Market forces are at the heart of financial mathematics giving rise
to market prices constantly in flux. From market prices flows financial
theory. Random walk models make sense of such prices and Monte Carlo
methods are the uniquely appropriate tool for their study.
The text begins with a thorough treatment of the geometric random walk
model for market prices. As an immediate consequence, lognormal price
distributions are derived and its practical use illustrated.
It is shown how a fundamental tenet of the random walk model, the
efficient market hypothesis, can be tested via Monte Carlo.
Coverage includes standard financial fundamentals such as measuring
return and risk, portfolio management, the Capital Asset Pricing
Model, and the Security Market Line.
Extensive coverage is provided for options including Black-Scholes
arbitrage pricing, binomial pricing, option payoff dynamics, option
trading strategies, and the pricing of exotic options not generally
The non-standard random walk dynamics due to heavytailed, and bi-modal
distributions are developed and applied to option pricing and payoffs.
The unique tool of option payoff expectations is introduced and
illustrated by application to a large number of option trading
strategies. This analysis is extended to non-standard distributions.
Extensive use of the Monte Carlo method is made throughout, from
illustrating concepts to practical financial calculation.
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