CONFERENCE ON MATHEMATICAL FINANCE
May 19, 20, and 21, 2000
University of Missouri - Columbia
CONFERENCE ON MATHEMATICAL FINANCE
May 19, 20, and 21, 2000
University of Missouri - Columbia
Abstract: We consider the role of options when markets in its underlying asset are frictionless and when this underlying has a volatility process and jump arrival rates which are arbitrarily stochastic. By combining a static option position with a particular dynamic hedging strategy, we characterize the option's time value as the (risk-neutral) expected benefit from being able to buy or sell one share of the underlying at the option's strike whenever the strike price is crossed. The buy/sell decision can be based on the post jump price, so that a rational investor buys on rises and sells on drops. Thus, an option provides liquidity at its strike even when the market doesn't. We next present two methods for extending this local liquidity to every price between the pre and post jump level. The first method involves holding a continuum of options of all strikes. The second method holds one option, but adjusts the dynamic hedging strategy. We discuss the advantages and disadvantages of each approach and consider the benefits of combining them.
