Boundary Conditions
Candlefocus EditorA boundary condition is a set limit placed on a financial option, with a minimum and maximum value that works to both protect the investor and aid in understanding the true value of the option. The concept of boundary conditions came into play prior to the advent of the binomial tree and Black-Scholes pricing models, and were used to provide an upper and lower limit for the pricing of call and put options.
When dealing with the concept of boundary conditions, it is important to understand that the minimum value for any option is zero. An option cannot be sold for less than this, as it would represent a financial loss. On the other hand, the maximum value for an option used to be set to the current value of the underlying asset.
However, in order to accurately reflect the true value of a financial option, it is important to differentiate between American and European options. An American option gives the investor the right to exercise the option prior to the expiry date, while a European option requires the option to be exercised only on the expiry date. As such, the boundary condition for an American option tends to be set slightly higher than that for a European option, as the American option has greater flexibility and therefore more value.
In conclusion, boundary conditions are a key concept when it comes to financial options. The use of boundary conditions allows for an upper and lower limit for potential pricing of an option, and this sets a minimum and maximum value to minimise financial risks and better reflect the true value of the option. The boundaries also vary between American and European Options, as the American option comes with more flexibility and therefore can be set to a higher price.