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This thesis is composed of two parts. The first parts deals with a
technique for pricing American-style contingent options. The
second part details a statistical arbitrage model using
statistical process control approaches.
We propose a novel simulation approach for pricing American-style
contingent claims. We develop an adaptive policy search algorithm
for obtaining the optimal policy in exercising an American-style
option. The option price is first obtained by estimating the
optimal option exercising policy and then evaluating the option
with the estimated policy through simulation. Both high-biased and
low-biased estimators of the option price are obtained. We show
that the proposed algorithm leads to convergence to the true
optimal policy with probability one. This policy search algorithm
requires little knowledge about the structure of the optimal
policy and can be naturally implemented using parallel computing
methods. As illustrative examples, computational results on
pricing regular American options and American-Asian options are
reported and they indicate that our algorithm is faster than
certain alternative American option pricing algorithms reported in
the literature.
Secondly, we investigate arbitrage opportunities arising from
continuous monitoring of the price difference of highly correlated
assets. By differentiating between two assets, we can separate
common macroeconomic factors that influence the asset price
movements from an idiosyncratic condition that can be monitored
very closely by itself. Since price movements are in line with
macroeconomic conditions such as interest rates and economic
cycles, we can easily see out of the normal behaviors on the price
changes. We apply a statistical process control approach for
monitoring time series with the serially correlated data. We use
various variance estimators to set up and establish trading
strategy thresholds.
