Price path: a new volatility measure
by Joanne Hill, Ph.D. and Matthew Celebuski
Many trading strategies rely on market levels or changes in those levels for allocation among asset
classes. In an option replication program, such as portfolio insurance, the option cost is paid throughout
the life of the program. Frequently, the estimated costs differ significantly from the actual cost even when
anticipated volatility estimates are realized.
An important reason for this discrepancy is that the order of the returns impacts the cost of an option
replication program but has no impact on the price of the option itself. That is, implied volatility may be
correctly estimated, but the sequence of price changes, or "price path," may signal trades more often than
historical volatility would suggest. Clearly, a volatility measure which focuses on the order of returns
would lead to a better understanding of the costs associated with these types of strategies.
Here, we introduce two possible measures that capture the order of returns for a particular time period
within a process that could generally be described as a random walk. In the short-run, a random walk
process can have a variety of return sequences, all having the same measured standard deviation, but also
having different dynamic trading strategy costs.