VIX futures and its closed‐form pricing through an affine GARCH model with realized variance

2020 ◽  
Vol 41 (1) ◽  
pp. 135-156
Author(s):  
Qi Wang ◽  
Zerong Wang
Keyword(s):  
Closed Form ◽  
Garch Model ◽  
Realized Variance ◽  
Vix Futures

Pricing the CBOE VIX Futures with the Heston-Nandi GARCH Model

2016 ◽  
Vol 37 (7) ◽  
pp. 641-659 ◽  
Author(s):  
Tianyi Wang ◽  
Yiwen Shen ◽  
Yueting Jiang ◽  
Zhuo Huang
Keyword(s):  
Garch Model ◽  
Vix Futures

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.

Pricing Bermudan Variance Swaptions Using Multinomial Trees

2019 ◽  
Keyword(s):  
Stochastic Volatility ◽  
Fair Value ◽  
Stochastic Volatility Model ◽  
Realized Variance ◽  
Variance Swaps ◽  
Early Exercise ◽  
Numerical Tests ◽  
Vix Options ◽  
Vix Futures ◽  
Volatility Model

In a recent study, Zhao et al. (2017) presented a tree methodology to evaluate the expected generalized realized variance in a general stochastic volatility model; it provided an efficient way of calculating the fair value of the strike for variance swaps. In this article, the authors expand the methodology to price nonlinear derivatives written on realized variance. They introduce a new option contract, a Bermudan variance swaption, defined as an option on variance swap with early exercise dates. Within the same framework they also show how to value forward-start variance swaps, VIX futures, and VIX options. Numerical tests show that the methodology is efficient and accurate.

Closed Form Solutions of Joint Water-Filling for Coordinated Transmission

2010 ◽  
Vol E93-B (12) ◽  
pp. 3461-3468 ◽  
Author(s):  
Bing LUO ◽  
Qimei CUI ◽  
Hui WANG ◽  
Xiaofeng TAO ◽  
Ping ZHANG
Keyword(s):  
Closed Form ◽  
Closed Form Solutions ◽  
Water Filling
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