منابع مشابه
Calibration of options on a reduced basis
∂tC + 1 2 σS∂SSC + rS∂SC − rC = 0, C(S, T ) = (S −K) (1) where r is the interest rate and σ the volatility. While in the original model σ is constant, it is common practice to calibrate (adjust) σ to allow (??) to reproduce market observations Ck at S0, t0, namely known calls with maturities Tk and strikes Kk, k=1..K. The calibration problem (also called the “smile”) is quite stiff. Avellaneda ...
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In [3] it was shown that by writing the solution of the Black-Scholes partial differential equation on a small set of basis functions the computing time can be dramatically reduced. In this study we explore the generalization of the technique to basket options.
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We present a reduced basis method for the simulation of American option pricing. To tackle this model numerically, we formulate the problem in terms of a time dependent variational inequality. Characteristic ingredients are a POD-greedy and an angle-greedy procedure for the construction of the primal and dual reduced spaces. Numerical examples are provided, illustrating the approximation qualit...
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15 صفحه اولCalibration of Barrier Options
A barrier option is a financial contract which is used to secure deals on volatile assets. The calibration of the volatility is an interesting mathematical and numerical problem which we analyze. In the process we will recall the modern tools of numerical analysis for fast solutions. We report also on the behavior of some optimization algorithms for this problem. Introduction A European option ...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2009
ISSN: 0377-0427
DOI: 10.1016/j.cam.2008.10.070