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

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Description

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.

Usage

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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

Value

A scalar defaultable volatility of an option

See Also

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

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

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