VIX Option Pricing and CBOE VIX Term Structure: A New Methodology for Volatility Derivatives Valuation

Using no arbitrage principle, we derive a relation between the drift term of risk-neutral dynamics for instantaneous variance and the term structure of forward variance. We show that the forward variance curve can be derived from options market. Based on the variance term structure, we derive a no arbitrage pricing model for VIX futures pricing. The model is the first no arbitrage model combining options market and VIX futures market. The model can be easily generalized to price other volatility derivatives.

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Volatility Timing: Pricing Barrier Options on DAX XETRA Index

Mathematics ◽

10.3390/math8050722 ◽

2020 ◽

Vol 8 (5) ◽

pp. 722

Author(s):

Carlos Esparcia ◽

Elena Ibañez ◽

Francisco Jareño

Keyword(s):

Option Pricing ◽

Term Structure ◽

Barrier Options ◽

Barrier Option ◽

Probability Term ◽

Volatility Timing ◽

The Right ◽

The Impact ◽

Complementary Study ◽

Frequency Current

This paper analyses the impact of different volatility structures on a range of traditional option pricing models for the valuation of call down and out style barrier options. The construction of a Risk-Neutral Probability Term Structure (RNPTS) is one of the main contributions of this research, which changes in parallel with regard to the Volatility Term Structure (VTS) in the main and traditional methods of option pricing. As a complementary study, we propose the valuation of options by assuming a constant or historical volatility. The study implements the GARCH (1,1) model with regard to the continuously compound returns of the DAX XETRA Index traded at daily frequency. Current methodology allows for obtaining accuracy forecasts of the realized market barrier option premiums. The paper highlights not only the importance of selecting the right model for option pricing, but also fitting the most accurate volatility structure.

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Option Pricing under the Jump Diffusion and Multifactor Stochastic Processes

Journal of Function Spaces ◽

10.1155/2019/9754679 ◽

2019 ◽

Vol 2019 ◽

pp. 1-12 ◽

Cited By ~ 3

Author(s):

Shican Liu ◽

Yanli Zhou ◽

Yonghong Wu ◽

Xiangyu Ge

Keyword(s):

Diffusion Process ◽

Option Pricing ◽

Stochastic Volatility ◽

Term Structure ◽

Implied Volatility ◽

Jump Diffusion ◽

Stochastic Volatility Model ◽

Heston Model ◽

Volatility Model ◽

Jump Diffusion Process

In financial markets, there exists long-observed feature of the implied volatility surface such as volatility smile and skew. Stochastic volatility models are commonly used to model this financial phenomenon more accurately compared with the conventional Black-Scholes pricing models. However, one factor stochastic volatility model is not good enough to capture the term structure phenomenon of volatility smirk. In our paper, we extend the Heston model to be a hybrid option pricing model driven by multiscale stochastic volatility and jump diffusion process. In our model the correlation effects have been taken into consideration. For the reason that the combination of multiscale volatility processes and jump diffusion process results in a high dimensional differential equation (PIDE), an efficient finite element method is proposed and the integral term arising from the jump term is absorbed to simplify the problem. The numerical results show an efficient explanation for volatility smirks when we incorporate jumps into both the stock process and the volatility process.

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GARCH Generated Volatility Indices of Bitcoin and CRIX

Journal of Risk and Financial Management ◽

10.3390/jrfm13060121 ◽

2020 ◽

Vol 13 (6) ◽

pp. 121 ◽

Cited By ~ 1

Author(s):

Pierre J. Venter ◽

Eben Maré

Keyword(s):

Option Pricing ◽

Term Structure ◽

Implied Volatility ◽

Conditional Heteroskedasticity ◽

Option Prices ◽

Pricing Model ◽

European Option ◽

Short Term ◽

Market Prices ◽

Option Pricing Model

In this paper, the pricing performance of the generalised autoregressive conditional heteroskedasticity (GARCH) option pricing model is tested when applied to Bitcoin (BTCUSD). In addition, implied volatility indices (30, 60-and 90-days) of BTCUSD and the Cyptocurrency Index (CRIX) are generated by making use of the symmetric GARCH option pricing model. The results indicate that the GARCH option pricing model produces accurate European option prices when compared to market prices and that the BTCUSD and CRIX implied volatility indices are similar when compared, this is consistent with expectations because BTCUSD is highly weighted when calculating the CRIX. Furthermore, the term structure of volatility indices indicate that short-term volatility (30 days) is generally lower when compared to longer maturities. Furthermore, short-term volatility tends to increase to higher levels when compared to 60 and 90 day volatility when large jumps occur in the underlying asset.

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