Solving option pricing problems numerical methods form an essential part. This paper discusses five numerical methods: Black-Scholes-Merton, Monte Carlo, Binomial, Trinomial, and Finite Difference. A comparison of these methods for both European and American put options shows a graphical...

Self-propelled jumping of two polymeric droplets on superhydrophobic surfaces is investigated by three-dimensional direct numerical simulations. Two identical droplets of a viscoelastic fluid slide, meet and coalesce on a surface with contact angle 180 degrees. The droplets are modelled by the...

To investigate the coupled conduction-radiation heat transfer in C/SiC composites, a multiscale numerical method is proposed in this paper. The multiscale method combines a three-scale physical model and a multiscale mathematical method for predicting the thermal conductivity of composite...

This paper presents and compares Newton-based methods from the applied mathematics literature for solving the matrix quadratic that underlies the recursive solution of linear DSGE models. The methods are compared using nearly 100 different models from the Macroeconomic Model Data Base (MMB) and...

The convolution method for the numerical solution of forward-backward stochastic differential equations (FBSDEs) was originally formulated using Euler time discretizations and a uniform space grid. In this paper, we utilize a tree-like spatial discretization that approximates the BSDE on the...

This paper studies dynamic programming for quantile preference models, in which the agent maximizes the stream of the future τ-quantile utilities, for τ ∈ (0,1). We suggest numerical methods, based on value function iterations, for solving the quantile recursive dynamic programming, and...

"Computational Methods in Finance is a book developed from the author's courses at Columbia University and the Courant Institute of New York University. This self-contained text is designed for graduate students in financial engineering and mathematical finance, as well as practitioners in the...

Modelling correlation between financial quantities is important in the accurate pricing of financial derivatives. In this paper, we introduce some stochasticity in correlation, by considering a regime-switching correlation model, in which the transition rates between regimes are given. We...

This paper studies the econometrics of computed dynamic models. Since these models generally lack a closed-form solution, their policy functions are approximated by numerical methods. Hence, the researcher can only evaluate an approximated likelihood associated with the approximated policy...

Can boundedly rational agents survive competition with fully rational agents? The authors develop a highly nonlinear heterogeneous agents model with rational forward looking versus boundedly rational backward looking agents and evolving market shares depending on their relative performance....

We study optimal monetary policy in a flexible state-dependent pricing framework, in which monopolistic competition and stochastic menu costs are the only distortions. We show analytically that it is optimal to commit to zero inflation in the long run. Moreover, our numerical simulations...

We compare the numerical methods that are most widely applied in the computation of the standard business cycle model with flexible labor. The numerical techniques imply economically insignificant differences with regard to business cycle summary statistics except for the volatility of...

A numerical method for solving a class of fractional optimal control problems (FOCPs) is presented. First, the FOCP is transformed into an equivalent variational problem, then using Lagrange polynomials, the problem is reduced to the problem of solving a system of algebraic equations. With the...

As 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 (BSDE). We can either solve the PDE to...

Solving economic models with heterogenous agents requires computing aggregate dynamics consistent with individual behaviors. This paper introduces the ?nite volume method from the mathe-matics literature to enlarge the set of numerical methods available to compute dynamics in continuous time....

Introduction -- The Neoclassical GrowthModel Under a Constant Savings Rate -- Optimal Growth: Continuous Time Analysis -- Optimal Growth: Discrete Time Analysis -- Numerical Solution Methods -- Endogenous Growth Models -- Additional Endogenous Growth Models -- Growth in Monetary Economies:...

Cover -- Title Page -- Copyright -- Contents -- Preface -- Who Should Read this Book? -- PART A Mathematical Foundation for One‐Factor Problems -- CHAPTER 1 Real Analysis Foundations for this Book -- 1.1 Introduction and Objectives -- 1.2 Continuous Functions -- 1.2.1 Formal Definition of...

The problem of periodic flow of an incompressible fluid through a pipe, which is driven by an oscillating pressure gradient (. a reciprocating piston), is investigated in the case of a large Reynolds number. This process is described by a singularly perturbed parabolic equation with a periodic...

The numerical analysis for the systems governed by distributed models of Hopfield-type neural networks is studied. When the state space is of dimensional one, a new scheme of numerical solutions based on finite element method (FEM) is constructed, in which the Gauss-Legendre quadrature of...

Spread options are multi-asset options whose payoffs depend on the difference of two underlying financial variables. In most cases, analytically closed form solutions for pricing such payoffs are not available, and the application of numerical pricing methods turns out to be non-trivial. We...

This paper formulates and analyzes a discretization scheme for a jump-diffusion process with general state-dependent drift, volatility, jump intensity, and jump size. The jump times of the process are constructed as time-changed Poisson arrival times, and the Euler method is used to generate the...

Market option prices in last 20 years confirmed deviations from the Black and Scholes (BS) models assumptions, especially on the BS implied volatility. Implied binomial trees (IBT) models capture the variations of the implied volatility known as "volatility smile". They provide a discrete...

Improving the resilience of the economy in the face of uncertain climate change damages involves irreversible investments to scale up new technologies that are less vulnerable to the effects of climate change. The benefit of having such options includes the avoided welfare cost of diverting...

Pricing different types of derivative contracts to minimize risk is a significant step for business sustainability. Whaley (2006) refers that for the European Puts and Calls, known as vanilla options, there is a closed form solution that delivers the 'fair' price of the option with respect to...

Non-stationary income processes are standard in quantitative life-cycle models, prompted by the observation that within-cohort income inequality increases with age. This paper generalizes Tauchen (1986) and Rouwenhorst's (1995) discretization methods to non-stationary AR(1) processes. We...

We study the semilinear partial differential equation (PDE) associated with the non-linear BSDE characterizing buyer's and seller's XVA in a framework that allows for asymmetries in funding, repo and collateral rates, as well as for early contract termination due to counterparty credit risk. We...

Improving the resilience of the economy in the face of uncertain climate change damages involves irreversible investments to scale up new technologies that are less vulnerable to the effects of climate change. The benefit of having such options includes the avoided welfare cost of diverting...

We introduce a fast and widely applicable numerical pricing method that uses recursive projections. The method is based on a simple grid sampling of value functions and state-price densities. Numerical illustrations with different American and Bermudan payoffs with dividend paying stocks in the...

This paper provides an introduction to real options, as well as highlighting some important issues that are often neglected by real options analysts. While many books and surveys have been written on real options, there are some ubiquitous concepts that are not well-understood by many authors...

The widely-used estimator of Berry, Levinsohn and Pakes (1995) produces estimates of consumer preferences from a discrete-choice demand model with random coefficients, market-level demand shocks and endogenous prices. We derive numerical theory results characterizing the properties of the nested...