Helper function (instrument pricing) for calibration of equitylinked 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
atthemoney volatility of the continuous process) and then price the instruments via equity linked default
intensity of the form $h(s + (1s)(S0/S_t)^p)$.
Usage
1 2 3 4  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)

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 
Bidoffer 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 
S0 
Current underlying price 
num_time_steps 
Time step count passed on to 
... 
Further arguments passed to both

relative_spread_tolerance 
Tolerance to apply in
calling 
num_variance_time_steps 
Number of time steps to use in
calling 