The Volatility Surface: A Practitioner's Guide

By Jim Gatheral. 2006

879 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/885c95df71a86cc5e31789cc49c2bf5c7e5986af

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

Pricing under rough volatility (2015, unknown): “We thus choose to proxy the value of a τ -maturity variance swap by the value of a τ -expiration log contract as explained for example in Chapter 11 of Gatheral (2006).”
Asymptotic formulae for implied volatility in the Heston model (2009, unknown): “The Heston model [20] introduced in 1993 has become one of the most widely used stochastic volatility models in the derivatives market (see [14], [28], [2], [3], [27]).”
Convergence of Heston to SVI (2010, methodology): “[3] J. Gatheral (2006), The Volatility Surface: A Practitioner’s Guide, John Wiley & Sons, Hoboken, NJ. [4] Roger W. Lee (2004), The Moment Formula for Implied Volatility at Extreme Strikes.”
Pricing and Hedging Volatility Derivatives (2008, unknown): “At time 0 it represents the fair variance strike, (13) From Equation (9) we know the value of this security at time 0 and we can derive the stochastic differential equation satisfied by the security X t T, as follows: (14) This price process has zero drift since it is a forward price process.”
On VIX futures in the rough Bergomi model (2017, unknown): “In this parameterization, variance swaps can be computed in closed form, as proved in Hendriks and Martini (2017), based on earlier works by Gatheral (2006) and Fukasawa (2011): Proposition 3.19 The fair strike (in total variance) of a variance swap in the eSSVI model reads σ0(t) 2t := −2E log ( St…”
Mimicking an Itô process by a solution of a stochastic differential equation (2010, methodology): “For example, Gatheral [17] uses it to compare the properties of a number of stochastic volatility models, and Antonov and Misirpashaev [2] and Piterbarg [30, 31, 32] combine it with parameter averaging techniques to produce pricing approximations based on approximations of the second conditional exp”
A regime-switching Heston model for VIX and S&P 500 implied volatilities (2014, background): “European call and put options on VIX have also become liquid, but these options are considerably exotic as they are really an option on a basket of S&P 500 options (the VIX is itself a basket of S&P 500 options; see [7, 8] or chapter 11 of [22]), and so pricing a European option on VIX is somewhat l”
Econophysics: Empirical facts and agent-based models (2009, unknown): “…finance and martingale modelling, more complex processes have been considered in order to take into account some empirical observations: jump processes (see e.g. Cont and Tankov (2004) for a textbook treatment) and stochastic volatility (e.g. Heston (1993); Gatheral (2006)) in particular.”
A NEW LOOK AT SHORT‐TERM IMPLIED VOLATILITY IN ASSET PRICE MODELS WITH JUMPS (2012, background): “Hence, jumps are typically introduced into the risk-neutral pricing models with the aim to capture this risk and modulate the ATM skew of the implied volatility σ̂ (t, k) at small t (see, e.g., equation (5.10) in Gatheral 2006).”
Options on realized variance by transform methods: a non-affine stochastic volatility model (2009, methodology): “…gives us the variance call function for a sequence of strikes simultaneously, we can apply the well-known Breeden and Litzenberger (1978) formula to obtain the density of realized variance as follows: RVðK Þ ¼ @2 @K2 CðK Þ: yNote that Gatheral(2006) uses slightly modified values for v0 and .”
Arbitrage-free SVI volatility surfaces (2012, background): “As shown in [5], the SVI parameterization is not arbitrary in the sense that the large-maturity limit of the Heston implied volatility smile is exactly SVI.”
ARBITRAGE BOUNDS FOR PRICES OF WEIGHTED VARIANCE SWAPS (2010, background): “The reader can consult Gatheral (2006) for information about variance swaps and more extended discussion of the basic facts presented below.”
COMPLEX LOGARITHMS IN HESTON‐LIKE MODELS (2010, methodology): “To the best of our knowledge this formulation first appeared in Bakshi et al. (1997)1 and later in, for example, Duffie et al. (2000) and Gatheral (2006): FORMULATION 1.”