New Numerical Scheme for Pricing American Option with Regime-Switching
New Numerical Scheme for Pricing American Option with Regime-Switching
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DOI：
10.1142/s0219024909005245
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发表时间：
2009-05
影响因子：
0.5
通讯作者：
A. Khaliq;R. Liu
中科院分区：
文献类型：
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作者：
A. Khaliq;R. Liu
研究了状态转换美式期权定价问题。我们通过扩展罚方法和采用θ-方法发展了新的数值格式。在制度转换的情况下，美式期权价格满足一个m自由边值问题的系统，其中m是市场所考虑的制度的数量。一个（最佳）早期行使边界与每个政权。直接执行θ方法将导致非线性方程组，需要在每个时间步长进行耗时的迭代过程。为了避免这种并发症，我们实现了一个隐式的方法，通过显式处理的非线性项和/或线性项从其他制度，从而在计算效率高的算法。我们建立了时间步长的上界条件，并证明了在该条件下，隐式格式满足离散形式的美式期权价值的正性约束。我们比较了隐式计划与树模型，概括了Cox-Ross-Rubinstein（CRR）二项式树模型，并与两个政权的情况下，由于Buffington和Elliott的解析近似解。数值算例验证了新隐式格式的精度和稳定性。
This paper is concerned with regime-switching American option pricing. We develop new numerical schemes by extending the penalty method approach and by employing the θ-method. With regime-switching, American option prices satisfy a system of m free boundary value problems, where m is the number of regimes considered for the market. An (optimal) early exercise boundary is associated with each regime. Straightforward implementation of the θ-method would result in a system of nonlinear equations requiring a time-consuming iterative procedure at each time step. To avoid such complications, we implement an implicit approach by explicitly treating the nonlinear terms and/or the linear terms from other regimes, resulting in computationally efficient algorithms. We establish an upper bound condition for the time step size and prove that under the condition the implicit schemes satisfy a discrete version of the positivity constraint for American option values. We compare the implicit schemes with a tree model that generalizes the Cox-Ross-Rubinstein (CRR) binomial tree model, and with an analytical approximation solution for two-regime case due to Buffington and Elliott. Numerical examples demonstrate the accuracy and stability of the new implicit schemes.