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Pricing Financial Instruments: The Finite Difference Method
Curt Randall,Domingo Tavella +1 more
TLDR
The Pricing Equations. as mentioned in this paper and the Finite-difference method are the most commonly used methods for finite difference methods in the literature, and they can be found in:Abstract:
The Pricing Equations. Analysis of Finite Difference Methods. Special Issues. Coordinate Transformations. Numerical Examples. Index.read more
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A general framework for discretely sampled realized variance derivatives in stochastic volatility models with jumps
TL;DR: A novel and efficient transform-based method to price swaps and options related to discretely-sampled realized variance under a general class of stochastic volatility models with jumps, utilizing frame duality and density projection method combined with a novel continuous-time Markov chain (CTMC) weak approximation scheme of the underlying variance process.
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Numerical Valuation of European and American Options under Kou's Jump-Diffusion Model
TL;DR: Numerical methods are developed for pricing European and American options under Kou's jump-diffusion model, which assumes the price of the underlying asset to behave like a geometrical Brownian motion with a drift and jumps whose size is log-double-exponentially distributed, which are very efficient.
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A closed-form analytical solution for the valuation of convertible bonds with constant dividend yield
TL;DR: In this paper, a closed-form analytical solution for pricing convertible bonds on a single underlying asset with constant dividend yield is presented in the form of a Taylor's series expansion, which contains infinitely many terms and thus is completely analytical and in a closed form.
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Numerical solution of linear and nonlinear Black-Scholes option pricing equations
TL;DR: This paper deals with the numerical solution of Black-Scholes option pricing partial differential equations by means of semidiscretization technique and indicates a fourth-order discretization with respect to the underlying asset variable allows a highly accurate approximation of the solution.
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Numerical pricing of options using high-order compact finite difference schemes
TL;DR: In this paper, the authors considered high-order compact schemes for quasilinear parabolic partial differential equations to discretise the Black-Scholes PDE for the numerical pricing of European and American options.