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1 Rainbow Option

An option that has a payoff based on the maximum or minimum of two (or more) risky assets and cash. For example, the payoff to a rainbow call is max (S_t, Q_t, K), where St and Qt are risky asset prices. This kind of option is often called two-color rainbow option, because the maximum and the minimum prices of two assets look very much like the shape of rainbow in a two-dimensional diagram, with two asset prices as the two axes.

2 Random Equation (Itô Equation)

The Itô equation as defined in equation A is a random equation. The domain of the equation is [0, ∞) × Ω with the first argument t denoting time and taking values continuously in the interval [0, ∞), and the second argument w denoting a random element taking values from a random set Ω. The range of the equation is the real numbers or real vectors. For simplicity, only the real numbers, denoted by R, are considered as the range of equation.

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3 Random Walk

Theories that stock price changes from day to day are at...