Quasi-Monte-Carlo: What's in It?
How does this method work? What makes it more accurate? It seems that this article is a good place to touch on this subject.

Generally, the Monte-Carlo method simulates some probabilistic laws. For example, it stresses market rates using random shocks given by a random number generator. Random shocks applied to sequential moments of time are supposed to be sampled from a normal distribution (or converted to one) and be independent from each other. Regular Monte-Carlo does very little to ensure these properties hold true for a limited sample. We usually complement random sampling with antithetic reflection to make sure the shocks are unbiased, on average.

Quasi-Monte-Carlo pre-processes shocks, scaling them to needed volatility and making them independent ("orthogonal") of each other. The mathematical technique invoked here is called Gram-Schmidt ortho-normalization. In other words, randomly sampled shocks are re-arranged first to obey the desired stochastic properties (i.e. made "quasi-random"), only then applied. Not surprisingly, Quasi-Monte-Carlo is about twice as accurate as the regular method, for the same number of paths (Figure 1).

Ortho-normalization comes at a small cost of computational time. We can control the use of this method with a quasi-random nodes parameter. Setting it to default (34 nodes) ensures that Quasi-Monte-Carlo applies for the entire length of mortgage life. Setting it to zero is equivalent to using regular Monte-Carlo. Setting it to any intermediate number (for example, 14 nodes) will tell the AD&Co. system to apply Quasi-Monte-Carlo for some limited, user-defined, horizon (120 months in this example), and run regular Monte-Carlo thereafter.

Volatility constants versus Volatility Term Structure
Since the inception of AD&Co. volatility index and posting volatility calibration results on our Market Analysis, we spoke to several puzzled users who thought we use these reported constants (Figure 2) in our OAS valuation system.

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