Closed-form option pricing for exponential Lévy models: a residue approach

2021 ◽  
Author(s):  
Jean-Philippe Aguilar ◽  
Justin Kirkby
Keyword(s):  
Option Pricing ◽  
Closed Form ◽  
Exponential Lévy Models

The closed-form option pricing formulas under the sub-fractional Poisson volatility models

2021 ◽  
Vol 148 ◽  
pp. 111012
Author(s):  
XiaoTian Wang ◽  
ZiJian Yang ◽  
PiYao Cao ◽  
ShiLin Wang
Keyword(s):  
Option Pricing ◽  
Closed Form ◽  
Volatility Models

scholarly journals Option Pricing: Channels, Target Zones and Sideways Markets

2020 ◽  
pp. 25-33
Author(s):  
Zura Kakushadze
Keyword(s):  
Interest Rate ◽  
Option Pricing ◽  
Closed Form ◽  
Economic Environment ◽  
Target Zones ◽  
Long Period ◽  
Current State

After a market downturn, especially in an uncertain economic environment such as the current state, there can be a relatively long period with a sideways market, where indexes, stocks, etc., move in channels with support and resistance levels. We discuss option pricing in such scenarios, in both cases of unattainable as well as attainable boundaries, and obtain closed-form option pricing formulas. Our results also apply to FX rates in target zones without interest rate pegging (USD/HKD, digital currencies, etc.).

An Analytical Approximation for Option Price under the Affine GARCH Model - A Comparison with the Closed-Form Solution of Heston-Nandi

GIS Business ◽  
2017 ◽  
Vol 12 (4) ◽  
pp. 32-46
Author(s):  
Noureddine Lahouel ◽  
Slaheddine Hellara
Keyword(s):  
Option Pricing ◽  
Closed Form ◽  
Empirical Work ◽  
Closed Form Solution ◽  
Garch Model ◽  
Analytical Approximation ◽  
Form Solution ◽  
Option Prices ◽  
European Option ◽  
Comparative Performance

In the option pricing theory, two important approaches have been developed to evaluate the prices of a European option. The first approach develops an almost closed-form option pricing formula under a specific GARCH process (Heston & Nandi, 2000). The second approach develops an analytical approximation for computing European option prices with more widespread NGARCH models (Duan, Gauthier & Simonato, 1999). The analytical approximation was also developed under GJR-GARCH and EGARCH models by Duan, Gauthier, Sasseville & Simonato (2006). However, no empirical work was performed to study the comparative performance of these two formulas (closed-form solution and analytical approximation). Also, it is possible to develop an analytical approximation under the specific GARCH model of Heston & Nandi (2000). In this paper, we have filled up those gaps. We started with the development of an analytical approximation, for computing European option prices, under Heston-Nandis GARCH model. In the second step, we carried out a comparative analysis of the three formulas using CAC 40 index returns from 31 December 1987 to 31 December 2013.

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