Option Pricing With Application of Levy Processes and the Minimal Variance Equivalent Martingale Measure Under Uncertainty

2017 ◽  
Vol 25 (2) ◽  
pp. 402-416 ◽  
Author(s):  
Piotr Nowak ◽  
Michal Pawlowski
Keyword(s):  
Option Pricing ◽  
Lévy Processes ◽  
Levy Processes ◽  
Martingale Measure ◽  
Equivalent Martingale Measure ◽  
Minimal Variance ◽  
Equivalent Martingale

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.

scholarly journals A Stroock formula for a certain class of Lévy processes and applications to finance

2005 ◽  
Vol 2005 (3) ◽  
pp. 211-235 ◽  
Author(s):  
M. Eddahbi ◽  
J. L. Solé ◽  
J. Vives
Keyword(s):  
Local Time ◽  
Lévy Processes ◽  
Tracking Error ◽  
Levy Processes ◽  
Martingale Measure ◽  
Financial Asset ◽  
Chaos Expansion ◽  
Call Option ◽  
European Call Option ◽  
Equivalent Martingale

We find a Stroock formula in the setting of generalized chaos expansion introduced by Nualart and Schoutens for a certain class of Lévy processes, using a Malliavin-type derivative based on the chaotic approach. As applications, we get the chaotic decomposition of the local time of a simple Lévy process as well as the chaotic expansion of the price of a financial asset and of the price of a European call option. We also study the behavior of the tracking error in the discrete delta neutral hedging under both the equivalent martingale measure and the historical probability.

Specification analysis of VXX option pricing models under Lévy processes

2021 ◽  
Author(s):  
Jiling Cao ◽  
Xinfeng Ruan ◽  
Shu Su ◽  
Wenjun Zhang
Keyword(s):  
Option Pricing ◽  
Lévy Processes ◽  
Levy Processes ◽  
Pricing Models ◽  
Specification Analysis

APPROXIMATING LÉVY PROCESSES WITH A VIEW TO OPTION PRICING

2010 ◽  
Vol 13 (01) ◽  
pp. 63-91 ◽  
Author(s):  
JOHN CROSBY ◽  
NOLWENN LE SAUX ◽  
ALEKSANDAR MIJATOVIĆ
Keyword(s):  
Option Pricing ◽  
Lévy Processes ◽  
Jump Diffusion ◽  
Levy Processes ◽  
Poisson Processes ◽  
Exotic Options ◽  
Option Prices ◽  
Barrier Option ◽  
Systematic Methodology ◽  
The Mean

We examine how to approximate a Lévy process by a hyperexponential jump-diffusion (HEJD) process, composed of Brownian motion and of an arbitrary number of sums of compound Poisson processes with double exponentially distributed jumps. This approximation will facilitate the pricing of exotic options since HEJD processes have a degree of tractability that other Lévy processes do not have. The idea behind this approximation has been applied to option pricing by Asmussen et al. (2007) and Jeannin and Pistorius (2008). In this paper we introduce a more systematic methodology for constructing this approximation which allow us to compute the intensity rates, the mean jump sizes and the volatility of the approximating HEJD process (almost) analytically. Our methodology is very easy to implement. We compute vanilla option prices and barrier option prices using the approximating HEJD process and we compare our results to those obtained from other methodologies in the literature. We demonstrate that our methodology gives very accurate option prices and that these prices are more accurate than those obtained from existing methodologies for approximating Lévy processes by HEJD processes.

Asymptotic option pricing under pure-jump Lévy processes via nonlinear regression

2011 ◽  
Vol 40 (2) ◽  
pp. 227-238 ◽  
Author(s):  
Seongjoo Song ◽  
Jaehong Jeong ◽  
Jongwoo Song
Keyword(s):  
Option Pricing ◽  
Nonlinear Regression ◽  
Lévy Processes ◽  
Levy Processes

A general control variate method for option pricing under Lévy processes

2012 ◽  
Vol 221 (2) ◽  
pp. 368-377 ◽  
Author(s):  
Kemal Dinçer Dingeç ◽  
Wolfgang Hörmann
Keyword(s):  
Option Pricing ◽  
Lévy Processes ◽  
Levy Processes ◽  
General Control ◽  
Control Variate

A Spectral Element Framework for Option Pricing Under General Exponential Lévy Processes

2013 ◽  
Vol 57 (2) ◽  
pp. 390-413 ◽  
Author(s):  
Pierre Garreau ◽  
David Kopriva
Keyword(s):  
Option Pricing ◽  
Lévy Processes ◽  
Spectral Element ◽  
Levy Processes

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.

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