Chapter 3The Consistency Problem

Whether cross-sectional option prices are consistent with the time-series properties of the underlying asset returns is probably the most fundamental of tests.

—David S. Bates


In the previous chapter, we discussed two different approaches for stochastic volatility parameter estimation: the cross-sectional one where we use a number of options prices for given strike prices (and possibly maturities); and the time-series approach where we use the stock prices over a certain period of time.

One natural question1 would therefore be the following: Will the theoretically invariant portion of the parameter-sets obtained by the two methods be the same?

More accurately, supposing we are at time c03-math-0001 and we use c03-math-0002 options with strikes c03-math-0003 and with maturity c03-math-0004, we have

3.1 equation

The above options could include calls or puts.

On the other hand, during the period c03-math-0006, we can ...

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