Derivatives: Swap Markets and Contracts

Question 1

Fixed Rate for Swap Contract

Answer 1

Fixed Rate = DFn / (DF1 + DF2 + DF3… + DFn)

• • DF: Discount Factor*
• • If annualized then Fixed rate must multiplied by the appropriate factor - semi-annual x2. *

Question 2

No arbitrage price on forward contract on treasury bond

Answer 2

Step one: NPV of next coupon payment PMT/1+r^t

Step two: (Vo - NPVcoupon) X 1+r^t’

• t = time to next coupon/365*
• t’ = forward length/365*
• Vo = price of bond now*
• r = effective rf%*

Question 3

Loss (or value of short position) on no arbitrage forward contract treasury bond

Answer 3

Step one: Current NPV of next coupon payment PMT/1+r^t*

Step two: V1 - NPVcoupon - (Original forward value) / 1+r^t*’

t* = Current time to coupon payment / 365

t*’ = Current time to expiration / 365

• Original calculation to determin forward’s first price…*
• Step one: NPV of next coupon payment PMT/1+r^t*
• Step two: (Vo - NPVcoupon) X 1+r^t’*
• t = time to next coupon/365*
• t’ = forward length/365*
• Vo = price of bond now*
• r = effective rf%*

Question 4

Determine Forward Rate Agreement rate from Spot Rate Curve (2X5)

Answer 4

= ({[(1+150d%)^150/360] / [(1+60d%)^60/360]} - 1) / 360/90

- curve moves in 30 day increments

Question 5

Loss (or gain) on short position on 2x5 FRA 30 days later

Answer 5

Step one expected Payoff = (FRAo - FRA1)(notional value)(90/360)

Step two PV of expected Payoff = payoff/1+120day%^(120/360)

- note: the PV is probably not going to be much less than step 1.