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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 |
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