price_with_intensity_link {ragtop}

Helper function (instrument pricing) for calibration of 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 then price the instruments via equity linked default intensity of the form $h(s + (1-s)(S0/S_t)^p)$.

Usage

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

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

S0

Current underlying price

num_time_steps

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

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