Pricing Tools in Financial Engineering
This chapter introduces the fundamental theorem of asset pricing which provides an unified pricing tool for pricing real-world assets. The theorem links asset prices to states of the world and state prices. We define an arbitrage opportunity in this framework and apply it to option pricing. The concepts of real-world and risk-neutral probabilities are introduced. We find that all properly normalized asset prices have a Martingale property under a properly selected synthetic probability measure. We explain how the fundamental theorem helps in specifying explicit stochastic differential equations that can be used in pricing and hedging in practice. Finally we develop the notion of binomial and trinomial ...
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