Stochastic Volatility Models used in Quantitative Finance
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- Опубліковано 31 бер 2022
- Today we review a history of stochastic volatility models that have been popularised in Quantitative Finance. We explore major developments in the financial markets that influenced the need for new models.
⦁ 1973: Option pricing model with closed form solution by Black and Scholes
⦁ 1976: First stochastic volatility models Merton and Cox and Ross
⦁ 1976: Leverage effect by Black
⦁ 1982: ARCH model by Engle
⦁ 1986: GARCH model by Bollerslev
⦁ 1987: Stochastic volatility model by Hull and White
⦁ 1987: Black Monday (19th Oct): DJIA drops more than 20% within one day
⦁ 1991: Stochastic Volatility Model by Stein and Stein
⦁ 1993: Introduction of the VIX on the S&P 100 by the CBOE
⦁ 1993: Stochastic volatility model by Heston
⦁ 1994: Local volatility model by Dupire (and independently Derman and Kani)
⦁ 1996: Jump Diffusion model with stochastic volatility (SVJ) by Bates
⦁ 1998: Rough volatility Comte and Renault
⦁ 2002: Realised variance by Barndorff-Nielsen and Shephard
⦁ 2003: New methodology for the VIX,
⦁ 2004: Introduction of VIX futures by CBOE
⦁ 2006: Introduction of VIX options by CBOE
⦁ 2008: VIX reaches its intraday high of 89.53 (on October 24)
⦁ 2009: Double Heston model by Christoffersen, Heston and Jacobs
There are many more models; CEV and SABR models, 3/2 and 4/2 models, local stochastic volatility models, stochastic volatility models with jumps (SVJJ), exponential Levy models, SVI parametrisation etc. but I think this all way too much for one video anyway.
Photo Credit: University of Maryland Article by BRIAN ULLMANN ’92 | PHOTO BY JOHN T. CONSOLI
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Thanks for watching all, let me know if you think there are any major contributions to Stochastic Volatility Models that I've missed out on!
very nice summary, just a minor typo. The model develop by Comte and Renault 1998 is not rough volatility (Hurst0.5). Rough volatilty was proposed by Alos, Leon and Vives (2006) to explain the short term behaviour in the volatilty surface.
I love this new way of presentation 🔥💯💯💯
Awesome stuff!!! Addicted to this channel.
Great infos as always, good job Jonathan!
Thank you! Great video.
great video. very helpful!
I liked so much this video, i would like to enter to this field, i think that you are giving an excellent idea about what someone should dominate, ofcourse i would like to know more about most recent advances since 2009.Thanks so much for your video
Awesome, substribed!!!
Can you suggest some sources that cover all of them...or where you found it to be the best (only for the rather better one's).
Great!
Thanks, very nice. Is there a book which cover these models comprehensively.
You can create a series that go through all these models.
What is the de facto model for vanilla options in equities? As I understand it's the bergomi model
Hi! I am Master Degree in Numerical Methods from Brazil. I started my research carrer originally concerning to the field of Mechanics. However, about a year i've progessively getting more interested for mathematical finance and correlated topics. In this context, I want to trully appreciate you and your channel for it. Currently, i am studing one of your recomendations (stochastic calculus for finance I) and my experience with it have been absolutely satisfactory.
I want to know if are there more finance mathematics/stochastic calculus books recomendations? (Specially in the subject of the volatility modeling)
Finally, as I said, i am from Brazil and therefore my english sometimes might not sound grammatically correct and polite as i wish it would. If this message was the case, please apologise me.
Thank you!!
Hi Bruno, thank you for your kind words. Yes I have more recommendations, I will try and make a video on these soon.
@@QuantPy First, thank you for reply my comment. That's awesome! Until then, I will continue to marathon your channel videos.
@@brunooww1 Os videos do canal são ótimos msm! Eu tenho buscado soluções para modelo de precificação de opções e o canal tem dado bons insights.
Are these models applicable in spot and futures markets?
16k views means there are 16k master of QF out there😂
Berniers model is not even discussed, this is the only option pricing model that worked when oil went to negative value.
Modelling a negative underlying and modelling stochastic volatility are two different things. Will aim to talk about negative underlying prices soon
What's Berniers model? Did you mean Bachelier by any chance?
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