Pricing Vix Options with Stochastic Volatility and Random Jumps

2012 ◽  
Author(s):  
Guang-Hua Lian ◽  
Song-Ping Zhu
Keyword(s):  
Stochastic Volatility ◽  
Vix Options ◽  
Random Jumps

scholarly journals PRICING AND HEDGING OF VIX OPTIONS FOR BARNDORFF-NIELSEN AND SHEPHARD MODELS

2019 ◽  
Vol 22 (08) ◽  
pp. 1950043 ◽  
Author(s):  
TAKUJI ARAI
Keyword(s):  
Fourier Transform ◽  
Stochastic Volatility ◽  
Numerical Experiments ◽  
Option Price ◽  
Call Option ◽  
Stochastic Volatility Models ◽  
Risky Assets ◽  
Volatility Models ◽  
Vix Options ◽  
Non Gaussian

The VIX call options for the Barndorff-Nielsen and Shephard models will be discussed. Derivatives written on the VIX, which is the most popular volatility measurement, have been traded actively very much. In this paper, we give representations of the VIX call option price for the Barndorff-Nielsen and Shephard models: non-Gaussian Ornstein–Uhlenbeck type stochastic volatility models. Moreover, we provide representations of the locally risk-minimizing strategy constructed by a combination of the underlying riskless and risky assets. Remark that the representations obtained in this paper are efficient to develop a numerical method using the fast Fourier transform. Thus, numerical experiments will be implemented in the last section of this paper.

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.

Joint pricing of VIX and SPX options with stochastic volatility and jump models

2015 ◽  
Vol 16 (1) ◽  
pp. 27-48 ◽  
Author(s):  
Thomas Kokholm ◽  
Martin Stisen
Keyword(s):  
Stochastic Volatility ◽  
Stochastic Volatility Model ◽  
Heston Model ◽  
Option Markets ◽  
Content Type ◽  
Volatility Index ◽  
Vix Options ◽  
Vix Futures ◽  
Volatility Model ◽  
Joint Pricing

Purpose – This paper studies the performance of commonly employed stochastic volatility and jump models in the consistent pricing of The CBOE Volatility Index (VIX) and The S&P 500 Index (SPX) options. With the existence of active markets for volatility derivatives and options on the underlying instrument, the need for models that are able to price these markets consistently has increased. Although pricing formulas for VIX and vanilla options are now available for commonly used models exhibiting stochastic volatility and/or jumps, it remains to be shown whether these are able to price both markets consistently. This paper fills this vacuum. Design/methodology/approach – In particular, the Heston model, the Heston model with jumps in returns and the Heston model with simultaneous jumps in returns and variance (SVJJ) are jointly calibrated to market quotes on SPX and VIX options together with VIX futures. Findings – The full flexibility of having jumps in both returns and volatility added to a stochastic volatility model is essential. Moreover, we find that the SVJJ model with the Feller condition imposed and calibrated jointly to SPX and VIX options fits both markets poorly. Relaxing the Feller condition in the calibration improves the performance considerably. Still, the fit is not satisfactory, and we conclude that one needs more flexibility in the model to jointly fit both option markets. Originality/value – Compared to existing literature, we derive numerically simpler VIX option and futures pricing formulas in the case of the SVJ model. Moreover, the paper is the first to study the pricing performance of three widely used models to SPX options and VIX derivatives.

scholarly journals The Impact of Overnight Periods on Option Pricing

2007 ◽  
Vol 42 (2) ◽  
pp. 517-533 ◽  
Author(s):  
Mark-Jan Boes ◽  
Feike C. Drost ◽  
Bas J. M. Werker
Keyword(s):  
Stochastic Volatility ◽  
Asset Price ◽  
Jump Process ◽  
Option Prices ◽  
Jump Risk ◽  
Price Process ◽  
Affine Model ◽  
Random Jumps ◽  
The Impact ◽  
Random Jump

AbstractThis paper investigates the effect of closed overnight exchanges on option prices. During the trading day, asset prices follow the literature's standard affine model that allows for stochastic volatility and random jumps. Independently, the overnight asset price process is modeled by a single jump. We find that the overnight component reduces the variation in the random jump process significantly. However, neither the random jumps nor the overnight jumps alone are able to empirically describe all features of option prices. We conclude that both random jumps during the day and overnight jumps are important in explaining option prices, where the latter account for about one quarter of total jump risk.

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