Correlation Structure of Time-Changed Lévy Processes
نویسندگان
چکیده
منابع مشابه
Correlation Structure of Time-Changed Lévy Processes
Time-changed Lévy processes include the fractional Poisson process, and the scaling limit of a continuous time random walk. They are obtained by replacing the deterministic time variable by a positive non-decreasing random process. The use of time-changed processes in modeling often requires the knowledge of their second order properties such as the correlation function. This paper provides the...
متن کاملVariance swaps on time-changed Lévy processes
We prove that a multiple of a log contract prices a variance swap, under arbitrary exponential Lévy dynamics, stochastically time-changed by an arbitrary continuous clock having arbitrary correlation with the driving Lévy process, subject to integrability conditions. We solve for the multiplier, which depends only on the Lévy process, not on the clock. In the case of an arbitrary continuous und...
متن کاملMinimal q-entropy martingale measures for exponential time-changed Lévy processes
In this paper, we consider structure preserving measure transforms for time-changed Lévy processes. Within this class of transforms preserving the time-changed Lévy structure, we derive equivalent martingale measures minimizing relative q-entropy. Structure preservation is found to be an inherent property of minimal q-entropy martingale measures under continuous time changes, whereas it imposes...
متن کاملPricing Barrier and Bermudan Style Options Under Time-Changed Lévy Processes: Fast Hilbert Transform Approach
We construct efficient and accurate numerical algorithms for pricing discretely monitored barrier and Bermudan style options under time-changed Lévy processes by applying the fast Hilbert transform method to the log-asset return dimension and quadrature rule to the dimension of log-activity rate of stochastic time change. Some popular stochastic volatility models, like the Heston model, can be ...
متن کاملVariation and share-weighted variation swaps on time-changed Lévy processes
For a family of functions G, we define the G-variation, which generalizes power variation; G-variation swaps, which pay the G-variation of the returns on an underlying share price F ; and share-weighted G-variation swaps, which pay the integral of F with respect to G-variation. For instance, the case G(x) = x reduces these notions to, respectively, quadratic variation, variance swaps, and gamma...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Communications in Applied and Industrial Mathematics
سال: 2014
ISSN: 2038-0909
DOI: 10.1685/journal.caim.483