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On nonexistence of non-constant volatility in the Black-Scholes formula
| 1. | School of Mathematical Sciences, Monash University, VIC 3800, Australia, Australia |
| [1] |
Lixin Wu, Fan Zhang. LIBOR market model with stochastic volatility. Journal of Industrial & Management Optimization, 2006, 2 (2) : 199-227. doi: 10.3934/jimo.2006.2.199 |
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Lishang Jiang, Baojun Bian. The regularized implied local volatility equations -A new model to recover the volatility of underlying asset from observed market option price. Discrete & Continuous Dynamical Systems - B, 2012, 17 (6) : 2017-2046. doi: 10.3934/dcdsb.2012.17.2017 |
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Martino Bardi, Annalisa Cesaroni, Daria Ghilli. Large deviations for some fast stochastic volatility models by viscosity methods. Discrete & Continuous Dynamical Systems - A, 2015, 35 (9) : 3965-3988. doi: 10.3934/dcds.2015.35.3965 |
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Jia Yue, Nan-Jing Huang. Neutral and indifference pricing with stochastic correlation and volatility. Journal of Industrial & Management Optimization, 2018, 14 (1) : 199-229. doi: 10.3934/jimo.2017043 |
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Kais Hamza, Fima C. Klebaner, Olivia Mah. Volatility in options formulae for general stochastic dynamics. Discrete & Continuous Dynamical Systems - B, 2014, 19 (2) : 435-446. doi: 10.3934/dcdsb.2014.19.435 |
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Jacinto Marabel Romo. A closed-form solution for outperformance options with stochastic correlation and stochastic volatility. Journal of Industrial & Management Optimization, 2015, 11 (4) : 1185-1209. doi: 10.3934/jimo.2015.11.1185 |
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Yaxian Xu, Ajay Jasra. Particle filters for inference of high-dimensional multivariate stochastic volatility models with cross-leverage effects. Foundations of Data Science, 2019, 1 (1) : 61-85. doi: 10.3934/fods.2019003 |
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Mourad Bellassoued, Raymond Brummelhuis, Michel Cristofol, Éric Soccorsi. Stable reconstruction of the volatility in a regime-switching local-volatility model. Mathematical Control & Related Fields, 2020, 10 (1) : 189-215. doi: 10.3934/mcrf.2019036 |
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Laurent Devineau, Pierre-Edouard Arrouy, Paul Bonnefoy, Alexandre Boumezoued. Fast calibration of the Libor market model with stochastic volatility and displaced diffusion. Journal of Industrial & Management Optimization, 2020, 16 (4) : 1699-1729. doi: 10.3934/jimo.2019025 |
| [10] |
Vinicius Albani, Uri M. Ascher, Xu Yang, Jorge P. Zubelli. Data driven recovery of local volatility surfaces. Inverse Problems & Imaging, 2017, 11 (5) : 799-823. doi: 10.3934/ipi.2017038 |
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Lorella Fatone, Francesca Mariani, Maria Cristina Recchioni, Francesco Zirilli. Pricing realized variance options using integrated stochastic variance options in the Heston stochastic volatility model. Conference Publications, 2007, 2007 (Special) : 354-363. doi: 10.3934/proc.2007.2007.354 |
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Yan Zhang, Yonghong Wu, Benchawan Wiwatanapataphee, Francisca Angkola. Asset liability management for an ordinary insurance system with proportional reinsurance in a CIR stochastic interest rate and Heston stochastic volatility framework. Journal of Industrial & Management Optimization, 2020, 16 (1) : 71-101. doi: 10.3934/jimo.2018141 |
| [13] |
Robert J. Elliott, Tak Kuen Siu. Stochastic volatility with regime switching and uncertain noise: Filtering with sub-linear expectations. Discrete & Continuous Dynamical Systems - B, 2017, 22 (1) : 59-81. doi: 10.3934/dcdsb.2017003 |
| [14] |
Shuang Li, Chuong Luong, Francisca Angkola, Yonghong Wu. Optimal asset portfolio with stochastic volatility under the mean-variance utility with state-dependent risk aversion. Journal of Industrial & Management Optimization, 2016, 12 (4) : 1521-1533. doi: 10.3934/jimo.2016.12.1521 |
| [15] |
Hwa-Sung Kim, Bara Kim, Jerim Kim. Catastrophe equity put options under stochastic volatility and catastrophe-dependent jumps. Journal of Industrial & Management Optimization, 2014, 10 (1) : 41-55. doi: 10.3934/jimo.2014.10.41 |
| [16] |
Qihong Chen. Recovery of local volatility for financial assets with mean-reverting price processes. Mathematical Control & Related Fields, 2018, 8 (3&4) : 625-635. doi: 10.3934/mcrf.2018026 |
| [17] |
Qinghua Ma, Zuoliang Xu, Liping Wang. Recovery of the local volatility function using regularization and a gradient projection method. Journal of Industrial & Management Optimization, 2015, 11 (2) : 421-437. doi: 10.3934/jimo.2015.11.421 |
| [18] |
Carey Caginalp, Gunduz Caginalp. Asset price volatility and price extrema. Discrete & Continuous Dynamical Systems - B, 2020, 25 (5) : 1935-1958. doi: 10.3934/dcdsb.2020010 |
| [19] |
Ian Knowles, Ajay Mahato. The inverse volatility problem for American options. Discrete & Continuous Dynamical Systems - S, 2020 doi: 10.3934/dcdss.2020235 |
| [20] |
Erik Ekström, Johan Tysk. A boundary point lemma for Black-Scholes type operators. Communications on Pure & Applied Analysis, 2006, 5 (3) : 505-514. doi: 10.3934/cpaa.2006.5.505 |
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