fit_to_option_market {ragtop}

Calibrate volatilities and equity-linked default intensity

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