VALUATION MODELS

There are two main models for options valuation: The Black & Scholes model for pricing European options and the binomial options pricing model for American options. There are plenty of reasons why options trade away from the equilibrium price suggested by the models, however. Leverage is one of the chief reasons. Options are always cheaper than the underlying and as such a market participant can, by buying options rather than buying the underlying, achieve a position with more upside for the same outlay (but also a far greater risk to his capital).

Options models can be of particular use to market-makers and arbitrageurs who are normally trying to maintain flat positions, but who buy and sell options where they see a perceived edge. The models assist their position hedging by revealing how many of the underlying to buy or sell to achieve a neutrality vis-a-vis directional price movements. In reality this relationship can be hard to manage as the theory relies on constant changes to the trader’s position in the underlying based on changes in the underlying’s price, but the underlying will often trade in a manner which makes this impossible, for instance making large jumps, particularly between the start and end of each trading day.

As American options can be exercised at any point up to and including the expiry date, and European options can only be exercised at the expiry date, American options should always be worth more than European options. By exercising an American option early the residual time value in the option is being sacrificed. There are a few situations in which this is worth doing however:

• When a stocks pays a dividend or reaches the cut-off date for future dividend payments, all things being equal, the stock will fall in value by the amount being paid out. As such, an in-the-money call will lose some of its intrinsic value. Exercising beforehand would lock in that in that intrinsic value. If this saved intrinsic value were greater than the foregone time value, exercising would be profitable.
• A deep in-the-money gold price put will often be exercised early so as to avoid the effects of inflation on the value of the resulting cash payoff, as all things being equal gold holds value, unlike cash.
• A deep in-the-money currency option will frequently be exercised early if there is a differential in the interest rates of the two currencies involved in the trade. If the currency to be received pays a higher interest rate, the buyer may exercise early so as to start receiving that interest as quickly as possible.                 Links