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From Constant to Rough: A Survey of Continuous Volatility Modeling
Mathematics, 2023 In this paper, we present a comprehensive survey of continuous stochastic volatility models, discussing their historical development and the key stylized facts that have driven the field.
Giulia Di Nunno +3 more
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Smiles & smirks: Volatility and leverage by jumps [PDF]
European Journal of Operational Research, 2022 We propose a novel flexible framework for the joint evolution of stock log-returns and their volatility based on time changed L ́evy process. The novelty of the approach stems from the generality of the jump structure we endow our model with, and the ability of the model to generate leverage effects out of the pure jump component.
Ballotta, L., Grégory, R.
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Option Pricing with Fractional Stochastic Volatilities and Jumps
Fractal and Fractional, 2023 Empirical studies suggest that asset price fluctuations exhibit “long memory”, “volatility smile”, “volatility clustering” and asset prices present “jump”.
Sumei Zhang, Hongquan Yong, Haiyang Xiao
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Option Pricing under Two-Factor Stochastic Volatility Jump-Diffusion Model
Complexity, 2020 Empirical evidence shows that single-factor stochastic volatility models are not flexible enough to account for the stochastic behavior of the skew, and certain financial assets may exhibit jumps in returns and volatility.
Guohe Deng
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Detecting Jump Risk and Jump-Diffusion Model for Bitcoin Options Pricing and Hedging
Mathematics, 2021 In this paper, we conduct a fast calibration in the jump-diffusion model to capture the Bitcoin price dynamics, as well as the behavior of some components affecting the price itself, such as the risk of pitfalls and its ambiguous effect on the evolution ...
Kuo-Shing Chen, Yu-Chuan Huang
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Risks, 2023 This research article provides criticism and arguments why the canonical framework for derivatives pricing is incomplete and why the delta-hedging approach is not appropriate.
Jussi Lindgren
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Financial market disruption and investor awareness: the case of implied volatility skew
Quantitative Finance and Economics, 2022 The crash of 1987 is considered one of the most significant events in the history of financial markets due to the severity and swiftness of market declines worldwide.
Hammad Siddiqi
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Volatility smile as relativistic effect [PDF]
Physica A: Statistical Mechanics and its Applications, 2017 We give an explicit formula for the probability distribution based on a relativistic extension of Brownian motion. The distribution 1) is properly normalized and 2) obeys the tower law (semigroup property), so we can construct martingales and self-financing hedging strategies and price claims (options). This model is a 1-constant-parameter extension of
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A volatility smile-based uncertainty index [PDF]
Annals of Finance, 2021 We propose a new uncertainty index based on the discrepancy of the smile of FX options. We show that our index spikes near turbulent periods, forecasts economic activity and its innovations hold a significant and negative equity premium. Unlike other uncertainty indexes, our index is supported by equilibrium models, which relate the difference of ...
José Valentim Machado Vicente +1 more
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Asymptotics of forward implied volatility [PDF]
, 2015 We prove here a general closed-form expansion formula for forward-start options and the forward implied volatility smile in a large class of models, including the Heston stochastic volatility and time-changed exponential L\'evy models.
Jacquier, Antoine, Roome, Patrick
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