摆动期权定价：带跳跃约束的BSDE方法
Swing Options Valuation: a BSDE with Constrained Jumps Approach
摘要：
基于带约束跳的倒向随机微分方程（BSDEs），提出了一种求解一类脉冲控制问题的概率方法.作为一个例子，我们的方法是用于定价摆动选项。我们处理的跳跃约束的惩罚过程，并应用离散时间向后计划，从而惩罚Btaglies跳跃。我们研究了这种数值方法的收敛性，相对于主要的近似参数：跳跃强度$λ$，惩罚参数$p > 0$和时间步长。特别地，我们得到了由于惩罚的顺序$(λp)^{α- \frac{1}{2}}, \forall α\in \left(0, \frac{1}{2}\right)$的误差的收敛速度。将该方法与蒙特卡罗方法相结合，求解了Black和Scholes框架下的（归一化）Swing期权的定价问题。我们提出了数值试验，并比较我们的结果与经典的迭代方法。
英文摘要：
We introduce a new probabilistic method for solving a class of impulse control problems based on their representations as Backward Stochastic Differential Equations (BSDEs for short) with constrained jumps. As an example, our method is used for pricing Swing options. We deal with the jump constraint by a penalization procedure and apply a discrete-time backward scheme to the resulting penalized BSDE with jumps. We study the convergence of this numerical method, with respect to the main approximation parameters: the jump intensity $λ$, the penalization parameter $p > 0$ and the time step. In particular, we obtain a convergence rate of the error due to penalization of order $(λp)^{α- \frac{1}{2}}, \forall α\in \left(0, \frac{1}{2}\right)$. Combining this approach with Monte Carlo techniques, we then work out the valuation problem of (normalized) Swing options in the Black and Scholes framework. We present numerical tests and compare our results with a classical iteration method.
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