Stochastic Volatility Models used in Quantitative Finance

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 ★ A data driven path to getting a job in Quant Finance https://www.quantpykit.com/ ★ QuantPy GitHub Collection of resources used on QuantPy YouTube channel. https://github.com/thequantpy Disclaimer: All ideas, opinions, recommendations and/or forecasts, expressed or implied in this content, are for informational and educational purposes only and should not be construed as financial product advice or an inducement or instruction to invest, trade, and/or speculate in the markets. Any action or refraining from action; investments, trades, and/or speculations made in light of the ideas, opinions, and/or forecasts, expressed or implied in this content, are committed at your own risk an consequence, financial or otherwise.