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 then price the instruments via equity linked default
intensity of the form $h(s + (1-s)(S0/S_t)^p)$.
price_with_intensity_link(
p,
s,
h,
variance_instruments,
variance_instrument_prices,
variance_instrument_spreads,
fit_instruments,
S0,
num_time_steps = 30,
...,
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
Current underlying price
Time step count passed on to find_present_value
while fitting instrument values
Further arguments passed to both
fit_variance_cumulation and to
find_present_value
Tolerance to apply in
calling fit_variance_cumulation
Number of time steps to use in
calling fit_variance_cumulation