Price Volatility and Underlying Causes

Securities valuation and security price volatility are inextricably bound together. After all, to know which factors determine the price of a security is to know why prices change when such factors change. The changes in factors drive the variation (i.e., volatility) in observed prices.

The relationship also can be understood, however, by beginning with volatility and tracking back to valuation. In this direction of analysis, we presume that we can know what various cash flows and/or terminal cash values will arise as a function of both time and the then-prevailing myriad possible states of the world. This approach, known to economists as the state-space approach,1 attempts with one or another different mathematical techniques to discount the future cash flows on both a time- and probability-weighted basis to arrive at a current-period valuation. By the same procedure, security prices at each future state-space can be determined as well.

Modern financial theory and practice are full of examples of this second approach to volatility and valuation; they include the seminal results of the Capital Asset Pricing Model, the Black-Scholes option formula, term and default structure models of the bond markets, and virtually all derivative models.

The approach we follow in this work, from valuation to volatility, is not quite as prevalent among theoreticians and practitioners as is the volatility-to-value approach. However, our model is capable ...

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