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Brownian bridge with random length and pinning point for modelling of financial informationJul 18 2019Developed countries are increasingly relying on gas storage to ensure security of supply. In this article we consider an approach to gas storage valuation in which the information about the time at which the holder of a gas storage contract should choose ... More
A model-free backward and forward nonlinear PDEs for implied volatilityJul 17 2019We derive a backward and forward nonlinear PDEs that govern the implied volatility of a contingent claim whenever the latter is well-defined. This would include at least any contingent claim written on a positive stock price whose payoff at a possibly ... More
Neural network regression for Bermudan option pricingJul 15 2019The pricing of Bermudan options amounts to solving a dynamic programming principle , in which the main difficulty, especially in large dimension, comes from the computation of the conditional expectation involved in the continuation value. These conditional ... More
Gittins' theorem under uncertaintyJul 12 2019We study dynamic allocation problems for discrete time multi-armed bandits under uncertainty, based on the the theory of nonlinear expectations. We show that, under strong independence of the bandits and with some relaxation in the definition of optimality, ... More
Stochastic mortality models: An infinite dimensional approachJul 11 2019Demographic projections of future mortality rates involve a high level of uncertainty and require stochastic mortality models. The current paper investigates forward mortality models driven by a (possibly infinite dimensional) Wiener process and a compensated ... More
Exponential stock models driven by tempered stable processesJul 11 2019We investigate exponential stock models driven by tempered stable processes, which constitute a rich family of purely discontinuous L\'{e}vy processes. With a view of option pricing, we provide a systematic analysis of the existence of equivalent martingale ... More
Tempered stable distributions and processesJul 11 2019We investigate the class of tempered stable distributions and their associated processes. Our analysis of tempered stable distributions includes limit distributions, parameter estimation and the study of their densities. Regarding tempered stable processes, ... More
Real-world forward rate dynamics with affine realizationsJul 11 2019We investigate the existence of affine realizations for L\'{e}vy driven interest rate term structure models under the real-world probability measure, which so far has only been studied under an assumed risk-neutral probability measure. For models driven ... More
Systemic Optimal Risk Transfer EquilibriumJul 09 2019We propose a novel concept of a Systemic Optimal Risk Transfer Equilibrium (SORTE), which is inspired by the B\"uhlmann's classical notion of an Equilibrium Risk Exchange. We provide sufficient general assumptions that guarantee existence, uniqueness, ... More
Tax- and expense-modified risk-minimization for insurance payment processesJul 09 2019We study the problem of determining risk-minimizing investment strategies for insurance payment processes in the presence of taxes and expenses. We consider the situation where taxes and expenses are paid continuously and symmetrically and introduce the ... More
A Class of Solvable Multidimensional Stopping Problems in the Presence of Knightian UncertaintyJul 09 2019We investigate the impact of Knightian uncertainty on the optimal timing policy of an ambiguity averse decision maker in the case where the underlying factor dynamics follow a multidimensional Brownian motion and the exercise payoff depends on either ... More
Existence of Lévy term structure modelsJul 08 2019L\'evy driven term structure models have become an important subject in the mathematical finance literature. This paper provides a comprehensive analysis of the L\'evy driven Heath-Jarrow-Morton type term structure equation. This includes a full proof ... More
An alternative approach on the existence of affine realizations for HJM term structure modelsJul 07 2019We propose an alternative approach on the existence of affine realizations for HJM interest rate models. It is applicable to a wide class of models, and simultaneously it is conceptually rather comprehensible. We also supplement some known existence results ... More
Existence of affine realizations for Lévy term structure modelsJul 04 2019We investigate the existence of affine realizations for term structure models driven by L\'evy processes. It turns out that we obtain more severe restrictions on the volatility than in the classical diffusion case without jumps. As special cases, we study ... More
Weak Limits of Random Coefficient Autoregressive Processes and their Application in Ruin TheoryJul 03 2019We prove that a large class of discrete-time insurance surplus processes converge weakly to a generalized Ornstein-Uhlenbeck process, under a suitable re-normalization and when the time-step goes to 0. Motivated by ruin theory, we use this result to obtain ... More
Election predictions are arbitrage-free: response to TalebJul 02 2019Taleb (2018) claimed a novel approach to evaluating the quality of probabilistic election forecasts via no-arbitrage pricing techniques and argued that popular forecasts of the 2016 U.S. Presidential election had violated arbitrage boundaries. We show ... More
Compact embeddings for spaces of forward rate curvesJul 02 2019The goal of this note is to prove a compact embedding result for spaces of forward rate curves. As a consequence of this result, we show that any forward rate evolution can be approximated by a sequence of finite dimensional processes in the larger state ... More
Markovian lifts of positive semidefinite affine Volterra type processesJul 02 2019We consider stochastic partial differential equations appearing as Markovian lifts of matrix valued (affine) Volterra type processes from the point of view of the generalized Feller property (see e.g., \cite{doetei:10}). We introduce in particular Volterra ... More
Affine realizations with affine state processes for stochastic partial differential equationsJun 30 2019The goal of this paper is to clarify when a stochastic partial differential equation with an affine realization admits affine state processes. This includes a characterization of the set of initial points of the realization. Several examples, as the HJMM ... More
Existence of affine realizations for stochastic partial differential equations driven by Lévy processesJun 30 2019The goal of this paper is to clarify when a semilinear stochastic partial differential equation driven by L\'evy processes admits an affine realization. Our results are accompanied by several examples arising in natural sciences and economics.
Correlators of Polynomial ProcessesJun 26 2019A process is polynomial if its extended generator maps any polynomial to a polynomial of equal or lower degree. Then its conditional moments can be calculated in closed form, up to the computation of the exponential of the so-called generator matrix. ... More
European Option Pricing of electricity under exponential functional of Lévy processes with Price-Cap principleJun 26 2019We propose a new model for electricity pricing based on the price cap principle. The particularity of the model is that the asset price is an exponential functional of a jump L\'evy process. This model can capture both mean reversion and jumps which are ... More
Small-time and large-time smile behaviour for the Rough Heston modelJun 21 2019We characterize the asymptotic small-time and large-time implied volatility smile for the rough Heston model introduced by El Euch, Jaisson and Rosenbaum. We show that the asymptotic short-maturity smile scales in qualitatively the same way as a general ... More
Decomposition formula for rough Volterra stochastic volatility modelsJun 17 2019The research presented in this article provides an alternative option pricing approach for a class of rough fractional stochastic volatility models. These models are increasingly popular between academics and practitioners due to their surprising consistency ... More
Decomposition formula for jump diffusion modelsJun 17 2019In this paper we derive a generic decomposition of the option pricing formula for models with finite activity jumps in the underlying asset price process (SVJ models). This is an extension of the well-known result by Alos (2012) for Heston (1993) SV model. ... More
A Clark-Ocone type formula via Ito calculus and its application to financeJun 16 2019An explicit martingale representation for random variables described as a functional of a Levy process will be given. The Clark-Ocone theorem shows that integrands appeared in a martingale representation are given by conditional expectations of Malliavin ... More
Option Pricing via Multi-path Autoregressive Monte Carlo ApproachJun 15 2019The pricing of financial derivatives, which requires massive calculations and close-to-real-time operations under many trading and arbitrage scenarios, were largely infeasible in the past. However, with the advancement of modern computing, the efficiency ... More
Long-run risk sensitive dyadic impulse controlJun 14 2019In this paper long-run risk sensitive optimisation problem is studied with dyadic impulse control applied to continuous-time Feller-Markov process. In contrast to the existing literature, focus is put on unbounded and non-uniformly ergodic case by adapting ... More
Stochastic PDEs for large portfolios with general mean-reverting volatility processesJun 13 2019In this article we consider a large structural market model of defaultable assets, where the asset value processes are modelled by using stochastic volatility models with default upon hitting a lower boundary. The volatility processes are picked from ... More
Deep Smoothing of the Implied Volatility SurfaceJun 12 2019We present an artificial neural network (ANN) approach to value financial derivatives. Atypically to standard ANN applications, practitioners equally use option pricing models to validate market prices and to infer unobserved prices. Importantly, models ... More
A Top-Down Approach for the Multiple Exercises and Valuation of Employee Stock OptionsJun 09 2019We propose a new framework to value employee stock options (ESOs) that captures multiple exercises of different quantities over time. We also model the ESO holder's job termination risk and incorporate its impact on the payoffs of both vested and unvested ... More
Deep learning calibration of option pricing models: some pitfalls and solutionsJun 08 2019Recent progress in the field of artificial intelligence, machine learning and also in computer industry resulted in the ongoing boom of using these techniques as applied to solving complex tasks in both science and industry. Same is, of course, true for ... More
An optimal transport problem with backward martingale constraints motivated by insider tradingJun 07 2019We study a single-period optimal transport problem on $\mathbb{R}^2$ with a covariance-type cost function $c(x,y) = (x_1-y_1)(x_2-y_2)$ and a backward martingale constraint. We show that a transport plan $\gamma$ is optimal if and only if there is a maximal ... More
A comparison principle between rough and non-rough Heston models - with applications to the volatility surfaceJun 07 2019We present a number of related comparison results, which allow to compare moment explosion times, moment generating functions and critical moments between rough and non-rough Heston models of stochastic volatility. All results are based on a comparison ... More
Funding Adjustments in Equity Linear ProductsJun 06 2019Valuation adjustments are nowadays a common practice to include credit and liquidity effects in option pricing. Funding costs arising from collateral procedures, hedging strategies and taxes are added to option prices to take into account the production ... More
Deep PPDEs for rough local stochastic volatilityJun 06 2019We introduce the notion of rough local stochastic volatility models, extending the classical concept to the case where volatility is driven by some Volterra process. In this setting, we show that the pricing function is the solution to a path-dependent ... More
Optimal auction duration: A price formation viewpointJun 04 2019We consider an auction market in which market makers fill the order book during a given time period while some other investors send market orders. We define the clearing price of the auction as the price maximizing the exchanged volume at the clearing ... More
Fair Pricing of Variable Annuities with Guarantees under the Benchmark ApproachJun 04 2019In this paper we consider the pricing of variable annuities (VAs) with guaranteed minimum withdrawal benefits. We consider two pricing approaches, the classical risk-neutral approach and the benchmark approach, and we examine the associated static and ... More
Generalized Expected Discounted Penalty Function at General Drawdown for Lévy Risk ProcessesJun 03 2019This paper considers an insurance surplus process modeled by a spectrally negative L\'{e}vy process. Instead of the time of ruin in the traditional setting, we apply the time of drawdown as the risk indicator in this paper. We study the joint distribution ... More
Sentiment-Driven Stochastic Volatility Model: A High-Frequency Textual Tool for EconomistsMay 31 2019We propose how to quantify high-frequency market sentiment using high-frequency news from NASDAQ news platform and support vector machine classifiers. News arrive at markets randomly and the resulting news sentiment behaves like a stochastic process. ... More
Pricing of counterparty risk and funding with CSA discounting, portfolio effects and initial marginMay 27 2019Jun 29 2019In this paper we extend the existing literature on xVA along three directions. First, we extend existing BSDE-based xVA frameworks to include initial margin by following the approach of Cr\'epey (2015a) and Cr\'epey (2015b). Next, we solve the consistency ... More
Pricing of counterparty risk and funding with CSA discounting, portfolio effects and initial marginMay 27 2019In this paper we extend the existing literature on xVA along three directions. First, we extend existing BSDE-based xVA frameworks to include initial margin by following the approach of Cr\'epey (2015a) and Cr\'epey (2015b). Next, we solve the consistency ... More
Machine Learning Tree and Exact Integration for Pricing American Options in High DimensionMay 22 2019In this paper we modify the Gaussian Process Regression Monte Carlo (GPR-MC) method introduced by Gouden\`ege et al. proposing two efficient techniques which allow one to compute the price of American basket options. In particular, we consider basket ... More
Machine Learning Tree and Exact Integration for Pricing American Options in High DimensionMay 22 2019May 24 2019In this paper we modify the Gaussian Process Regression Monte Carlo (GPR-MC) method introduced by Gouden\`ege et al. proposing two efficient techniques which allow one to compute the price of American basket options. In particular, we consider basket ... More
Machine Learning for Pricing American Options in High-Dimensional Markovian and non-Markovian modelsMay 22 2019Jun 19 2019In this paper we propose two efficient techniques which allow one to compute the price of American basket options. In particular, we consider a basket of assets that follow a multi-dimensional Black-Scholes dynamics. The proposed techniques, called GPR ... More
Risk-Sensitive Credit Portfolio Optimization under Partial Information and Contagion RiskMay 20 2019This paper studies the finite time risk-sensitive portfolio optimization in a regime-switching credit market with physical and information-induced default contagion. The Markovian regime-switching process is assumed to be unobservable, which has countable ... More
Hedging crop yields against weather uncertainties -- a weather derivative perspectiveMay 18 2019The effects of weather on agriculture in recent years have become a major concern across the globe. Hence, the need for an effective weather risk management tool (weather derivatives) for agricultural stakeholders. However, most of these stakeholders ... More
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 2019Jun 26 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
The Black-Scholes Equation in Presence of ArbitrageApr 17 2019Jun 19 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
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