equivalent_bs_vola_to_jump function

Find straight Black-Scholes volatility equivalent to jump process with a given default risk

Find Black-Scholes volatility based on known interest rates and hazard rates, using an at-the-money put option at the given tenor to set the standard price.

equivalent_bs_vola_to_jump(
  jump_process_vola,
  time,
  const_short_rate = 0,
  const_default_intensity = 0,
  discount_factor_fcn = function(T, t, ...) {     exp(-const_short_rate * (T - t)) },
  survival_probability_fcn = function(T, t, ...) {     exp(-const_default_intensity * (T
    - t)) },
  dividends = NULL,
  borrow_cost = 0,
  dividend_rate = 0,
  relative_tolerance = 1e-06,
  max.iter = 100
)

Arguments

• jump_process_vola: Volatility of default-free process

• time: Time to expiration of associated option contracts

• const_short_rate: A constant to use for the instantaneous interest rate in case discount_factor_fcn

  is not given

• const_default_intensity: A constant to use for the instantaneous default intensity in case survival_probability_fcn

  is not given

• discount_factor_fcn: A function for computing present values to time t of various cashflows occurring during this timestep, with arguments T, t

• survival_probability_fcn: (Implied argument) A function for probability of survival, with arguments T, t and T>t.

• dividends: A data.frame with columns time, fixed, and proportional. Dividend size at the given time is then expected to be equal to fixed + proportional * S / S0. Fixed dividends will be converted to proportional for purposes of this algorithm.

• borrow_cost: A continuous rate for stock borrow costs

• dividend_rate: A continuous accumulation rate for the stock, affecting the drift

• relative_tolerance: Relative tolerance in instrument price defining the root-finder halting condition

• max.iter: Maximum number of root-finder iterations allowed

Returns

A scalar defaultable volatility of an option

See Also

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

Other Equity Independent Default Intensity: american_implied_volatility(), american(), black_scholes_on_term_structures(), blackscholes(), equivalent_jump_vola_to_bs(), implied_volatilities_with_rates_struct(), implied_volatilities(), implied_volatility_with_term_struct(), implied_volatility()