Description Usage Arguments Value References

The function `newton.raphson.root`

is a general root finder which
can find the zero of any function whose derivative is available.
In this package, it is called by `irr.solve`

and by
`GenBSImplied`

. It can be used in other situations as
well - see the examples below.

1 2 3 4 5 6 7 8 9 | ```
newton.raphson.root(
f,
guess = 0,
lower = -Inf,
upper = Inf,
max.iter = 100,
toler = 1e-06,
convergence = 1e-08
)
``` |

`f` |
The function whose zero is to be found. An R function object that takes one numeric argument and returns a list of two components (value and gradient). In an IRR application, these two components will be the NPV and the DV01/10000. In an implied volatility application, the components will be the option price and the vega. See also the examples below |

`guess` |
The starting value (guess) from which the solver starts searching for the IRR |

`lower` |
The lower end of the interval within which to search for the root |

`upper` |
The upper end of the interval within which to search for the root |

`max.iter` |
The maximum number of iterations of the Newton-Raphson procedure |

`toler` |
The criterion to determine whether a zero has been
found. If the value of the function exceeds |

`convergence` |
The relative tolerance threshold used to
determine whether the Newton-Raphson procedure has
converged. The procedure terminates when the last step is less
than |

The function returns `NA`

under either of two conditions: (a)
the procedure did not converge after `max.iter`

iterations,
or (b) the procedure converged but the function value is not zero
within the limits of `toler`

at this point. The second
condition usually implies that the procedure has converged to a
non zero local minimum from which there is no downhill gradient.

If the iterations converge to a genuine root (within the limits of
`toler`

), then it returns the root that was found.

The Newton Raphson solver was converted from C++ code in the Boost library

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