implied_jump_process_volatility function

Implied volatility of any instrument

Use the grid solver to generate instrument prices via find_present_value and run them through a bisective root search method until a constant volatility matching the provided instrument price has been found.

implied_jump_process_volatility(
  instrument_price,
  instrument,
  ...,
  starting_volatility_estimate = 0.85,
  relative_tolerance = 0.005,
  max.iter = 100,
  max_vola = 4
)

Arguments

• instrument_price: Target price for root finder
• instrument: Instrument to search for the target price on, passed as the sole instrument to find_present_value
• ...: Additional arguments to be passed on to find_present_value
• starting_volatility_estimate: Bisection method original guess
• relative_tolerance: Relative tolerance in instrument price defining the root-finder halting condition
• max.iter: Maximum number of root-finder iterations allowed
• max_vola: Maximum volatility to try

Returns

A list of present values, with the same names as instruments

Details

Unlike american_implied_volatility, this routine allows for any legal term structures and equity-linked default intensities. For that reason, it eschews the control variate tricks that make american_implied_volatility so much faster.

Note that equity-linked default intensities can result in instrument prices that are not monotonic in volatility. This bisective root finder will find a solution but not necessarily any particular one.

Examples

implied_jump_process_volatility(
    25, AmericanOption(maturity=1.1, strike=100, callput=-1),
    S0=100, num_time_steps=50, relative_tolerance=1.e-3)

See Also

find_present_value for the underlying pricing algorithm, implied_volatility_with_term_struct for European options without equity dependence of default intensity, american_implied_volatility for the same on American options

Other Implied Volatilities: american_implied_volatility(), equivalent_bs_vola_to_jump(), equivalent_jump_vola_to_bs(), fit_variance_cumulation(), implied_volatilities_with_rates_struct(), implied_volatilities(), implied_volatility_with_term_struct(), implied_volatility()

Other Equity Dependent Default Intensity: find_present_value(), fit_to_option_market_df(), fit_variance_cumulation(), form_present_value_grid()