OPTION PRICING FOR TRUNCATED LÉVY PROCESSES

By Svetlana Boyarchenko, Sergei Levendorskii. 2000

269 citations recorded by the source corpus.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/7e772062a2cdc74583c3f112429333a34cf268d1

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Citations in the corpus

A transform approach to compute prices and Greeks of barrier options driven by a class of Lévy processes (2008, methodology): “• KoBoL/CGMY model ([11, 14]) In the KoBoL model (also called CGMY model), the measure μ has a continuous density k, and it holds that”
Financial market models with Lévy processes and time-varying volatility. (2008, methodology): “In the continuous-time market, if (Xt)t∈[0,T ] is the KR process with parameters (α, k+, k−, r+, r−, p+, p−, m) where α ∈ (0, 1) ∪ (1, 2), k+, k−, r− ∈ (0,∞), r+ ∈ (0, 1), { p+, p− ∈ (1/2− α,∞) \ {0}, if α ∈ (0, 1), p+, p− ∈ (1− α,∞) \ {0}, if α ∈ (1, 2) , (23)”
Wavelet Galerkin pricing of American options on Lévy driven assets (2005, methodology): “We also mention here the extended Koponen family (Boyarchenko and Levendorski 2000) (also referred to as KoBoL (Boyarchenko and Levendorski 2002c), temperated or truncated tempered stable processes or truncated Lévy flights in physics and later used in Carr et al. (2000) under the name of CGMY…”
Tempering stable processes (2007, methodology): “They were also introduced in mathematical finance to model stochastic volatility (the CGMY model in [8, 9]), (the Ornstein-Uhlenbeck–based model in [3, 4]); option pricing based on such processes was considered in [6], just to mention a few.”
Wiener–Hopf factorization and distribution of extrema for a family of Lévy processes (2010, unknown): “ers ci control the total “intensity” of positive/negative jumps. The processes in β-family are similar to the generalized tempered stable processes (see [15]) which were also named KoBoL processes in [9] and [10] ν(x)=c+ e−α+x xλ+ I{x>0} +c− eα−x |x|λ− I{x<0}. In fact we can obtain the above m”
Fast deterministic pricing of options on Lévy driven assets (2002, background): “3 Regular Lévy processes of exponential type The characteristic exponents of the regular Lévy processes of exponential type [7, 8] satisfy (both under historical and equivalent martingale measures from a wide class) the following conditions: For some constants c > 0, ν ∈ (0, 2], ν ′ < ν, α ∈ R, λ− <”
Asymptotics for Exponential Levy Processes and Their Volatility Smile: Survey and New Results (2012, background): “, [64], [89], [23], [24], [25], [34], [106].”
Normal Modified Stable Processes (2001, background): “…(1994), Koponen (1995), Mantegna and Stanley (2000), Boyarchenko and Levendorskii (1999), Boyarchenko and Levendorskii (2000a), Boyarchenko and Levendorskii (2000b), Boyarchenko and Levendorskii (2000c), Boyarchenko and Levendorskii (2000d), Carr, Geman, Madan, and Yor (2001), and Rosinski (2001).”
Models for Heavy-tailed Asset Returns (2010, methodology): “The (exponentially smoothed) TLD was not recognized in finance until the introduction of the KoBoL (Boyarchenko and Levendorskii, 2000) and CGMY models (Carr et al., 2002).”
Tempered stable distributions and processes (2013, unknown): “The following particular cases are known in the literature: • β = β− is a KoBol distribution, see [5]; • α = α− and β = β− is a CGMY-distribution, see [6], also called classical tempered stable distribution in [32]; • β = β− and λ = λ− is the infinitely divisible distribution associated to a truncat”
PRICING OF THE AMERICAN PUT UNDER LÉVY PROCESSES (2004, methodology): “compute h∗ = ln[φr (−i)], the optimal exercise log-price of the perpetual American put (see [9, 10] and Chapter 5 in [12]), and choose an integer N so that N ≥ N1 − h∗/δ; 3.”