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3,600
On three filtering problems arising in mathematical finance
q-fin.CP
Three situations in which filtering theory is used in mathematical finance are illustrated at different levels of detail. The three problems originate from the following different works: 1) On estimating the stochastic volatility model from observed bilateral exchange rate news, by R. Mahieu, and P. Schotman; 2) A stat...
finance
3,601
A method of moments approach to pricing double barrier contracts driven by a general class of jump diffusions
q-fin.CP
We present the method of moments approach to pricing barrier-type options when the underlying is modelled by a general class of jump diffusions. By general principles the option prices are linked to certain infinite dimensional linear programming problems. Subsequently approximating those systems by finite dimensional ...
finance
3,602
Optimal systems of subalgebras for a nonlinear Black-Scholes equation
q-fin.CP
The main object of our study is a four dimensional Lie algebra which describes the symmetry properties of a nonlinear Black-Scholes model. This model implements a feedback effect which is typical for an illiquid market. The structure of the Lie algebra depends on one parameter, i.e. we have to do with a one-parametric ...
finance
3,603
Bayesian inference with an adaptive proposal density for GARCH models
q-fin.CP
We perform the Bayesian inference of a GARCH model by the Metropolis-Hastings algorithm with an adaptive proposal density. The adaptive proposal density is assumed to be the Student's t-distribution and the distribution parameters are evaluated by using the data sampled during the simulation. We apply the method for th...
finance
3,604
Markov Chain Monte Carlo on Asymmetric GARCH Model Using the Adaptive Construction Scheme
q-fin.CP
We perform Markov chain Monte Carlo simulations for a Bayesian inference of the GJR-GARCH model which is one of asymmetric GARCH models. The adaptive construction scheme is used for the construction of the proposal density in the Metropolis-Hastings algorithm and the parameters of the proposal density are determined ad...
finance
3,605
Defaultable bonds with an infinite number of Levy factors
q-fin.CP
A market with defaultable bonds where the bond dynamics is in a Heath-Jarrow-Morton setting and the forward rates are driven by an infinite number of Levy factors is considered. The setting includes rating migrations driven by a Markov chain. All basic types of recovery are investigated. We formulate necessary and suff...
finance
3,606
On the Performance of Delta Hedging Strategies in Exponential Lévy Models
q-fin.CP
We consider the performance of non-optimal hedging strategies in exponential L\'evy models. Given that both the payoff of the contingent claim and the hedging strategy admit suitable integral representations, we use the Laplace transform approach of Hubalek et al. (2006) to derive semi-explicit formulas for the resulti...
finance
3,607
Appraisal of a contour integral method for the Black-Scholes and Heston equations
q-fin.CP
A contour integral method recently proposed by Weideman [IMA J. Numer. Anal., to appear] for integrating semi-discrete advection-diffusion PDEs, is extended for application to some of the important equations of mathematical finance. Using estimates for the numerical range of the spatial operator, optimal contour parame...
finance
3,608
Simulation de trajectoires de processus continus
q-fin.CP
Continuous time stochastic processes are useful models especially for financial and insurance purposes. The numerical simulation of such models is dependant of the time discrete discretization, of the parametric estimation and of the choice of a random number generator. The aim of this paper is to provide the tools for...
finance
3,609
Sequential optimizing investing strategy with neural networks
q-fin.CP
In this paper we propose an investing strategy based on neural network models combined with ideas from game-theoretic probability of Shafer and Vovk. Our proposed strategy uses parameter values of a neural network with the best performance until the previous round (trading day) for deciding the investment in the curren...
finance
3,610
Basket Options Valuation for a Local Volatility Jump-Diffusion Model with the Asymptotic Expansion Method
q-fin.CP
In this paper we discuss the basket options valuation for a jump-diffusion model. The underlying asset prices follow some correlated local volatility diffusion processes with systematic jumps. We derive a forward partial integral differential equation (PIDE) for general stochastic processes and use the asymptotic expan...
finance
3,611
Computational LPPL Fit to Financial Bubbles
q-fin.CP
The log-periodic power law (LPPL) is a model of asset prices during endogenous bubbles. If the on-going development of a bubble is suspected, asset prices can be fit numerically to the LPPL law. The best solutions can then indicate whether a bubble is in progress and, if so, the bubble critical time (i.e., when the bub...
finance
3,612
Indifference of Defaultable Bonds with Stochastic Intensity models
q-fin.CP
The utility-based pricing of defaultable bonds in the case of stochastic intensity models of default risk is discussed. The Hamilton-Jacobi- Bellman (HJB) equations for the value functions is derived. A finite difference method is used to solve this problem. The yield-spreads for both buyer and seller are extracted. Th...
finance
3,613
Dynamics on/in financial markets: dynamical decoupling and stylized facts
q-fin.CP
Stylized facts can be regarded as constraints for any modeling attempt of price dynamics on a financial market, in that an empirically reasonable model has to reproduce these stylized facts at least qualitatively. The dynamics of market prices is modeled on a macro-level as the result of the dynamic coupling of two dyn...
finance
3,614
Fast Correlation Greeks by Adjoint Algorithmic Differentiation
q-fin.CP
We show how Adjoint Algorithmic Differentiation (AAD) allows an extremely efficient calculation of correlation Risk of option prices computed with Monte Carlo simulations. A key point in the construction is the use of binning to simultaneously achieve computational efficiency and accurate confidence intervals. We illus...
finance
3,615
Smooth Value Functions for a Class of Nonsmooth Utility Maximization Problems
q-fin.CP
In this paper we prove that there exists a smooth classical solution to the HJB equation for a large class of constrained problems with utility functions that are not necessarily differentiable or strictly concave. The value function is smooth if admissible controls satisfy an integrability condition or if it is contin...
finance
3,616
Analysis of the sensitivity to discrete dividends : A new approach for pricing vanillas
q-fin.CP
The incorporation of a dividend yield in the classical option pricing model of Black- Scholes results in a minor modification of the Black-Scholes formula, since the lognormal dynamic of the underlying asset is preserved. However, market makers prefer to work with cash dividends with fixed value instead of a dividend y...
finance
3,617
Numerical methods for optimal insurance demand under marked point processes shocks
q-fin.CP
This paper deals with numerical solutions of maximizing expected utility from terminal wealth under a non-bankruptcy constraint. The wealth process is subject to shocks produced by a general marked point process. The problem of the agent is to derive the optimal insurance strategy which allows "lowering" the level of t...
finance
3,618
Constrained NonSmooth Utility Maximization on the Positive Real Line
q-fin.CP
We maximize the expected utility of terminal wealth in an incomplete market where there are cone constraints on the investor's portfolio process and the utility function is not assumed to be strictly concave or differentiable. We establish the existence of the optimal solutions to the primal and dual problems and their...
finance
3,619
Stability of central finite difference schemes for the Heston PDE
q-fin.CP
This paper deals with stability in the numerical solution of the prominent Heston partial differential equation from mathematical finance. We study the well-known central second-order finite difference discretization, which leads to large semi-discrete systems with non-normal matrices A. By employing the logarithmic sp...
finance
3,620
Swing Options Valuation: a BSDE with Constrained Jumps Approach
q-fin.CP
We introduce a new probabilistic method for solving a class of impulse control problems based on their representations as Backward Stochastic Differential Equations (BSDEs for short) with constrained jumps. As an example, our method is used for pricing Swing options. We deal with the jump constraint by a penalization p...
finance
3,621
The computation of Greeks with multilevel Monte Carlo
q-fin.CP
We study the use of the multilevel Monte Carlo technique in the context of the calculation of Greeks. The pathwise sensitivity analysis differentiates the path evolution and reduces the payoff's smoothness. This leads to new challenges: the inapplicability of pathwise sensitivities to non-Lipschitz payoffs often makes ...
finance
3,622
Bayesian Model Choice of Grouped t-copula
q-fin.CP
One of the most popular copulas for modeling dependence structures is t-copula. Recently the grouped t-copula was generalized to allow each group to have one member only, so that a priori grouping is not required and the dependence modeling is more flexible. This paper describes a Markov chain Monte Carlo (MCMC) method...
finance
3,623
Defaultable Bonds via HKA
q-fin.CP
To construct a no-arbitrage defaultable bond market, we work on the state price density framework. Using the heat kernel approach (HKA for short) with the killing of a Markov process, we construct a single defaultable bond market that enables an explicit expression of a defaultable bond and credit spread under quadrati...
finance
3,624
Exact Simulation of the 3/2 Model
q-fin.CP
This paper discusses the exact simulation of the stock price process underlying the 3/2 model. Using a result derived by Craddock and Lennox using Lie Symmetry Analysis, we adapt the Broadie-Kaya algorithm for the simulation of affine processes to the 3/2 model. We also discuss variance reduction techniques and find th...
finance
3,625
Analytic results and weighted Monte Carlo simulations for CDO pricing
q-fin.CP
We explore the possibilities of importance sampling in the Monte Carlo pricing of a structured credit derivative referred to as Collateralized Debt Obligation (CDO). Modeling a CDO contract is challenging, since it depends on a pool of (typically about 100) assets, Monte Carlo simulations are often the only feasible ap...
finance
3,626
Comparison of Two Numerical Methods for Computation of American Type of the Floating Strike Asian Option
q-fin.CP
We present a numerical approach for solving the free boundary problem for the Black-Scholes equation for pricing American style of floating strike Asian options. A fixed domain transformation of the free boundary problem into a parabolic equation defined on a fixed spatial domain is performed. As a result a nonlinear t...
finance
3,627
Pricing of average strike Asian call option using numerical PDE methods
q-fin.CP
In this paper, a standard PDE for the pricing of arithmetic average strike Asian call option is presented. A Crank-Nicolson Implicit Method and a Higher Order Compact finite difference scheme for this pricing problem is derived. Both these schemes were implemented for various values of risk free rate and volatility. Th...
finance
3,628
Duality and Convergence for Binomial Markets with Friction
q-fin.CP
We prove limit theorems for the super-replication cost of European options in a Binomial model with friction. The examples covered are markets with proportional transaction costs and the illiquid markets. The dual representation for the super-replication cost in these models are obtained and used to prove the limit the...
finance
3,629
Multilevel Monte Carlo method for jump-diffusion SDEs
q-fin.CP
We investigate the extension of the multilevel Monte Carlo path simulation method to jump-diffusion SDEs. We consider models with finite rate activity, using a jump-adapted discretisation in which the jump times are computed and added to the standard uniform dis- cretisation times. The key component in multilevel analy...
finance
3,630
Multiplicative noise, fast convolution, and pricing
q-fin.CP
In this work we detail the application of a fast convolution algorithm computing high dimensional integrals to the context of multiplicative noise stochastic processes. The algorithm provides a numerical solution to the problem of characterizing conditional probability density functions at arbitrary time, and we applie...
finance
3,631
Adjoints and Automatic (Algorithmic) Differentiation in Computational Finance
q-fin.CP
Two of the most important areas in computational finance: Greeks and, respectively, calibration, are based on efficient and accurate computation of a large number of sensitivities. This paper gives an overview of adjoint and automatic differentiation (AD), also known as algorithmic differentiation, techniques to calcul...
finance
3,632
Fast resolution of a single factor Heath-Jarrow-Morton model with stochastic volatility
q-fin.CP
This paper considers the single factor Heath-Jarrow-Morton model for the interest rate curve with stochastic volatility. Its natural formulation, described in terms of stochastic differential equations, is solved through Monte Carlo simulations, that usually involve rather large computation time, inefficient from a pra...
finance
3,633
Arbitrage-free Self-organizing Markets with GARCH Properties: Generating them in the Lab with a Lattice Model
q-fin.CP
We extend our studies of a quantum field model defined on a lattice having the dilation group as a local gauge symmetry. The model is relevant in the cross-disciplinary area of econophysics. A corresponding proposal by Ilinski aimed at gauge modeling in non-equilibrium pricing is realized as a numerical simulation of t...
finance
3,634
Quasi-Monte Carlo methods for the Heston model
q-fin.CP
In this paper, we discuss the application of quasi-Monte Carlo methods to the Heston model. We base our algorithms on the Broadie-Kaya algorithm, an exact simulation scheme for the Heston model. As the joint transition densities are not available in closed-form, the Linear Transformation method due to Imai and Tan, a p...
finance
3,635
Counterparty Risk Valuation: A Marked Branching Diffusion Approach
q-fin.CP
The purpose of this paper is to design an algorithm for the computation of the counterparty risk which is competitive in regards of a brute force "Monte-Carlo of Monte-Carlo" method (with nested simulations). This is achieved using marked branching diffusions describing a Galton-Watson random tree. Such an algorithm le...
finance
3,636
Fast computation of vanilla prices in time-changed models and implied volatilities using rational approximations
q-fin.CP
We present a new numerical method to price vanilla options quickly in time-changed Brownian motion models. The method is based on rational function approximations of the Black-Scholes formula. Detailed numerical results are given for a number of widely used models. In particular, we use the variance-gamma model, the CG...
finance
3,637
The potential approach in practice
q-fin.CP
The potential approach is a general and simple method for modelling interest rates, foreign exchange rates, and in principle other types of financial assets. This paper takes data on some liquid interest rate derivatives, and fits potential models using a small finite-state Markov chain as the base Markov process.
finance
3,638
Interlinkages and structural changes in cross-border liabilities: a network approach
q-fin.CP
We study the international interbank market through a geometrical and a topological analysis of empirical data. The geometrical analysis of the time series of cross-country liabilities shows that the systematic information of the interbank international market is contained in a space of small dimension, from which a to...
finance
3,639
A New Kind of Finance
q-fin.CP
Finance has benefited from the Wolfram's NKS approach but it can and will benefit even more in the future, and the gains from the influence may actually be concentrated among practitioners who unintentionally employ those principles as a group.
finance
3,640
Multilevel Monte Carlo methods for applications in finance
q-fin.CP
Since Giles introduced the multilevel Monte Carlo path simulation method [18], there has been rapid development of the technique for a variety of applications in computational finance. This paper surveys the progress so far, highlights the key features in achieving a high rate of multilevel variance convergence, and su...
finance
3,641
An Asymptotic Expansion Formula for Up-and-Out Barrier Option Price under Stochastic Volatility Model
q-fin.CP
This paper derives a new semi closed-form approximation formula for pricing an up-and-out barrier option under a certain type of stochastic volatility model including SABR model by applying a rigorous asymptotic expansion method developed by Kato, Takahashi and Yamada (2012). We also demonstrate the validity of our app...
finance
3,642
Analysis of multilevel Monte Carlo path simulation using the Milstein discretisation
q-fin.CP
The multilevel Monte Carlo path simulation method introduced by Giles ({\it Operations Research}, 56(3):607-617, 2008) exploits strong convergence properties to improve the computational complexity by combining simulations with different levels of resolution. In this paper we analyse its efficiency when using the Milst...
finance
3,643
An extension of Paulsen-Gjessing's risk model with stochastic return on investments
q-fin.CP
We consider in this paper a general two-sided jump-diffusion risk model that allows for risky investments as well as for correlation between the two Brownian motions driving insurance risk and investment return. We first introduce the model and then find the integro-differential equations satisfied by the Gerber-Shiu f...
finance
3,644
The first passage time problem for mixed-exponential jump processes with applications in insurance and finance
q-fin.CP
This paper stidies the first passage times to constant boundaries for mixed-exponential jump diffusion processes. Explicit solutions of the Laplace transforms of the distribution of the first passage times, the joint distribution of the first passage times and undershoot (overshoot) are obtained. As applications, we pr...
finance
3,645
Pricing American options via multi-level approximation methods
q-fin.CP
In this article we propose a novel approach to reduce the computational complexity of various approximation methods for pricing discrete time American options. Given a sequence of continuation values estimates corresponding to different levels of spatial approximation and time discretization, we propose a multi-level l...
finance
3,646
Pricing approximations and error estimates for local Lévy-type models with default
q-fin.CP
We find approximate solutions of partial integro-differential equations, which arise in financial models when defaultable assets are described by general scalar L\'evy-type stochastic processes. We derive rigorous error bounds for the approximate solutions. We also provide numerical examples illustrating the usefulness...
finance
3,647
Pricing TARN Using a Finite Difference Method
q-fin.CP
Typically options with a path dependent payoff, such as Target Accumulation Redemption Note (TARN), are evaluated by a Monte Carlo method. This paper describes a finite difference scheme for pricing a TARN option. Key steps in the proposed scheme involve tracking of multiple one-dimensional finite difference solutions,...
finance
3,648
A robust tree method for pricing American options with CIR stochastic interest rate
q-fin.CP
We propose a robust and stable lattice method which permits to obtain very accurate American option prices in presence of CIR stochastic interest rate without any numerical restriction on its parameters. Numerical results show the reliability and the accuracy of the proposed method.
finance
3,649
Monte Carlo approximation to optimal investment
q-fin.CP
This paper sets up a methodology for approximately solving optimal investment problems using duality methods combined with Monte Carlo simulations. In particular, we show how to tackle high dimensional problems in incomplete markets, where traditional methods fail due to the curse of dimensionality.
finance
3,650
CORN: Correlation-Driven Nonparametric Learning Approach for Portfolio Selection -- an Online Appendix
q-fin.CP
This appendix proves CORN's universal consistency. One of Bin's PhD thesis examiner (Special thanks to Vladimir Vovk from Royal Holloway, University of London) suggested that CORN is universal and provided sketch proof of Lemma 1.6, which is the key of this proof. Based on the proof in Gy\"prfi et al. [2006], we thus p...
finance
3,651
Explicit implied volatilities for multifactor local-stochastic volatility models
q-fin.CP
We consider an asset whose risk-neutral dynamics are described by a general class of local-stochastic volatility models and derive a family of asymptotic expansions for European-style option prices and implied volatilities. Our implied volatility expansions are explicit; they do not require any special functions nor do...
finance
3,652
On Modeling Economic Default Time: A Reduced-Form Model Approach
q-fin.CP
In the aftermath of the global financial crisis, much attention has been paid to investigating the appropriateness of the current practice of default risk modeling in banking, finance and insurance industries. A recent empirical study by Guo et al.(2008) shows that the time difference between the economic and recorded ...
finance
3,653
A note on Keen's model: The limits of Schumpeter's "Creative Destruction"
q-fin.CP
This paper presents a general solution for a recent model by Keen for endogenous money creation. The solution provides an analytic framework that explains all significant dynamical features of Keen's model and their parametric dependence, including an exact result for both the period and subsidence rate of the Great Mo...
finance
3,654
A hybrid approach for the implementation of the Heston model
q-fin.CP
We propose a hybrid tree-finite difference method in order to approximate the Heston model. We prove the convergence by embedding the procedure in a bivariate Markov chain and we study the convergence of European and American option prices. We finally provide numerical experiments that give accurate option prices in th...
finance
3,655
Over-the-counter market models with several assets
q-fin.CP
We study two classes of over-the-counter markets specified by systems of ODE's, in the spirit of Duffie-Garleanu-Pedersen, Econometrica, 2005. We first compute the steady states for many of these ODE's. Then we obtain the prices at which investors trade with each other at these steady states. Finally, we study the stab...
finance
3,656
A Taylor series approach to pricing and implied vol for LSV models
q-fin.CP
Using classical Taylor series techniques, we develop a unified approach to pricing and implied volatility for European-style options in a general local-stochastic volatility setting. Our price approximations require only a normal CDF and our implied volatility approximations are fully explicit (ie, they require no spec...
finance
3,657
Fast Convergence of Regress-Later Estimates in Least Squares Monte Carlo
q-fin.CP
Many problems in financial engineering involve the estimation of unknown conditional expectations across a time interval. Often Least Squares Monte Carlo techniques are used for the estimation. One method that can be combined with Least Squares Monte Carlo is the "Regress-Later" method. Unlike conventional methods wher...
finance
3,658
Asymptotic expansion for characteristic function in Heston stochastic volatility model with fast mean-reverting correction
q-fin.CP
In this note, we derive the characteristic function expansion for logarithm of the underlying asset price in corrected Heston model as proposed by Fouque and Lorig.
finance
3,659
Exact simulation pricing with Gamma processes and their extensions
q-fin.CP
Exact path simulation of the underlying state variable is of great practical importance in simulating prices of financial derivatives or their sensitivities when there are no analytical solutions for their pricing formulas. However, in general, the complex dependence structure inherent in most nontrivial stochastic vol...
finance
3,660
A central limit theorem for Latin hypercube sampling with dependence and application to exotic basket option pricing
q-fin.CP
We consider the problem of estimating $\mathbb{E} [f(U^1, \ldots, U^d)]$, where $(U^1, \ldots, U^d)$ denotes a random vector with uniformly distributed marginals. In general, Latin hypercube sampling (LHS) is a powerful tool for solving this kind of high-dimensional numerical integration problem. In the case of depende...
finance
3,661
Pricing of vanilla and first generation exotic options in the local stochastic volatility framework: survey and new results
q-fin.CP
Stochastic volatility (SV) and local stochastic volatility (LSV) processes can be used to model the evolution of various financial variables such as FX rates, stock prices, and so on. Considerable efforts have been devoted to pricing derivatives written on underliers governed by such processes. Many issues remain, thou...
finance
3,662
Computation of the "Enrichment" of a Value Functions of an Optimization Problem on Cumulated Transaction-Costs through a Generalized Lax-Hopf Formula
q-fin.CP
The Lax-Hopf formula simplifies the value function of an intertemporal optimization (infinite dimensional) problem associated with a convex transaction-cost function which depends only on the transactions (velocities) of a commodity evolution: it states that the value function is equal to the marginal fonction of a fin...
finance
3,663
Pricing of basket options I
q-fin.CP
Pricing of high-dimensional options is a deep problem of the Theoretical Financial Mathematics. In this article we present a new class of L\'{e}vy driven models of stock markets. In our opinion, any market model should be based on a transparent and intuitively easily acceptable concept. In our case this is a linear sys...
finance
3,664
Efficient tree methods for pricing digital barrier options
q-fin.CP
We propose an efficient lattice procedure which permits to obtain European and American option prices under the Black and Scholes model for digital options with barrier features. Numerical results show the accuracy of the proposed method.
finance
3,665
Estimate nothing
q-fin.CP
In the econometrics of financial time series, it is customary to take some parametric model for the data, and then estimate the parameters from historical data. This approach suffers from several problems. Firstly, how is estimation error to be quantified, and then taken into account when making statements about the fu...
finance
3,666
Accelerating Implicit Finite Difference Schemes Using a Hardware Optimized Tridiagonal Solver for FPGAs
q-fin.CP
We present a design and implementation of the Thomas algorithm optimized for hardware acceleration on an FPGA, the Thomas Core. The hardware-based algorithm combined with the custom data flow and low level parallelism available in an FPGA reduces the overall complexity from 8N down to 5N serial arithmetic operations, a...
finance
3,667
The role of information in a two-traders market
q-fin.CP
In a very simple stock market, made by only two \emph{initially equivalent} traders, we discuss how the information can affect the performance of the traders. More in detail, we first consider how the portfolios of the traders evolve in time when the market is \emph{closed}. After that, we discuss two models in which a...
finance
3,668
High-Order Splitting Methods for Forward PDEs and PIDEs
q-fin.CP
This paper is dedicated to the construction of high-order (in both space and time) finite-difference schemes for both forward and backward PDEs and PIDEs, such that option prices obtained by solving both the forward and backward equations are consistent. This approach is partly inspired by Andreasen & Huge, 2011 who re...
finance
3,669
Multilevel Monte Carlo For Exponential Lévy Models
q-fin.CP
We apply multilevel Monte Carlo for option pricing problems using exponential L\'{e}vy models with a uniform timestep discretisation to monitor the running maximum required for lookback and barrier options. The numerical results demonstrate the computational efficiency of this approach. We derive estimates of the conve...
finance
3,670
The acceptance-rejection method for low-discrepancy sequences
q-fin.CP
Generation of pseudorandom numbers from different probability distributions has been studied extensively in the Monte Carlo simulation literature. Two standard generation techniques are the acceptance-rejection and inverse transformation methods. An alternative approach to Monte Carlo simulation is the quasi-Monte Carl...
finance
3,671
Asymptotics for $d$-dimensional Lévy-type processes
q-fin.CP
We consider a general d-dimensional Levy-type process with killing. Combining the classical Dyson series approach with a novel polynomial expansion of the generator A(t) of the Levy-type process, we derive a family of asymptotic approximations for transition densities and European-style options prices. Examples of stoc...
finance
3,672
Macroprudential oversight, risk communication and visualization
q-fin.CP
This paper discusses the role of risk communication in macroprudential oversight and of visualization in risk communication. Beyond the soar in data availability and precision, the transition from firm-centric to system-wide supervision imposes vast data needs. Moreover, except for internal communication as in any orga...
finance
3,673
Leveraged {ETF} implied volatilities from {ETF} dynamics
q-fin.CP
The growth of the exhange-traded fund (ETF) industry has given rise to the trading of options written on ETFs and their leveraged counterparts {(LETFs)}. We study the relationship between the ETF and LETF implied volatility surfaces when the underlying ETF is modeled by a general class of local-stochastic volatility mo...
finance
3,674
Valuation of Barrier Options using Sequential Monte Carlo
q-fin.CP
Sequential Monte Carlo (SMC) methods have successfully been used in many applications in engineering, statistics and physics. However, these are seldom used in financial option pricing literature and practice. This paper presents SMC method for pricing barrier options with continuous and discrete monitoring of the barr...
finance
3,675
Splitting and Matrix Exponential approach for jump-diffusion models with Inverse Normal Gaussian, Hyperbolic and Meixner jumps
q-fin.CP
This paper is a further extension of the method proposed in Itkin, 2014 as applied to another set of jump-diffusion models: Inverse Normal Gaussian, Hyperbolic and Meixner. To solve the corresponding PIDEs we accomplish few steps. First, a second-order operator splitting on financial processes (diffusion and jumps) is ...
finance
3,676
Multilevel path simulation for weak approximation schemes
q-fin.CP
In this paper we discuss the possibility of using multilevel Monte Carlo (MLMC) methods for weak approximation schemes. It turns out that by means of a simple coupling between consecutive time discretisation levels, one can achieve the same complexity gain as under the presence of a strong convergence. We exemplify thi...
finance
3,677
High Performance Financial Simulation Using Randomized Quasi-Monte Carlo Methods
q-fin.CP
GPU computing has become popular in computational finance and many financial institutions are moving their CPU based applications to the GPU platform. Since most Monte Carlo algorithms are embarrassingly parallel, they benefit greatly from parallel implementations, and consequently Monte Carlo has become a focal point ...
finance
3,678
Approximating the zero-coupon bond price in a general one-factor model with constant coefficients
q-fin.CP
We consider a general one-factor short rate model, in which the instantaneous interest rate is driven by a univariate diffusion with time independent drift and volatility. We construct recursive formula for the coefficients of the Taylor expansion of the bond price and its logarithm around $\tau=0$, where $\tau$ is tim...
finance
3,679
Fast and Simple Method for Pricing Exotic Options using Gauss-Hermite Quadrature on a Cubic Spline Interpolation
q-fin.CP
There is a vast literature on numerical valuation of exotic options using Monte Carlo, binomial and trinomial trees, and finite difference methods. When transition density of the underlying asset or its moments are known in closed form, it can be convenient and more efficient to utilize direct integration methods to ca...
finance
3,680
Analysis of Spin Financial Market by GARCH Model
q-fin.CP
A spin model is used for simulations of financial markets. To determine return volatility in the spin financial market we use the GARCH model often used for volatility estimation in empirical finance. We apply the Bayesian inference performed by the Markov Chain Monte Carlo method to the parameter estimation of the GAR...
finance
3,681
Perturbation analysis of a nonlinear equation arising in the Schaefer-Schwartz model of interest rates
q-fin.CP
We deal with the interest rate model proposed by Schaefer and Schwartz, which models the long rate and the spread, defined as the difference between the short and the long rates. The approximate analytical formula for the bond prices suggested by the authors requires a computation of a certain constant, defined via a n...
finance
3,682
Exact solution of a generalized version of the Black-Scholes equation
q-fin.CP
We analyze a generalized version of the Black-Scholes equation depending on a parameter $a\!\in \!(-\infty,0)$. It satisfies the martingale condition and coincides with the Black-Scholes equation in the limit case $a\nearrow 0$. We show that the generalized equation is exactly solvable in terms of Hermite polynomials a...
finance
3,683
Valuation of Variable Annuities with Guaranteed Minimum Withdrawal and Death Benefits via Stochastic Control Optimization
q-fin.CP
In this paper we present a numerical valuation of variable annuities with combined Guaranteed Minimum Withdrawal Benefit (GMWB) and Guaranteed Minimum Death Benefit (GMDB) under optimal policyholder behaviour solved as an optimal stochastic control problem. This product simultaneously deals with financial risk, mortali...
finance
3,684
Convergence of an Euler scheme for a hybrid stochastic-local volatility model with stochastic rates in foreign exchange markets
q-fin.CP
We study the Heston-Cox-Ingersoll-Ross++ stochastic-local volatility model in the context of foreign exchange markets and propose a Monte Carlo simulation scheme which combines the full truncation Euler scheme for the stochastic volatility component and the stochastic domestic and foreign short interest rates with the ...
finance
3,685
Valuation Algorithms for Structural Models of Financial Interconnectedness
q-fin.CP
Much research in systemic risk is focused on default contagion. While this demands an understanding of valuation, fewer articles specifically deal with the existence, the uniqueness, and the computation of equilibrium prices in structural models of interconnected financial systems. However, beyond contagion research, t...
finance
3,686
Liquidity costs: a new numerical methodology and an empirical study
q-fin.CP
We consider rate swaps which pay a fixed rate against a floating rate in presence of bid-ask spread costs. Even for simple models of bid-ask spread costs, there is no explicit strategy optimizing an expected function of the hedging error. We here propose an efficient algorithm based on the stochastic gradient method to...
finance
3,687
A hybrid tree/finite-difference approach for Heston-Hull-White type models
q-fin.CP
We study a hybrid tree-finite difference method which permits to obtain efficient and accurate European and American option prices in the Heston Hull-White and Heston Hull-White2d models. Moreover, as a by-product, we provide a new simulation scheme to be used for Monte Carlo evaluations. Numerical results show the rel...
finance
3,688
Anomalous volatility scaling in high frequency financial data
q-fin.CP
Volatility of intra-day stock market indices computed at various time horizons exhibits a scaling behaviour that differs from what would be expected from fractional Brownian motion (fBm). We investigate this anomalous scaling by using empirical mode decomposition (EMD), a method which separates time series into a set o...
finance
3,689
IMEX schemes for a Parabolic-ODE system of European Options with Liquidity Shocks
q-fin.CP
The coupled system, where one is a degenerate parabolic equation and the other has not a diffusion term arises in the modeling of European options with liquidity shocks. Two implicit-explicit (IMEX) schemes that preserve the positivity of the differential problem solution are constructed and analyzed. Numerical experim...
finance
3,690
Application of Operator Splitting Methods in Finance
q-fin.CP
Financial derivatives pricing aims to find the fair value of a financial contract on an underlying asset. Here we consider option pricing in the partial differential equations framework. The contemporary models lead to one-dimensional or multidimensional parabolic problems of the convection-diffusion type and generaliz...
finance
3,691
Estimating the Algorithmic Complexity of Stock Markets
q-fin.CP
Randomness and regularities in Finance are usually treated in probabilistic terms. In this paper, we develop a completely different approach in using a non-probabilistic framework based on the algorithmic information theory initially developed by Kolmogorov (1965). We present some elements of this theory and show why i...
finance
3,692
Chebyshev Interpolation for Parametric Option Pricing
q-fin.CP
Recurrent tasks such as pricing, calibration and risk assessment need to be executed accurately and in real-time. Simultaneously we observe an increase in model sophistication on the one hand and growing demands on the quality of risk management on the other. To address the resulting computational challenges, it is nat...
finance
3,693
Approximations of Bond and Swaption Prices in a Black-Karasiński Model
q-fin.CP
We derive semi-analytic approximation formulae for bond and swaption prices in a Black-Karasi\'{n}ski interest rate model. Approximations are obtained using a novel technique based on the Karhunen-Lo\`{e}ve expansion. Formulas are easily computable and prove to be very accurate in numerical tests. This makes them usefu...
finance
3,694
Numerical analysis on local risk-minimization forexponential Lévy models
q-fin.CP
We illustrate how to compute local risk minimization (LRM) of call options for exponential L\'evy models. We have previously obtained a representation of LRM for call options; here we transform it into a form that allows use of the fast Fourier transform method suggested by Carr & Madan. In particular, we consider Mert...
finance
3,695
Portfolio Optimization under Local-Stochastic Volatility: Coefficient Taylor Series Approximations & Implied Sharpe Ratio
q-fin.CP
We study the finite horizon Merton portfolio optimization problem in a general local-stochastic volatility setting. Using model coefficient expansion techniques, we derive approximations for the both the value function and the optimal investment strategy. We also analyze the `implied Sharpe ratio' and derive a series a...
finance
3,696
Nonparametric and arbitrage-free construction of call surfaces using l1-recovery
q-fin.CP
This paper is devoted to the application of an $l_1$ -minimisation technique to construct an arbitrage-free call-option surface. We propose a nononparametric approach to obtaining model-free call option surfaces that are perfectly consistent with market quotes and free of static arbitrage. The approach is inspired from...
finance
3,697
Double-jump stochastic volatility model for VIX: evidence from VVIX
q-fin.CP
The paper studies the continuous-time dynamics of VIX with stochastic volatility and jumps in VIX and volatility. Built on the general parametric affine model with stochastic volatility and jump in logarithm of VIX, we derive a linear relation between the stochastic volatility factor and VVIX index. We detect the exist...
finance
3,698
A State-Space Estimation of the Lee-Carter Mortality Model and Implications for Annuity Pricing
q-fin.CP
In this article we investigate a state-space representation of the Lee-Carter model which is a benchmark stochastic mortality model for forecasting age-specific death rates. Existing relevant literature focuses mainly on mortality forecasting or pricing of longevity derivatives, while the full implications and methods ...
finance
3,699
New Analytical Solutions of a Modified Black-Scholes Equation with the European Put Option
q-fin.CP
Using Maple, we compute some analytical solutions of a modified Black-Scholes equation, recently proposed, in the case of the European put option. We show that the modified Black-Scholes equation with the European put option is exactly solvable in terms of associated Laguerre polynomials. We make some numerical experim...
finance