Define Boundary Conditions

 

Boundary Conditions

What do you mean by boundary conditions?

The maximum and lowest values used to determine where the price of an option must lay are known as boundary conditions. Boundary conditions are used to predict what an option's price may be, although the option's real price might be greater or lower than the boundary condition.

Because options cannot be priced in negative money, the minimum boundary value for all options contracts is always zero. Meanwhile, maximum boundary values vary based on whether the option is a call or a put, as well as whether it is an American or European option.

TAKEAWAYS IMPORTANT

• Prior to the development of the binomial tree and Black-Scholes pricing models, boundary conditions were employed to establish the minimum and maximum permissible values for call and put options.

• Because American options can be exercised before expiration, boundary requirements differ depending on whether the option is American or European.

• Because an option cannot be sold for a negative sum of money, its absolute minimum value is zero.

• The current value of the underlying asset is used as the maximum value in a border condition.

Understanding the Concept of Boundary Conditions

Investors and traders depended largely on boundary conditions to define the lowest and maximum potential values for the call and put options they were pricing before the emergence of binomial tree pricing models and the Black-Scholes model. Because American options can be exercised early, these boundary criteria differ depending on whether the option is American or European.

The ability to exercise at any time before the expiration date has an impact on how the price is determined, and American options will trade at a higher premium than identical European options as a result of this feature.

Boundary Conditions (Minimum and Maximum)

Because an option cannot be sold for a negative sum of money, its absolute minimum value is zero. The current value of the underlying asset is used as the maximum value in a border condition. If the underlying asset's price is higher than the price specified in the call option, the investor will not exercise the option since doing so would result in the investor paying more than the market price. Both a European and an American call fall within this category.

When the underlying asset has no value, such as in the case of a company's bankruptcy when the underlying security is a stock, the maximum value of a put option is achieved. The current value of the exercise price is the highest value estimated for a European put option. This is because European options cannot be exercised at any time and must be executed at a certain price upon expiration. An American choice must have at least the same value as a European option.

While an asset's maximum value might theoretically be set to infinity (i.e., an asset's value could grow indefinitely), this is deemed impractical. The underlying asset's value will most likely fall within a suitable range that may be predicted using standard deviations or other stochastic approaches.