A Simple Option Formula for General Jump-Diffusion and Other Exponential Levy Processes

By Alan L. Lewis. 2001

402 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/ab02892efd35d388f366dcdf76f09540f2d1b322

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Citations in the corpus

The characteristic function of rough Heston models (2016, methodology): “Once the characteristic function is obtained, classical methods are available to obtain call prices C(K,T ) = E[ST −K]+, see [8, 24, 32] and the survey [41].”
Option Pricing in Stochastic Volatility Models of the Ornstein‐Uhlenbeck type (2003, methodology): “Hence, formula (4.2) can be computed numerically for any θ ∈ (1, θ+) using adaptive integration software packages or more sophisticated algorithms as described in Carr and Madan (1999), Raible (2000), and Lewis (2001).”
Option Pricing by Transform Methods: Extensions, Unification, and Error Control (2004, methodology): “In the case ofG = G3 with b0 = b1 = 1 andα = 0, Pan (2002), following Davies, gives sampling error bounds.”
Pricing and Hedging in Exponential Lévy Models: Review of Recent Results (2011, background): “This idea was first introduced to finance by Carr and Madan [11] (for European calls and puts) and later extended and generalized by many authors including [43, 37, 36, 19].”
Numerical solution of two asset jump diffusion models for option valuation (2008, methodology): “Using the marginal jump distribution and the diffusion parameters, a European solution in 1D can be computed [31] as well as a cumulative distribution function for the price process at the expiry time.”
Estimating the Parameters of Stochastic Volatility Models Using Option Price Data (2015, methodology): “…family of methods usefully labeled as quadrature methods, which include the methods of Carr and Madan (1999), Duffie, Pan, and Singleton (2000), and Lewis (2001), recover option prices (or components thereof) via inversion integrals or related identities involving the Fourier transform of the…”
Extension of stochastic volatility equity models with the Hull–White interest rate process (2012, methodology): “The COS algorithm relies heavily on the availability of the characteristic function of the price process, which is guaranteed if we stay within the AJD class, see Duffie-Pan-Singleton [13], Lee [25] and Lewis [26].”
Pricing long-dated insurance contracts with stochastic interest rates and stochastic volatility (2009, neutral): “see Lucić (2003), Hong (2004), Kruse and Nögel (2005) and Brigo and Mercurio (2006)).”
Maximum likelihood estimation of the double exponential jump-diffusion process (2007, methodology): “Carr and Madan (1999), Lewis (2001), Broadie and Yamamoto (2003), and Cont and Tankov (2004) also use variations of the FFT method to develop an option pricing formula under DEJD specification. dH́alluin et al. (2004) develop robust numerical methods for pricing contingent claims under jump…”
FOURIER TRANSFORM METHODS FOR REGIME-SWITCHING JUMP-DIFFUSIONS AND THE PRICING OF FORWARD STARTING OPTIONS (2011, methodology): “…generalized Fourier transform Π̂, integrability along the contour ℑ(z) = ν in some strip SΠ in order to guarantee the Inversion Theorem and existence of the expectation EQ[eνX(T )] (see Lee (2004) for log-strike transform, Lewis (2002) or the recent Eberlein et al. (2009) for log-price transform).”
PRICING DISCRETELY MONITORED BARRIER OPTIONS AND DEFAULTABLE BONDS IN LÉVY PROCESS MODELS: A FAST HILBERT TRANSFORM APPROACH (2008, neutral): “Raible (2000), Lewis (2001), and Boyarchenko and Levendorskii (2002) take Fourier transform in the state variable similar to our approach in this paper, but interpret the result as a complex Fourier transform (also known as generalized Fourier transform or two-sided or bilateral Laplace transform…”
Fourier Inversion Formulas in Option Pricing and Insurance (2009, methodology): “Lewis (2001) and other authors consider payoffs which are explicit functions of eX , such as the usual call and put payoffs g1 and g2 in (2.2).”
A Novel Pricing Method for European Options Based on Fourier-Cosine Series Expansions (2008, neutral): “Fourier integrals and cosine series.”
A class of Lévy process models with almost exact calibration to both barrier and vanilla FX options (2010, neutral): “Then using results of Lipton (2001), Lewis (2001) and Kangro et al. (2004), and recalling that VðU,K expð xÞ, Þ represents the undiscounted price, we can write Ii,1 i M=2 ¼ Z 1 0þ bi expðð1 ibiÞxÞ 1þ’ 2 Uexpð ðrf rd Þ Þþ 1 ’ 2 Kexpð xÞ dx Z 1 0þ bi expðð1 ibiÞxÞ Re Z jImðzÞþ1 0 ð zÞSðt0Þ ðKexpð…”