... More

Precise asymptotics: robust stochastic volatility modelsNov 01 2018We present a new methodology to analyze large classes of (classical and rough) stochastic volatility models, with special regard to short-time and small noise formulae for option prices. Our main tool is the theory of regularity structures, which we use ... More

Forward transition ratesOct 31 2018The idea of forward rates stems from interest rate theory. It has natural connotations to transition rates in multi-state models. The generalization from the forward mortality rate in a survival model to multi-state models is non-trivial and several definitions ... More

Forward transition ratesOct 31 2018Apr 01 2019The idea of forward rates stems from interest rate theory. It has natural connotations to transition rates in multi-state models. The generalization from the forward mortality rate in a survival model to multi-state models is non-trivial and several definitions ... More

Affine Jump-Diffusions: Stochastic Stability and Limit TheoremsOct 31 2018Affine jump-diffusions constitute a large class of continuous-time stochastic models that are particularly popular in finance and economics due to their analytical tractability. Methods for parameter estimation for such processes require ergodicity in ... More

Geometrically Convergent Simulation of the Extrema of Lévy ProcessesOct 25 2018We develop a novel Monte Carlo algorithm for the simulation from the joint law of the position, the running supremum and the time of the supremum of a general L\'{e}vy process at an arbitrary finite time. We prove that the bias decays geometrically, in ... More

Term structure modeling for multiple curves with stochastic discontinuitiesOct 23 2018The goal of the paper is twofold. On the one hand, we develop the first term structure framework which takes stochastic discontinuities explicitly into account. Stochastic discontinuities are a key feature in interest rate markets, as for example the ... More

Cliquet option pricing in a jump-diffusion Lévy modelOct 23 2018We investigate the pricing of cliquet options in a jump-diffusion model. The considered option is of monthly sum cap style while the underlying stock price model is driven by a drifted L\'{e}vy process entailing a Brownian diffusion component as well ... More

Optimal electricity demand response contracting with responsiveness incentivesOct 22 2018Nov 07 2018Despite the success of demand response programs in retail electricity markets in reducing average consumption, the literature shows failure to reduce the variance of consumers' responses. This paper aims at designing demand response contracts which allow ... More

Modelling information flow in stochastic optimal control: How Meyer-$σ$-fields settle the clash between exogenous and endogenous jumpsOct 19 2018In stochastic control one seeks to find an intervention policy that optimally controls a stochastic system. Delicate issues arise when the considered system can jump due to both exogenous shocks and endogenous controls. Here one has to specify what the ... More

Optimal hedging under fast-varying stochastic volatilityOct 19 2018In a market with a rough or Markovian mean-reverting stochastic volatility there is no perfect hedge. Here it is shown how various delta-type hedging strategies perform and can be evaluated in such markets. A precise characterization of the hedging cost, ... More

Dynkin games with incomplete and asymmetric informationOct 17 2018Nov 03 2018We study Nash equilibria for a two-player zero-sum optimal stopping game with incomplete and asymmetric information. In our set-up, the drift of the underlying diffusion process is unknown to one player (incomplete information feature), but known to the ... More

Vanna-Volga Method for Normal VolatilitiesOct 17 2018Vanna-volga is a popular method for interpolation/extrapolation of volatility smiles. The technique is widely used in the FX markets context, due to its ability to consistently construct the entire lognormal smile using only three lognormal market quotes. ... More

On the sensitivity analysis of energy quanto optionsOct 12 2018In recent years there has been an advent of quanto options in energy markets. The structure of the payoff is rather a different type from other markets since it is written as a product of an underlying energy index and a measure of temperature. In the ... More

Lifting the Heston modelOct 11 2018How to reconcile the classical Heston model with its rough counterpart? We introduce a lifted version of the Heston model with n multi-factors, sharing the same Brownian motion but mean reverting at different speeds. Our model nests as extreme cases the ... More