Option Pricing by Transform Methods: Extensions, Unification, and Error Control

By Roger Lee. 2004

368 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/c8e2a40c85d8cb20840d39f3d623e31127706118

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Citations in the corpus

Lévy Processes in Finance: Inverse Problems and Dependence Modelling (2004, neutral): “Similar analysis has recently appeared in [63].”
Option Pricing: Valuation Models and Applications (2004, positive): “A simple approach to valuation, when risks cannot all be hedged, is to resort to a general equilibrium analysis. Pioneered by Lucas (1978) and Cox et al.”
Asymptotic formulae for implied volatility in the Heston model (2009, neutral): “By Cauchy’s integral theorem, we now have ( ∫ γδ,R + ∫ γǫ,δ + ∫ γUǫ + ∫ Γ± R,ǫ,δ − ∫ ζ1+2ǫ ) φt(−k) ik − k2 exp ( ikθ̄t/2 ) dk = 0, (41) Recall that the curves ζ1+2ǫ and γ1+2ǫ are defined in (29) and (28) respectively and rewrite (41) as ( ∫ γ1+2ǫ + ∫ ζ1+2ǫ ) φt(−k) ik − k2 e ikθ̄t/2dk = ( ∫ γδ,R + ”
Robust numerical valuation of European and American options under the CGMY process (2007, background): “0 Table 1: The input parameters (from [32]) for evaluating a European call option under a Variance Gamma process.”
PRICING DISCRETELY MONITORED BARRIER OPTIONS AND DEFAULTABLE BONDS IN LÉVY PROCESS MODELS: A FAST HILBERT TRANSFORM APPROACH (2008, neutral): “1, we need to repeatedly compute operators P(Q) for single-barrier (double-barrier) options, and at the final stage compute the operator R. In this section we will develop effective discrete approximations for these operators based on the approximation theory for analytic functions. In Section 6.2, ”
Asymptotics for Exponential Levy Processes and Their Volatility Smile: Survey and New Results (2012, neutral): “A complementary method is proposed in [27]; additional information can be found in [68].”
A simple recursive numerical method for Bermudan option pricing under Lévy processes (2006, methodology): “The FFT improves computational speed and error control relative to the FT methods, see Carr and Madan (1999) and Lee (2004), thus it is logical to want to use its considerable power in this setting.”
COMPLEX LOGARITHMS IN HESTON‐LIKE MODELS (2010, methodology): “The optimal choice of α is considered in Lee [2004] and Lord and Kahl [2007]. If we use equations (1)-(2) to evaluate the option price, discontinuities in a characteristic function will clearly lead to discontinuities in the integrand of (1).”
THE MOMENT FORMULA FOR IMPLIED VOLATILITY AT EXTREME STRIKES (2004, neutral): “See Lee (2001).”
FOURIER TRANSFORM METHODS FOR REGIME-SWITCHING JUMP-DIFFUSIONS AND THE PRICING OF FORWARD STARTING OPTIONS (2011, methodology): “In order to justify the previous equalities, some conditions are required: existence of the 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-str”
A note on scale functions and the time value of ruin for Levy insurance risk processes (2010, neutral): “…vast literature of Laplace transform methods, which has grown extensively over the last few years, and has found numerous applications in option pricing (e.g.: Duffie, Pan and Singleton, 2000; Lee, 2004) and integro-differential equations (e.g.: Kythe and Puri, 2002; Babolian and Shamloo, 2008).”
SMALL-TIME ASYMPTOTICS FOR IMPLIED VOLATILITY UNDER THE HESTON MODEL (2009, methodology): “Using similar notation to Lee [26], we set”
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].”
Stochastic Volatility of Volatility and Variance Risk Premia (2013, positive): “Note that thismodel belongs to the class ofa fine models since the the BNS model itself is affine and the new (additional) time change is given by the time integral of an affine process, see Keller-Ressel (2008).”
Pricing swaps and options on quadratic variation under stochastic time change models—discrete observations case (2010, methodology): “For complete details see [ 19 ] and Carr and Madan original paper [9].”
Not-so-complex logarithms in the Heston model (2006, background): “Various authors [SZ99, Lee05, Sep04] propose the idea to keep track of the number of jumps by comparing G(uk) and G(uk+1) where uk and uk+1 are adjacent points in their respective numerical integration scheme.”