8,004 research outputs found
Conditional hitting time estimation in a nonlinear filtering model by the Brownian bridge method
The model consists of a signal process which is a general Brownian
diffusion process and an observation process , also a diffusion process,
which is supposed to be correlated to the signal process. We suppose that the
process is observed from time 0 to at discrete times and aim to
estimate, conditionally on these observations, the probability that the
non-observed process crosses a fixed barrier after a given time . We
formulate this problem as a usual nonlinear filtering problem and use optimal
quantization and Monte Carlo simulations techniques to estimate the involved
quantities
Conditional sampling for barrier option pricing under the LT method
We develop a conditional sampling scheme for pricing knock-out barrier
options under the Linear Transformations (LT) algorithm from Imai and Tan
(2006). We compare our new method to an existing conditional Monte Carlo scheme
from Glasserman and Staum (2001), and show that a substantial variance
reduction is achieved. We extend the method to allow pricing knock-in barrier
options and introduce a root-finding method to obtain a further variance
reduction. The effectiveness of the new method is supported by numerical
results
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