Grant: Discovery Grants Program - Individual

The aim of this research project is to improve dynamic programming-based approximations for options pricing in low-, intermediate-, and high-dimensional state spaces. Stochastic dynamic programming is a recursive method that usually requires an approximation of the Bellman value function at each step of the recursion. In the context of options valuing, the Bellman value function is the value of the option to be priced. The best approximation depends on the dimension of the state space and the dynamics of the (Markov) state process, among other specificities of the problem to be solved. Here, the optimal design is case sensitive. Low- and high-dimensional dynamic programs for options pricing are relatively well documented in the literature. However, an additional effort in terms of efficiency improvement has to be done. Practical problems in option pricing often have intermediate dimensions in between two and five. Examples include affine term-structure models and multiple geometric Brownian motions. The literature on intermediate-dimensional dynamic programs for options pricing is sparse. Here, a significant effort has to be done, not only in terms of efficiency improvement, but also in terms of the design of new methods. There are several ways to improve stochastic dynamic programs for options pricing: 1. Adapt and use the extensive literature on DP and/or Monte Carlo simulation and their applications in various specific fields; 2. Realize part of the experiment in a closed form; 3. Use more precise and possibly smoother interpolations of the Bellman value function at each decision date; 4. Search for the effective dimension of the Bellman equation and reduce the complexity of the problem to be solved; 5. Combine between reduction of variance techniques; 6. Couple between DP and quasi-Monte Carlo.