4.06.2005

Q: What's the 6-month forward rate...

... 2 years from now given the following spot rates?

Period Years to Maturity Spot Rate
1 .5 4.250%
2 1 4.750%
3 1.5 5.050%
4 2.0 7.000%
5 2.5 8.750%
6 3.0 9.250%

A: 4th period forward rate can be derived from spot rates of 5th period and4th period. Forward rate = [(1 + 5th_spot_rate / 2)^5 / (1 + 4th_spot_rate / 2)^4] -1 = [(1 + 0.0875/2)5/(1 + 0.0700/2)4] -1 = 7.95%. Annualized the rate one gets 15.9%. Bonus Points

  • forward rates assess the future interest rate for some period in the future. Useful when one can't decide how long to hold a bond, such as 4 periods or 5 periods.
  • The notation (1)f(4): the subscript before "f" is the length of time that the rate applies (ie. 1 period=6 months). The subscript after "f" refers to the period when the forward rate begins (ie. 4 periods = 2 years into the future).

Category: C++ Quant > Debt > Valuation

No comments:

Post a Comment