fit_to_option_market: Calibrate volatilities and equity-linked default intensity

In brianboonstra/ragtop: Pricing Equity Derivatives with Extensions of Black-Scholes

Description

Given derivative instruments (subclasses of GridPricedInstrument, though typically either AmericanOption or EuropeanOption objects), along with their prices and spreads, calibrate variance cumulation (the at-the-money volatility of the continuous process) and equity linked default intensity of the form $h(s + (1-s)(S0/S_t)^p)$.

Usage

fit_to_option_market(
  variance_instruments,
  variance_instrument_prices,
  variance_instrument_spreads,
  fit_instruments,
  fit_instrument_prices,
  fit_instrument_spreads,
  fit_instrument_weights,
  S0,
  num_time_steps = 30,
  const_short_rate = 0,
  discount_factor_fcn = function(T, t) {     exp(-const_short_rate * (T - t)) },
  ...,
  base_default_intensity = 0.05,
  relative_spread_tolerance = 0.15,
  num_variance_time_steps = 30
)

Arguments

variance_instruments	A list of instruments in strictly increasing order of maturity, from which the volatility term structure will be inferred. Once the calibration is finished, the chosen parameters will reproduce the prices of these instruments with fairly high precision.
variance_instrument_prices	Central price targets for the variance instruments
variance_instrument_spreads	Bid-offer spreads used to normalize errors in variance instrument prices during term structure fitting
fit_instruments	A list of instruments in any order, from which the mispricing penalties used for judging fit quality will be computed
fit_instrument_prices	Central price targets for the variance instruments
fit_instrument_spreads	Bid-offer spreads used to normalize errors in fit instrument prices during default intensity
fit_instrument_weights	Weights applied to relative errors in fit instrument prices before summing to form the penalty
S0	Current underlying price
num_time_steps	Time step count passed on to find_present_value while fitting instrument values
const_short_rate	A constant to use for the instantaneous interest rate in case discount_factor_fcn is not given
discount_factor_fcn	A function for computing present values to time t of various cashflows occurring during this timestep, with arguments T, t
...	Further arguments passed to penalty_with_intensity_link
base_default_intensity	Overall default intensity (in natural units)
relative_spread_tolerance	Tolerance to apply in calling fit_variance_cumulation
num_variance_time_steps	Number of time steps to use in calling fit_variance_cumulation

Details

In its present form, this function uses a brain-dead grid search.

See Also

penalty_with_intensity_link for the penalty function used as an optimization target

brianboonstra/ragtop documentation built on March 7, 2020, 2:23 p.m.