equivalent_jump_vola_to_bs {ragtop}

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

Description

Find default-free volatility (i.e. volatility of a Wiener process with a companion jump process to default) based on known interest rates and hazard rates, using and at-the-money put option at the given tenor to set the standard price.

Usage

equivalent_jump_vola_to_bs(
  bs_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

bs_vola

BlackScholes volatility of an option with no default assumption

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

borrow_cost

Stock borrow cost, affecting the drift rate

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

Value

A scalar volatility

See Also

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