Implied volatility of any instrument

Description

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.

Usage

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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

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.

Value

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

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 Equity Dependent Default Intensity: find_present_value, fit_to_option_market_df, fit_variance_cumulation, form_present_value_grid

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

Examples

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

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