equivalent_jump_vola_to_bs: Find jump process volatility with a given default risk from a...

In brianboonstra/ragtop: Pricing Equity Derivatives with Extensions of Black-Scholes

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()

brianboonstra/ragtop documentation built on March 7, 2020, 2:23 p.m.