7,913 research outputs found
Option pricing with Lévy-Stable processes generated by Lévy-Stable integrated variance.
We show how to calculate European-style option prices when the log-stock price process follows a Lévy-Stable process with index parameter 1≤α≤2 and skewness parameter -1≤β≤1. Key to our result is to model integrated variance as an increasing Lévy-Stable process with continuous paths in ΤLévy-Stable processes; Stable Paretian hypothesis; Stochastic volatility; α-stable processes; Option pricing; Time-changed Brownian motion;
Option pricing with Lévy-Stable processes generated by Lévy-Stable integrated variance.
We show how to calculate European-style option prices when the log-stock price process follows a Lévy-Stable process with index parameter 1≤α≤2 and skewness parameter -1≤β≤1. Key to our result is to model integrated variance as an increasing Lévy-Stable process with continuous paths in ΤCommodity markets; Commodity prices; Lévy process; Hedging techniques;
Option pricing with Lévy-Stable processes generated by Lévy-Stable Integrated Variance
In this paper we show how to calculate European-style option prices when the log-stock price process follows a L´evy-Stable process with index parameter 1 ≤ α ≤ 2 and skewness parameter −1 ≤ β ≤ 1. Key to our result is to model integrated variance RT t σ2 sds as an increasing L´evy-Stable process with continuous paths
Convex Hulls of L\'evy Processes
Let , , be a L\'evy process in starting at the
origin. We study the closed convex hull of . In
particular, we provide conditions for the integrability of the intrinsic
volumes of the random set and find explicit expressions for their means
in the case of symmetric -stable L\'evy processes. If the process is
symmetric and each its one-dimensional projection is non-atomic, we establish
that the origin a.s. belongs to the interior of for all . Limit
theorems for the convex hull of L\'evy processes with normal and stable limits
are also obtained.Comment: 11 page
The hitting time of zero for a stable process
For any two-sided jumping -stable process, where , we
find an explicit identity for the law of the first hitting time of the origin.
This complements existing work in the symmetric case and the spectrally
one-sided case; cf. Yano-Yano-Yor (2009) and Cordero (2010), and Peskir (2008)
respectively. We appeal to the Lamperti-Kiu representation of
Chaumont-Pant\'i-Rivero (2011) for real-valued self-similar Markov processes.
Our main result follows by considering a vector-valued functional equation for
the Mellin transform of the integrated exponential Markov additive process in
the Lamperti-Kiu representation. We conclude our presentation with some
applications
Valuation of asset and volatility derivatives using decoupled time-changed L\'evy processes
In this paper we propose a general derivative pricing framework which employs
decoupled time-changed (DTC) L\'evy processes to model the underlying asset of
contingent claims. A DTC L\'evy process is a generalized time-changed L\'evy
process whose continuous and pure jump parts are allowed to follow separate
random time scalings; we devise the martingale structure for a DTC
L\'evy-driven asset and revisit many popular models which fall under this
framework. Postulating different time changes for the underlying L\'evy
decomposition allows to introduce asset price models consistent with the
assumption of a correlated pair of continuous and jump market activities; we
study one illustrative DTC model having this property by assuming that the
instantaneous activity rates follow the the so-called Wishart process. The
theory developed is applied to the problem of pricing claims depending not only
on the price or the volatility of an underlying asset, but also to more
sophisticated derivatives that pay-off on the joint performance of these two
financial variables, like the target volatility option (TVO). We solve the
pricing problem through a Fourier-inversion method; numerical computations
validating our technique are provided.Comment: 30 Pages, 5 Tables, 3 figures. Third revised version: numerical
analysis extende
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