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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