A Reduced Basis for Option Pricing
A Reduced Basis for Option Pricing
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期权定价的基础减少
DOI：
10.2139/ssrn.1685382
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发表时间：
2010
期刊：
影响因子：
--
通讯作者：
O. Pironneau
中科院分区：
文献类型：
--
作者：
R. Cont;Nicolas Lantos;O. Pironneau
我们介绍了一个有效的数值解的偏积分微分方程（PIDE），出现在期权定价理论的减少基方法。我们的方法构造的解决方案作为一个线性组合的基函数构造从一系列的Black-Scholes解决方案具有不同的挥发性。我们表明，这种先验选择的基础上，导致稀疏表示的期权定价函数，产生的近似误差呈指数衰减的基函数的数量。一个Galerkin方法，使用这个基础上解决定价偏微分方程的CEV扩散模型和默顿跳跃扩散模型的常用的有限差分和有限元方法相比，具有更好的数值性能。我们还比较了我们的方法与数值正交分解（POD）。最后，我们表明，这种方法可以有利地用于局部波动函数的校准。
We introduce a reduced basis method for the efficient numerical solution of partial integro-differential equations (PIDEs) which arise in option pricing theory. Our method constructs the solution as a linear combination of basis functions constructed from a sequence of Black-Scholes solutions with different volatilities. We show that this a priori choice of basis leads to a sparse representation of option pricing functions, yielding an approximation error which decays exponentially in the number of basis functions. A Galerkin method using this basis for solving the pricing PDE is shown to have better numerical performance relative to commonly used finite-difference and finite-element methods for the CEV diffusion model and the Merton jump diffusion model. We also compare our method with a numerical proper orthogonal decomposition (POD). Finally, we show that this approach may be used advantageously for the calibration of local volatility functions.