Abstract
We introduce a new Brownian path generation method using a second degree polynomial chaos expansion, and use a conjugate gradient algorithm to find the orthogonal transformation that minimizes the mean truncation dimension of this polynomial. We combine the new path generation method with a control variate technique based on the same second degree polynomial chaos expansion, and apply the method to estimation of equity option prices under the Black--Scholes framework and interest rate option prices under the Libor Market Model. We use numerical results to compare the new method with some other path generation methods from the literature.
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