The Variance Gamma Process and Option Pricing

1998 ◽  
Vol 2 (1) ◽  
pp. 79-105 ◽  
Author(s):  
Dilip B. Madan ◽  
Peter P. Carr ◽  
Eric C. Chang
Keyword(s):  
Option Pricing ◽  
Gamma Process ◽  
Variance Gamma ◽  
Variance Gamma Process

OPTION PRICING IN THE VARIANCE-GAMMA MODEL UNDER THE DRIFT JUMP

2018 ◽  
Vol 21 (04) ◽  
pp. 1850018 ◽  
Author(s):  
ROMAN V. IVANOV
Keyword(s):  
Option Pricing ◽  
Drift Rate ◽  
Research Direction ◽  
Gamma Process ◽  
Gamma Model ◽  
Hyperbolic Functions ◽  
Variance Gamma ◽  
Variance Gamma Process ◽  
Variance Gamma Model ◽  
Analytical Expressions

This paper continues elements of the research direction of the work of Madan et al. [(1998) The variance gamma process and option pricing, European Finance Review 2, 79–105] and gives analytical expressions for the prices of digital and European call options in the variance-gamma model under the assumption that the linear drift rate of stock log-returns can suddenly jump downwards. The time of the jump is taken to be exponentially distributed. The formulas obtained require the computation of some generalized hyperbolic functions.

scholarly journals A Study of Option Pricing Using Variance Gamma Process

2012 ◽  
Vol 25 (1) ◽  
pp. 55-66
Author(s):  
Hyun-Eui Lee ◽  
Seong-Joo Song
Keyword(s):  
Option Pricing ◽  
Gamma Process ◽  
Variance Gamma ◽  
Variance Gamma Process

LOCALLY RISK-NEUTRAL VALUATION OF OPTIONS IN GARCH MODELS BASED ON VARIANCE-GAMMA PROCESS

2012 ◽  
Vol 15 (02) ◽  
pp. 1250015 ◽  
Author(s):  
LIE-JANE KAO
Keyword(s):  
Option Pricing ◽  
Sufficient Conditions ◽  
Garch Model ◽  
Gamma Process ◽  
Type Model ◽  
Underlying Asset ◽  
Variance Gamma ◽  
Variance Gamma Process ◽  
Black Scholes ◽  
Risk Neutral

This study develops a GARCH-type model, i.e., the variance-gamma GARCH (VG GARCH) model, based on the two major strands of option pricing literature. The first strand of the literature uses the variance-gamma process, a time-changed Brownian motion, to model the underlying asset price process such that the possible skewness and excess kurtosis on the distributions of asset returns are considered. The second strand of the literature considers the propagation of the previously arrived news by including the feedback and leverage effects on price movement volatility in a GARCH framework. The proposed VG GARCH model is shown to obey a locally risk-neutral valuation relationship (LRNVR) under the sufficient conditions postulated by Duan (1995). This new model provides a unified framework for estimating the historical and risk-neutral distributions, and thus facilitates option pricing calibration using historical underlying asset prices. An empirical study is performed comparing the proposed VG GARCH model with four competing pricing models: benchmark Black–Scholes, ad hoc Black–Scholes, normal NGARCH, and stochastic volatility VG. The performance of the VG GARCH model versus these four competing models is then demonstrated.

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