Option Valuation under Stochastic Volatility

By Alan L. Lewis. 2000

628 citations recorded by the source corpus.

Subfields: Finance

View Paper: https://www.semanticscholar.org/paper/484e271a2199ff86525323ec67d1bfb2716e3397

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Citations in the corpus

The Shape and Term Structure of the Index Option Smirk: Why Multifactor Stochastic Volatility Models Work So Well (2009, neutral): “[35] Lewis, A.”
Equivalent and absolutely continuous measure changes for jump-diffusion processes (2005, neutral): “martingale framework (see also Remark 2.7 below), extending the classical results by Novikov [23] and Kazamaki [15]. Discussions of measure changes in a ﬁnance context can be found in Sin [30], Lewis [20], Delbaen and Shirakawa [5, 6]. Wong and Heyde [32] give necessary and suﬃcient conditions for t”
Pricing swaps and options on quadratic variation under stochastic time change models—discrete observations case (2010, methodology): “Indeed, assuming that the risk-neutral process for instantaneous variance is: dvt = κvt(θ − vt)dt + ²v3/2t dW̃t, t ∈ [0, T ], (69) with θ a known constant, Heston[23] and Lewis[24] solve for the characteristic function of XT in closed form.”
Consistent Modelling of VIX and Equity Derivatives Using a 3/2 plus Jumps Model (2012, methodology): “For equity derivatives pricing requires the performance of a numerical Fourier inversion, such as those presented in [9] and [25].”
General closed-form basket option pricing bounds (2016, neutral): “However the numerical inversion is not restricted to this approach and can be performed by using alternative representations, as in Lewis (2000) and Lee (2004).”
Forecasting Financial Volatilities with Extreme Values: The Conditional Autoregressive Range (CARR) Model (2005, background): “For insightful implementations of GARCH diffusion models to derivative pricing, see Duan (1995, 1997), Ritchken and Trevor (1999), Heston and Nandi (2000), and the recent book by Lewis (2000).”
Option Pricing by Transform Methods: Extensions, Unification, and Error Control (2004, methodology): “Outside of that family, Lewis (2000), Schöbel-Zhu (1999), and Zhu (2000) obtain characteristic functions also for non-affine volatility and interest rate models.”
Asymptotics of Implied Volatility far from Maturity (2009, background): “This result also appears in Chapter 6 of [10] for stochastic volatility models under a heuristic asymptotic factorization assumption on the function Mτ .”
Approximation and Calibration of Short-Term Implied Volatilities under Jump-Diffusion Stochastic Volatility (2007, methodology): “Lewis (2000) derives the asymptotic expansion of implied volatility assuming small volatility of volatility.”
A Simple Option Formula for General Jump-Diffusion and Other Exponential Levy Processes (2001, neutral): “As shown in Lewis (2000), payoff transforms ( ) ˆ w z for typical claims exist and are regular in their own strips w S in the complex z-plane, just like characteristic functions.”
Options on realized variance by transform methods: a non-affine stochastic volatility model (2009, methodology): “Comparison between true model implied volatilities and the Medvedev and Scaillet (2007) expansion for a maturity of one month.”
A stochastic volatility model and optimal portfolio selection (2013, neutral): “…ðtÞÞ dt þ r ffiffiffiffiffiffiffiffiffiY ðtÞp dW2ðtÞ: ð5Þ If, taking n ¼ 1=2 and having the same choices for Aðy; tÞ;Bðy; tÞ as above, we get another model in which ZðtÞ follows the dynamics dZðtÞ ¼ ½kZ þ ðr2 khÞZ2 dt rZ3=2 dW2ðtÞ; the latter is called a ‘3/2 model’ in the literature (Lewis 2000).”
Extended Libor Market Models with Stochastic Volatility (2001, positive): “Following the ideas in Lewis (2000), let us introduce the Laplace transform ( )( ) , ( );s U TtE e L t V t s− ≡ where s is the complex-valued argument to the Laplace-transform.”