R: Fit piecewise constant volatilities to a set of equity...

fit_variance_cumulation {ragtop}

R Documentation

Fit piecewise constant volatilities to a set of equity options

Description

Given a set of equity options with increasing tenors, along with target prices for those options, and a set of equity-lined default SDE parameters, fit a vector of piecewise constant volatilities and an associated cumulative variance function to them.

Usage

fit_variance_cumulation(
  S0,
  eq_options,
  mid_prices,
  spreads = NULL,
  initial_vols_guess = 0.55 + 0 * mid_prices,
  use_impvol = TRUE,
  relative_spread_tolerance = 0.01,
  force_same_grid = FALSE,
  num_time_steps = 40,
  const_short_rate = 0,
  const_default_intensity = 0,
  discount_factor_fcn = function(T, t, ...) {     exp(-const_short_rate * (T - t)) },
  survival_probability_fcn = function(T, t, ...) {     exp(-const_default_intensity * (T
    - t)) },
  default_intensity_fcn = function(t, S, ...) {     const_default_intensity + 0 * S },
  dividends = NULL,
  borrow_cost = 0,
  dividend_rate = 0,
  ...
)

Arguments

`S0`	Current stock price
`eq_options`	A list of options to find prices for. Each must have fields `callput`, `maturity`, and `strike`. This list must be in strictly increasing order of maturity.
`mid_prices`	Prices to match
`spreads`	Spreads within which any match is tolerable
`initial_vols_guess`	Initial set of volatilities to try in the root finder
`use_impvol`	Judge fit quality on implied vol distance rather than price distance
`relative_spread_tolerance`	Tolerance multiplier on bid-ask spreads taken from vol normalization
`force_same_grid`	Price all options on the same grid, rather than having smaller timestep sizes for earlier maturities
`num_time_steps`	Minimum number of time steps in the grid
`const_short_rate`	A constant to use for the instantaneous interest rate in case `discount_factor_fcn` is not given
`const_default_intensity`	A constant to use for the instantaneous default intensity in case `default_intensity_fcn` is not given
`discount_factor_fcn`	A function for computing present values to time `t` of various cashflows occurring, with arguments `T`, `t`
`survival_probability_fcn`	A function for probability of survival, with arguments `T`, `t` and `T>t`. E.g. with a constant volatility `s` this takes the form `(T-t)s^2`. This argument is only used in normalization of prices to vols for root finder tolerance, and is therefore entirely optional
`default_intensity_fcn`	A function for computing default intensity occurring during this timestep, dependent on time and stock price, with arguments `t`, `S`. Should be consistent with `survival_probability_fcn` if specified
`dividends`	A `data.frame` with columns `time`, `fixed`, and `proportional`. Dividend size at the given `time` is
`borrow_cost`	Stock borrow cost, affecting the drift rate
`dividend_rate`	Continuous dividend rate, affecting the drift rate
`...`	Futher arguments to `find_present_value`

Details

By default, the fitting happens in implied Black-Scholes volatility space for better normalization. That is to say, the fitting does pricing using the full SDE and PDE solver via find_present_value, but judges fit quality on the basis of running resulting prices through a nonlinear transformation that just happens to come from the straight Black-Scholes model.

Value