Constant Elasticity of Variance Model for Option Pricing

[newbie73]

Does QuantLib have a CEV model for options pricing?  The example European and American option pricers shown in the Python installation don't seem to make use of a CeV adjustment.

How could I approximate this if it is not currently available in the QL library?

Thanks,

- Luis

[newbie73]

Standard Black Scholes process for Stock Price S:
dS = (m * S * dt) + (vol * S * dz), where:
m = drift
S = stock price
dt = delta time
vol = std. dev of S
dz = random motion

CeV Black Scholes process for Stock Price S:

a = vol * S(1-rho), where:
rho = coefficient of elasticity

dS = (m * S * dt) + (vol * [S^a] * dz)

if a == 1, dS becomes a standard black scholes process

Given the above, is it possible to estimate this using existing classes/functions?  

newbie73 wrote

Does QuantLib have a CEV model for options pricing?  The example European and American option pricers shown in the Python installation don't seem to make use of a CeV adjustment.

How could I approximate this if it is not currently available in the QL library?

Thanks,

- Luis

[Ferdinando M. Ametrano-3]

On 9/26/07, newbie73 <[hidden email]> wrote:
> Does QuantLib have a CEV model for options pricing?

not really. Anyway the available Black formulaimplementation (see
ql/pricingengines/blackformula.hpp)  takes displaced diffusion into
account.
In a displaced diffusion model the lognormal variable is (S+a). It has
been shown that displaced diffusion is equivalent to CEV over a large
range of interesting parameter values.

See Joshi "Concepts and practice of Mathematical Finance" 14.2 or
Rebonato "Modern Pricing of Interest-Rate Derivatives" 11.3 for more
details.

Of course if you're willing to contribute a proper CEV implementation
it would be more than welcome

ciao -- Nando

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