Given that either increases to + mA + VA or decreases to rj+ mA - OVA...

 

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Given that either increases to + mA + VA or decreases to rj+ m₂A - OVA in the next period, where A is the passage of time in years between two periods and √50 = 7.071, calculate the implied by the above interest rate tree (round to 2 decimals) and explain what means in fixed income securities. (2%) b) Following Question 2-a, extend the above binomial tree of interest rates to 3 steps given E(r₂) = 5.1%. (2%) c) What is the risk-neutral probability in period i-0? (Round to 2 decimals) (4%) d) What is the risk-neutral probability in period i=1? (Round to 2 decimals) (5%) e) What is the risk-neutral probability in period i-2? (Round to 2 decimals) (6%) 1) What are the possible N₁ and N₂ for the swap? (3%) g) What is the fair swap rate e, such that the value of the swap is 0 at inception? (6%) h) What is the swap's spot rate duration in Period i-1 after the exchange of cash flow when the interest rate goes up? (3%) i) Describe the dynamic replication strategies of the swap from Firm A's perspective using the short-term bond maturing in the next period and the long-term bond maturing in Period i-3 (10%) 2. Binomial Tree Pricing Time Periodi 0 Maturity yield 2 With probability of "up" movement p-0.6 0 0 i. Maturity i-2 ii. 2.33% iv. 0.5 2.33% 1 3.0782% 0.5 1 5.1042% 2.28% 1.5 3.6815% A modified index amortizing swap (henceforth, the swap) is a swap whose notional value decreases over time depending on the interest rate scenario. Consider the index amortizing swap with initial notional No = 100 with the following characteristics: Amortization schedule: a. If r < 0.02 then 100% reduction in notional; b. If 0.02 ≤r <0.04 then 50% reduction in notional; c. If 0.04 < < 0.06 then 20% reduction in notional; 1 2 d. If r 20.06 then no reduction in notional; At i-O no amortization takes place (lockout period). 7.0284% 4.2% 1.3716% 2 4.3085% In Period i (i=1, 2), Firm A pays Bank B cx N, XA with a fixed swap rate c, while Bank B pays Firm A r X N, XA with a floating rate r. N, is the notional in Period i; A is the time passage between two periods, r, is the 1-period interest rate in Period i. For example, if at time i-1 the interest rate went up to 4.5 % (r₂ = 0.045), then the notional to apply to the current payment is not N₂ =100 but N₁ =x (1-20%) =80; if at time i-2 the interest rate went down to 3.5% (r₂ = 0.035), then the notional N₂ = 80 ×(1-50%) = 40 Given that either increases to + mA + VA or decreases to rj+ m₂A - OVA in the next period, where A is the passage of time in years between two periods and √50 = 7.071, calculate the implied by the above interest rate tree (round to 2 decimals) and explain what means in fixed income securities. (2%) b) Following Question 2-a, extend the above binomial tree of interest rates to 3 steps given E(r₂) = 5.1%. (2%) c) What is the risk-neutral probability in period i-0? (Round to 2 decimals) (4%) d) What is the risk-neutral probability in period i=1? (Round to 2 decimals) (5%) e) What is the risk-neutral probability in period i-2? (Round to 2 decimals) (6%) 1) What are the possible N₁ and N₂ for the swap? (3%) g) What is the fair swap rate e, such that the value of the swap is 0 at inception? (6%) h) What is the swap's spot rate duration in Period i-1 after the exchange of cash flow when the interest rate goes up? (3%) i) Describe the dynamic replication strategies of the swap from Firm A's perspective using the short-term bond maturing in the next period and the long-term bond maturing in Period i-3 (10%) 2. Binomial Tree Pricing Time Periodi 0 Maturity yield 2 With probability of "up" movement p-0.6 0 0 i. Maturity i-2 ii. 2.33% iv. 0.5 2.33% 1 3.0782% 0.5 1 5.1042% 2.28% 1.5 3.6815% A modified index amortizing swap (henceforth, the swap) is a swap whose notional value decreases over time depending on the interest rate scenario. Consider the index amortizing swap with initial notional No = 100 with the following characteristics: Amortization schedule: a. If r < 0.02 then 100% reduction in notional; b. If 0.02 ≤r <0.04 then 50% reduction in notional; c. If 0.04 < < 0.06 then 20% reduction in notional; 1 2 d. If r 20.06 then no reduction in notional; At i-O no amortization takes place (lockout period). 7.0284% 4.2% 1.3716% 2 4.3085% In Period i (i=1, 2), Firm A pays Bank B cx N, XA with a fixed swap rate c, while Bank B pays Firm A r X N, XA with a floating rate r. N, is the notional in Period i; A is the time passage between two periods, r, is the 1-period interest rate in Period i. For example, if at time i-1 the interest rate went up to 4.5 % (r₂ = 0.045), then the notional to apply to the current payment is not N₂ =100 but N₁ =x (1-20%) =80; if at time i-2 the interest rate went down to 3.5% (r₂ = 0.035), then the notional N₂ = 80 ×(1-50%) = 40

Answer rating: 100% (QA)

a The implied volatility can be calculated as 50 7071 Volatility sigma in fixed income pricing refer... View the full answer