Multi-Asset Option Pricing Based on Exponential Lévy Process

2013 ◽  
Vol 380-384 ◽  
pp. 4537-4540
Author(s):  
Nan Liu ◽  
Mei Ling Wang ◽  
Xue Bin Lü
Keyword(s):  
Differential Equation ◽  
Fourier Transform ◽  
Option Pricing ◽  
Numerical Method ◽  
Martingale Measure ◽  
Esscher Transform ◽  
Equivalent Martingale Measure ◽  
Integro Differential Equation ◽  
Equivalent Martingale ◽  
The Fourier Transform

The multi-dimensional Esscher transform was used to find a locally equivalent martingale measure to price the options based on multi-asset. An integro-differential equation was driven for the prices of multi-asset options. The numerical method based on the Fourier transform was used to calculate some special multi-asset options in exponential Lévy models. As an example we give the calculation of extreme options.

Workspace Generation As a Diffusion Process

2000 ◽  
Author(s):  
Yunfeng Wang ◽  
Gregory S. Chirikjian
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Fourier Transform ◽  
Density Function ◽  
Type Equation ◽  
Diffusion Type ◽  
Solvable In Closed Form ◽  
Rigid Body Motions ◽  
The Fourier Transform ◽  
Kinematic Properties

Abstract In this paper we show that the workspace of a highly articulated manipulator can be found by solving a partial differential equation. This diffusion-type equation describes the evolution of the workspace density function depending on manipulator length and kinematic properties. The support of the workspace density function is the workspace of the manipulator. The PDE governing workspace density evolution is solvable in closed form using the Fourier transform on the group of rigid-body motions. We present numerical results that use this technique.

scholarly journals Regime-Switching Risk: To Price or Not to Price?

2011 ◽  
Vol 2011 ◽  
pp. 1-14 ◽  
Author(s):  
Tak Kuen Siu
Keyword(s):  
Relative Entropy ◽  
Regime Switching ◽  
Martingale Measure ◽  
Martingale Measures ◽  
Equivalent Martingale Measure ◽  
Equivalent Martingale Measures ◽  
Black Scholes ◽  
Normative Issues ◽  
Equivalent Martingale ◽  
Markovian Regime Switching

Should the regime-switching risk be priced? This is perhaps one of the important “normative” issues to be addressed in pricing contingent claims under a Markovian, regime-switching, Black-Scholes-Merton model. We address this issue using a minimal relative entropy approach. Firstly, we apply a martingale representation for a double martingale to characterize the canonical space of equivalent martingale measures which may be viewed as the largest space of equivalent martingale measures to incorporate both the diffusion risk and the regime-switching risk. Then we show that an optimal equivalent martingale measure over the canonical space selected by minimizing the relative entropy between an equivalent martingale measure and the real-world probability measure does not price the regime-switching risk. The optimal measure also justifies the use of the Esscher transform for option valuation in the regime-switching market.

Elastic stresses in rotating orthotropic discs of variable thickness

1973 ◽  
Vol 8 (3) ◽  
pp. 176-181 ◽  
Author(s):  
H V Lakshminarayana ◽  
H Srinath
Keyword(s):  
Differential Equation ◽  
Fourier Transform ◽  
Variable Thickness ◽  
Stress Function ◽  
Orthotropic Material ◽  
Elastic Stresses ◽  
Rotating Discs ◽  
Governing Differential Equation ◽  
The Fourier Transform ◽  
Thickness Function

The stress-function equation in polar co-ordinates for thin rotating discs made of orthotropic material is generalized by assuming that the variation of thickness is radial. In order to make this equation tractable, the thickness function is assumed to be hyperbolic. The resulting governing differential equation is solved in a closed from by use of the Fourier transform technique. As a numerical example, the solution is given for annular discs. Curves are included which show the effect of anisotropy and variation of thickness on the stresses and displacements. Some limiting cases are also considered.

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