Assume that the 1-year, 2-year, 3-year, and 4-year zero rates are respectively r = 3%, 72...

 

Transcribed Image Text:

Assume that the 1-year, 2-year, 3-year, and 4-year zero rates are respectively r₁ = 3%, 72 = 3.4%, r3 = 3.7%, and r4 = 3.9% with continuous compounding. Thus, the price of ZCB Z(0, t) are given by Z(0, t) = ett for 1 ≤ t ≤ 4. - (1) Consider a European receiver swaption that gives the holder the right to enter into a 3-year receiving swap in a year, i.e., a 1-year into 3-year (or a 1-year by 4-year) receiver swaption, where a fixed rate (strike) of 4.5% is received and floating is paid. The principal is $1000 and payments are exchanged annually. (a) Determine the forward swap rate yo[1, 4]. (b) Assume the swap rate volatility is 30%, apply the Black's formula to calculate the price of the receiver swaption. (2) Assume that the floor rate (strike) is also 4.5%. The principal underlying the floor is $1,000 and the reset frequency is 1 year. Assume that the volatility is 30% for all floorlets. Determine the price of floor from 1 to 4 years. Observe that the price of floor is larger than that of the receiver swaption obtained in the last problem. Assume that the 1-year, 2-year, 3-year, and 4-year zero rates are respectively r₁ = 3%, 72 = 3.4%, r3 = 3.7%, and r4 = 3.9% with continuous compounding. Thus, the price of ZCB Z(0, t) are given by Z(0, t) = ett for 1 ≤ t ≤ 4. - (1) Consider a European receiver swaption that gives the holder the right to enter into a 3-year receiving swap in a year, i.e., a 1-year into 3-year (or a 1-year by 4-year) receiver swaption, where a fixed rate (strike) of 4.5% is received and floating is paid. The principal is $1000 and payments are exchanged annually. (a) Determine the forward swap rate yo[1, 4]. (b) Assume the swap rate volatility is 30%, apply the Black's formula to calculate the price of the receiver swaption. (2) Assume that the floor rate (strike) is also 4.5%. The principal underlying the floor is $1,000 and the reset frequency is 1 year. Assume that the volatility is 30% for all floorlets. Determine the price of floor from 1 to 4 years. Observe that the price of floor is larger than that of the receiver swaption obtained in the last problem.

Answer rating: 100% (QA)

1 a The forward swap rate y1 4 is the rate per annum applied to the notional principal of 1000 payable at the end of each year over the 3year period I... View the full answer