Explicit Density Approximations for Local Volatility Models Using Heat Kernel Expansions
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F16%3A10330192" target="_blank" >RIV/00216208:11320/16:10330192 - isvavai.cz</a>
Alternative codes found
RIV/64941663:_____/16:N0000001
Result on the web
<a href="http://dx.doi.org/10.1007/s11009-015-9463-6" target="_blank" >http://dx.doi.org/10.1007/s11009-015-9463-6</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s11009-015-9463-6" target="_blank" >10.1007/s11009-015-9463-6</a>
Alternative languages
Result language
angličtina
Original language name
Explicit Density Approximations for Local Volatility Models Using Heat Kernel Expansions
Original language description
Heat kernel perturbation theory is a tool for constructing explicit approximation formulas for the solutions of linear parabolic equations. We review the crux of this perturbative formalism and then apply it to differential equations which govern the transition densities of several local volatility processes. In particular, we compute all the heat kernel coefficients for the CEV and quadratic local volatility models; in the later case, we are able to use these to construct an exact explicit formula for the processes' transition density. We then derive low order approximation formulas for the cubic local volatility model, an affine-affine short rate model, and a generalized mean reverting CEV model. We finally demonstrate that the approximation formulas are accurate in certain model parameter regimes via comparison to Monte Carlo simulations.
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BB - Applied statistics, operational research
OECD FORD branch
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Result continuities
Project
<a href="/en/project/GA13-34480S" target="_blank" >GA13-34480S: Management of Extreme Financial Events</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Methodology and Computing in Applied Probability
ISSN
1387-5841
e-ISSN
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Volume of the periodical
18
Issue of the periodical within the volume
3
Country of publishing house
US - UNITED STATES
Number of pages
21
Pages from-to
847-867
UT code for WoS article
000380698400012
EID of the result in the Scopus database
2-s2.0-84941670239