variance_cumulation_from_vols function

Create a variance cumulation function from a volatility term structure

Given a volatility term structure, create a corresponding variance cumulation function. The function assumes piecewise constant forward volatility, with the final such forward volatility extending to infinity.

variance_cumulation_from_vols(vols_df)

Arguments

• vols_df: A data.frame with numeric columns time (in increasing order) and volatility (not decreasing so quickly as to give negative forward variance)

Returns

A function taking two time arguments, which returns the cumulated variance from the second to the first

Examples

vc = variance_cumulation_from_vols(
  data.frame(time=c(0.1,2,3),
  volatility=c(0.2,0.5,1.2)))
vc(1.5, 0)