penalty_with_intensity_link: Helper function (volatility-normalized pricing error) for...

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

Description

Given a set SDE parameters, form a volatility term structure that fairly precisely matches the supplied prices of the variance_instruments. Then use that term structure and the default intensity to price all the fit_instruments, and compare them to the fit_instrument_prices.

Usage

penalty_with_intensity_link(
  p,
  s,
  h,
  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)) },
  ...,
  relative_spread_tolerance = 0.15,
  num_variance_time_steps = 30
)

Arguments

p	Power of default intensity
s	Proportion of constant default intensity
h	Base default intensity
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 price_with_intensity_link
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

Forms implied Black-Scholes volatilities from all supplied mid prices, and their implied bid and offer prices, as well as from the prices computed by the grid solver. Each instrument is then assigned an error term component in proportion to its weight and the pricing error (in implied vol terms) divided by the spread (also in implied vol terms).

See Also

price_with_intensity_link for the pricing function

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