Discount Curve
(TODO) Discount curve obtained from yields by interpolation
Input:
- : the maturities,
- : the discount factors
- : the initial short-term interest rate
- : the initial time
- : an interpolation method, a class
cfl:Interpolation
Output:
the discount curve
where the yield curve is the -interpolation of the market yields to maturity
Discount curve obtained from yields by log interpolation
Input:
- : the maturities,
- : the discount factors
- : the initial time
- : an interpolation method, a class
cfl:Interpolation
Output:
- : the discount curve, where the function is the -interpolation of the logs of the market discount factors:
Algorithm:
Step 1 (The logarithms of discount factors)
Compute the logarithms of market discount factors:
where and thus .
Step 2 (Interpolation)
Compute the interpolated function
Step 3
Return
(TODO) Discount curve obtained from swap rates by log interpolation
Input:
- : the time interval between payments given as year fraction
- : the vector of swap rates, where is the current swap rate in the contract with time interval and the number of payments
- : the initial time given as year fraction
- : an interpolation method, a class
cfl::Interpolation
Output:
The discount curve on .
Algorithm:
Step 1
Compute the discount factors for maturities
Step 2
We apply the -interpolation to , where
Forward Curve
Forward curve obtained from cost-of-carry rates by interpolation
Input:
- : the spot price
- : the maturities,
- : the forward prices
- : the initial cost-of-carry rate
- : the initial time = the issue time for forwards,
- : an interpolation method, a class
cfl:Interpolation
Output:
the forward curve
where the cost-of-carry function is the -interpolation of the market cost-of-carry rates
Algorithm:
Step 1 (Cost-of-carry rates)
Compute the market cost-of-carry rates:
Step 2 (Interpolation)
Compute function
Step 3
Return
(TODO) Forward curve obtained by log interpolation
Input:
- : the market spot price
- : the maturities,
- : the market forward prices
- : the initial time,
- : an interpolation method, a class
cfl::Interpolation
Output:
The forward curve
where the function is the -interpolation of the logs of the market spot and forward prices:
Other Curves
(TODO) Volatility curve obtained from variances by interpolation
Input:
- : the maturities,
- : the implied volatilities
- : the initial time,
- : an interpolation method
Output:
the volatility curve
where the variance function is the -interpolation of the market variances:
(TODO) Forward exchange curve obtained from cost-of-carry rates by interpolation
Input:
- : the current spot exchange rate
- : the discount factors in domestic currency
- : the discount factors in foreign currency
- : the maturities of the discount factors,
- : the initial time given as year fraction
- : an interpolation method, a class
cfl::Interpolation
Output:
The forward exchange curve
where the cost-of-carry rate curve is obtained by the -interpolation of the market cost-of-carry rates , and .
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