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.
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
)Power of default intensity
Proportion of constant default intensity
Base default intensity
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.
Central price targets for the variance instruments
Bid-offer spreads used to normalize errors in variance instrument prices during term structure fitting
A list of instruments in any order, from which the mispricing penalties used for judging fit quality will be computed
Central price targets for the variance instruments
Bid-offer spreads used to normalize errors in fit instrument prices during default intensity
Weights applied to relative errors in fit instrument prices before summing to form the penalty
Current underlying price
Time step count passed on to find_present_value
while fitting instrument values
A constant to use for the instantaneous interest rate in case discount_factor_fcn
is not given
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
Tolerance to apply in
calling fit_variance_cumulation
Number of time steps to use in
calling fit_variance_cumulation
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).
price_with_intensity_link for the pricing function