Post by Sapphire Capital on Jul 11, 2008 22:00:03 GMT 4
Markovian Projection to a Displaced Volatility Heston Model
ALEXANDRE ANTONOV
Numerix - Quantitative Research
MATTHIEU ARNEGUY
Numerix
NICOLAS AUDET
Numerix - Quantitative Research
--------------------------------------------------------------------------------
March 12, 2008
Abstract:
Markovian Projection is an optimal approximation of a complex underlying process with a simpler one, keeping essential properties of the initial process. The Heston process, as the Markovian Projection target, is an example.
In this article, we generalize the results of Markovian Projection onto a Heston model to a wider class of approximating models, a Heston model with displaced volatility. As an important application, we derive an effective approximation for FX/EQ options for the Heston model, coupled with correlated Gaussian interest rates.
The main technical result is an option evaluation for correlated Heston/Lognormal processes. Unlike the case of exactly solvable (affine) zero correlation or its uncorrelated displacement generalization,considered by Andreasen, non-trivial correlations destroy affine structure and exact solvability.
Using the powerful technique of Markovian Projection onto a Heston model with displaced volatility, we produce an effective approximation and present its numerical confirmation.
papers.ssrn.com/sol3/Delivery.cfm/SSRN_ID1106223_code340600.pdf?abstractid=1106223&mirid=2
ALEXANDRE ANTONOV
Numerix - Quantitative Research
MATTHIEU ARNEGUY
Numerix
NICOLAS AUDET
Numerix - Quantitative Research
--------------------------------------------------------------------------------
March 12, 2008
Abstract:
Markovian Projection is an optimal approximation of a complex underlying process with a simpler one, keeping essential properties of the initial process. The Heston process, as the Markovian Projection target, is an example.
In this article, we generalize the results of Markovian Projection onto a Heston model to a wider class of approximating models, a Heston model with displaced volatility. As an important application, we derive an effective approximation for FX/EQ options for the Heston model, coupled with correlated Gaussian interest rates.
The main technical result is an option evaluation for correlated Heston/Lognormal processes. Unlike the case of exactly solvable (affine) zero correlation or its uncorrelated displacement generalization,considered by Andreasen, non-trivial correlations destroy affine structure and exact solvability.
Using the powerful technique of Markovian Projection onto a Heston model with displaced volatility, we produce an effective approximation and present its numerical confirmation.
papers.ssrn.com/sol3/Delivery.cfm/SSRN_ID1106223_code340600.pdf?abstractid=1106223&mirid=2