Pricing of Range Accrual Notes with Double Barriers

The range accrual note which is also called range accrual option or range accumulation option is a kind of path-dependent financial derivative. The pricing of
path-dependent derivative is most difficult because the entire price history of the underlying asset price must be considered. So investors have to keep their eyes on the
whole underlying price path rather than the terminal price as in the plain vanilla option. In this thesis, the range accrual note without barriers will be discussed first
and the range accrual note with double barriers later.
The range accrual note is a combination of a series of binary options with each option covering a short period, typically one day or one week. The payoff of the range
accrual note is the sum of the payoffs of the component binary options. The component notes, in turn, pay off when the underlying price or rate falls within a predefined range. We monitor the closing prices of the covering period to see if the underlying asset price falls within the predefined range. The note accrues the payoffs when the underlying reference point is within a predefined range and accrues zero when outside that range, the payoffs accumulated at maturity.
With barriers, the range accrual note stops accumulating payoffs when the underlying asset price touches the barrier. The total payoff of the range accrual note with double barriers is determined according to the accumulated accruals before the note knocks out and pays off at maturity. If the barriers are not touched, the note
accumulates as the range accrual note without barriers. It can be decomposed into a series of double barrier knock out binary options. Because of the characteristics of the range accrual note, monitoring is applied daily or weekly.
Up to now, there is no exact closed form solution to price the discretely monitored barrier option. So this thesis uses numerical method to price the range accrual note with double barriers.