implied_volatilities function

Implied volatilities of european-exercise options under Black-Scholes or a jump-process extension

Find default-free volatilities based on known interest rates and hazard rates, using a given option price.

implied_volatilities(
  option_price,
  callput,
  S0,
  K,
  r,
  time,
  const_default_intensity = 0,
  divrate = 0,
  borrow_cost = 0,
  dividends = NULL,
  relative_tolerance = 1e-06,
  max.iter = 100,
  max_vola = 4
)

Arguments

• option_price: Present option values (may be a vector)
• callput: 1 for calls, -1 for puts (may be a vector)
• S0: initial underlying price (may be a vector)
• K: strike (may be a vector)
• r: risk-free interest rate (may be a vector)
• time: Time from 0 until expiration (may be a vector)
• const_default_intensity: hazard rate of underlying default (may be a vector)
• divrate: A continuous rate for dividends and other cashflows such as foreign interest rates (may be a vector)
• borrow_cost: A continuous rate for stock borrow costs (may be a vector)
• 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 proprtional for purposes of this algorithm.
• relative_tolerance: Relative tolerance in option price to achieve before halting the search
• max.iter: Number of iterations to try before abandoning the search
• max_vola: Maximum volatility to try in the search

Returns

Scalar volatilities

See Also

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

Other European Options: black_scholes_on_term_structures(), blackscholes(), implied_volatilities_with_rates_struct(), 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(), equivalent_jump_vola_to_bs(), implied_volatilities_with_rates_struct(), implied_volatility_with_term_struct(), implied_volatility()