Hi all,
I am new to Quantitative Finance and would like to ask 2 questions:
1. In using LSMC to price American-styled derivative, for example we need to value American-styled Asian Option that has payoff = ((\frac{S_{t}+S_{t-1}+...+S_{t-29}}{30}-K)^{+}); what is the rationale to take the continued holding value at time t = (f(b_{1},b_{2},..,b_{k})), where (b_{i} ) is a basis function of the regression and is a function of (S_{t},S_{t-1},...,S_{t-29})
2. How do different ways of choosing basis functions affect the efficiency of LSMC and the convergence of the final result returned by the LSMC? In the context of choosing basis functions for highly dimensional LSMC ( for example in the above example, we have 30 variables involved), are there any methods to choose basis functions?
I have heard about using Sparse Grids and Piecewise Linear Sparse Grids to deal with highly dimensional problem. Are there any thoughts on that?
I really appreciate any enlightening discussions.
I am new to Quantitative Finance and would like to ask 2 questions:
1. In using LSMC to price American-styled derivative, for example we need to value American-styled Asian Option that has payoff = ((\frac{S_{t}+S_{t-1}+...+S_{t-29}}{30}-K)^{+}); what is the rationale to take the continued holding value at time t = (f(b_{1},b_{2},..,b_{k})), where (b_{i} ) is a basis function of the regression and is a function of (S_{t},S_{t-1},...,S_{t-29})
2. How do different ways of choosing basis functions affect the efficiency of LSMC and the convergence of the final result returned by the LSMC? In the context of choosing basis functions for highly dimensional LSMC ( for example in the above example, we have 30 variables involved), are there any methods to choose basis functions?
I have heard about using Sparse Grids and Piecewise Linear Sparse Grids to deal with highly dimensional problem. Are there any thoughts on that?
I really appreciate any enlightening discussions.