Three decades of explosive growth, empirical and theoretical discoveries have transformed finance into a sophisticated mathematical science. Our tour begins with the financial market landscape, its residents and fundamental principles of the "price of risk" and "arbitrage."
The lack of arbitrage drives markets toward equilibria and provides exact prices for stock options and futures; modern finance uses the notion of "risk-neutral probability measures," but one may also employ quantum mechanical time evolution with non-Hermitian Hamiltonians or path integral methods to accomplish this.
Practial applications of making markets for interest-rate futures using statistical arbitrage, term-structure dynamics and the pricing of options are discussed.
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