In statistics, stochastic volatility models are those in which the variance of a stochastic process is itself randomly distributed. They are used in the field of mathematical finance to evaluate derivative securities, such as options. The name derives from the models' treatment of the underlying security's volatility as a random process, governed by state variables such as the price level of the underlying security, the tendency of volatility to revert to some long-run mean value, and the variance of the volatility process itself, among others. Stochastic volatility models are one approach to resolve a shortcoming of the Black–Scholes model. In particular, models based on Black-Scholes assume that the underlying volatility is constant over the life of the derivative, and unaffected by the changes in the price level of the underlying security. However, these models cannot explain long-observed features of the implied volatility surface such as volatility smile and skew, which indicate that implied volatility does tend to vary with respect to strike price and expiry. By assuming that the volatility of the underlying price is a stochastic process rather than a constant, it becomes possible to model derivatives more accurately. The early history of stochastic volatility has multiple roots (i.e. stochastic process, option pricing and econometrics), it is reviewed in Chapter 1 of Neil Shephard (2005) "Stochastic Volatility," Oxford University Press. (Wikipedia).
Lots of ways to estimate volatility. In this map, I parse out implied volatility (forward looking) and deterministic (constant) and focus on stochastic volatility: volatility that changes over time, either via (conditional) recent volatility and/or random shocks. For more financial risk vi
From playlist Volatility
Risk Management Lesson 4A: Volatility
First part of Lesson 4. Topics: - Definitions of volatility - Basic assumptions (do they hold?) - Arch and G-arch models (brief overview)
From playlist Risk Management
IDTIMWYTIM: Stochasticity - THAT'S Random
Hank helps us understand the difference between the colloquial meaning of randomness, and the scientific meaning, which is also known as stochasticity. We will learn how, in fact, randomness is surprisingly predictable. Like SciShow: http://www.facebook.com/scishow Follow SciShow: http://
From playlist Uploads
Time Varying Volatility and GARCH in Risk Management
These classes are all based on the book Trading and Pricing Financial Derivatives, available on Amazon at this link. https://amzn.to/2WIoAL0 Check out our website http://www.onfinance.org/ Follow Patrick on twitter here: https://twitter.com/PatrickEBoyle In Todays video let's learn abo
From playlist Risk Management
What are Volatility Swaps? Financial Derivatives - Trading Volatility
In todays class we learn about what a volatility swap is. These classes are all based on the book Trading and Pricing Financial Derivatives, available on Amazon at this link. https://amzn.to/2WIoAL0 Check out our website http://www.onfinance.org/ Follow Patrick on twitter here: https:/
From playlist The Term Structure of Volatility
Volatility Trading - Call and Put Options - Trading Tutorial
These classes are all based on the book Derivatives For The Trading Floor, available on Amazon at this link. https://amzn.to/3GdLi2s Check out our website http://www.onfinance.org/ Follow Patrick on twitter here: https://twitter.com/PatrickEBoyle What is volatility trading? Volatility
From playlist Class 4 The Greeks & Dynamic Hedging
FRM: Volatility: Moving Average Approaches
Within stochastic volatility, moving average is the simplest approach. It simply calculates volatility as the unweighted standard deviation of a window of X trading days. Here I show the three "flavors:" population variance (volatility = SQRT[variance]), sample, and simple. For more financ
From playlist Volatility
What is Implied Volatility? Options Trading Tutorial.
These classes are all based on the book Trading and Pricing Financial Derivatives, available on Amazon at this link. https://amzn.to/2WIoAL0 Check out our website http://www.onfinance.org/ Follow Patrick on twitter here: https://twitter.com/PatrickEBoyle
From playlist The Term Structure of Volatility
Introduction to the paper https://arxiv.org/abs/2002.06707
From playlist Research
8 2 Stochastic Volatility Part 2
BEM1105x Course Playlist - https://www.youtube.com/playlist?list=PL8_xPU5epJdfCxbRzxuchTfgOH1I2Ibht Produced in association with Caltech Academic Media Technologies. ©2020 California Institute of Technology
From playlist BEM1105x Course - Prof. Jakša Cvitanić
Martin Larsson: Affine Volterra processes and models for rough volatility
Abstract: Motivated by recent advances in rough volatility modeling, we introduce affine Volterra processes, defined as solutions of certain stochastic convolution equations with affine coefficients. Classical affine diffusions constitute a special case, but affine Volterra processes are n
From playlist Probability and Statistics
Grégoire Loeper: Reconstruction by optimal transport: applications in cosmology and finance
Abstract: Following the seminal work by Benamou and Brenier on the time continuous formulation of the optimal transport problem, we show how optimal transport techniques can be used in various areas, ranging from "the reconstruction problem" cosmology to a problem of volatility calibration
From playlist Mathematics in Science & Technology
Dylan Possamaï: Principal Agent Modelling - lecture 3
CIRM HYBRID EVENT These lectures will consist in an overview of recent progresses made in contracting theory, using the so-called dynamic programming approach. The basic situation is that of a Principal wanting to hire an Agent to do a task on his behalf, and who has to be properly incenti
From playlist Probability and Statistics
Risk Management of Option Books with Arbitrage-Free Neural-SDE Market Models (SIAM FME)
SIAM Activity Group on FME Virtual Talk Series Join us for a series of online talks on topics related to mathematical finance and engineering and running every two weeks until further notice. The series is organized by the SIAM Activity Group on Financial Mathematics and Engineering. Spe
From playlist SIAM Activity Group on FME Virtual Talk Series
6 6 Black Scholes Merton pricing Part 3
BEM1105x Course Playlist - https://www.youtube.com/playlist?list=PL8_xPU5epJdfCxbRzxuchTfgOH1I2Ibht Produced in association with Caltech Academic Media Technologies. ©2020 California Institute of Technology
From playlist BEM1105x Course - Prof. Jakša Cvitanić
8 1 Stochastic Volatility Part 1
BEM1105x Course Playlist - https://www.youtube.com/playlist?list=PL8_xPU5epJdfCxbRzxuchTfgOH1I2Ibht Produced in association with Caltech Academic Media Technologies. ©2020 California Institute of Technology
From playlist BEM1105x Course - Prof. Jakša Cvitanić
Christa Cuchiero: Rough volatility from an affine point of view
Abstract: We represent Hawkes process and their Volterra long term limits, which have recently been used as rough variance processes, as functionals of infinite dimensional affine Markov processes. The representations lead to several new views on affine Volterra processes considered by Abi
From playlist Probability and Statistics
The Volatility Smile - Options Trading Lessons
The volatility smile is a real-life pattern that is observed when different strikes of option, with the same underlying and same expiration date are plotted on a graph. These classes are all based on the book Trading and Pricing Financial Derivatives, available on Amazon at this link. htt
From playlist The Term Structure of Volatility
10 9 Forward rates models Part 3
BEM1105x Course Playlist - https://www.youtube.com/playlist?list=PL8_xPU5epJdfCxbRzxuchTfgOH1I2Ibht Produced in association with Caltech Academic Media Technologies. ©2020 California Institute of Technology
From playlist BEM1105x Course - Prof. Jakša Cvitanić