vanillaOption

Syntax

vanillaOption(settlement, maturity, evalDate, spot, strike, riskFree, divYield, volatility, isCall, style, basis, calendar, [method=`BS], [kwargs], [mode=0])

Arguments

Note: Scalar inputs will be automatically expanded to match the length of other vector inputs. All vector inputs must be of equal length.

settlement is a DATE scalar or vector indicating the settlement date.

maturity is a DATE scalar or vector indicating the maturity date.

evalDate is a DATE scalar or vector indicating the evaluation date.

spot is a numeric scalar or vector indicating the spot price.

strike is a numeric scalar or vector indicating the strike price.

riskFree is a numeric scalar or vector indicating the risk-free interest rate.

divYield is a numeric scalar or vector indicating the dividend yield.

volatility is a numeric scalar or vector indicating the volatility.

isCall is a Boolean scalar or vector.

  • true: buy (call option)
  • false: sell (put option)

style is a STRING scalar or vector indicating the option exercise style. It can be ‘european’ or ‘american’.

basis is an INT/STRING scalar or vector indicating the day-count basis. It can be:

  • 0/"Thirty360US": US (NASD) 30/360
  • 1/"ActualActual": actual/actual
  • 2/"Actual360": actual/360
  • 3/"Actual365": actual/365
  • 4/"Thirty360EU": European 30/360

calendar is a STRING scalar or vector indicating the trading calendar(s). See Trading Calendar for more information.

method (optional) is a STRING scalar indicating the pricing method:

  • 'BS' (default): Black-Scholes model (for European options only).
  • 'FDBS': Finite Difference method + Black-Scholes model.
  • 'heston': Heston model (for European options only).
  • 'FDHeston': Finite Difference method + Heston model.
  • 'PTDHeston': Piecewise Time Dependent Heston model (for European options only).

kwargs (optional) is a dictionary specifying other required parameters. Leave it unspecified when method='BS'. The key-values pairs should be:

  • When method='FDBS':
    • 'xGrid': A scalar or vector with integers greater than 1, indicating the number of spatial grids used for discretization in the finite difference method.
    • 'tGrid': A scalar or vector with positive integers, indicating the number of time grids used for discretization in the finite difference method. tGrid must be greater than 0.
    • 'dampingSteps': A scalar or vector with non-negative integers, representing the number of damping steps applied in the finite difference solution process.
  • When method='heston':
    • 'theta': A numeric scalar or vector representing the long-term mean of the variance.
    • 'kappa': A numeric scalar or vector indicating the speed of mean reversion for the variance.
    • 'rho': A numeric scalar or vector representing the correlation coefficient between the asset price and volatility.
    • 'sigma': A numeric scalar or vector representing the volatility of volatility.
  • When method='FDHeston':
    • 'theta': A numeric scalar or vector representing the long-term mean of the variance.
    • 'kappa': A numeric scalar or vector indicating the speed of mean reversion for the variance.
    • 'rho': A numeric scalar or vector representing the correlation coefficient between the asset price and volatility.
    • 'sigma': A numeric scalar or vector representing the volatility of volatility.
    • 'xGrid': An scalar or vector with integers greater than 1, indicating the number of spatial grids used for discretization in the finite difference method.
    • 'vGrid': An scalar or vector with integers greater than 1, indicating the number of volatility grids used for discretization in the finite difference method.
    • 'tGrid': An scalar or vector with positive integers, indicating the number of time grids used for discretization in the finite difference method. tGrid must be greater than 0.
    • 'dampingSteps': An scalar or vector with non-negative integers, representing the number of damping steps applied in the finite difference solution process.
  • When method='PTDHeston':
    • 'times': A numeric vector or array indicating the time points when conditions change.
    • 'theta': A numeric scalar or vector representing the long-term mean of the variance.
    • 'kappa': A numeric scalar or vector indicating the speed of mean reversion for the variance.
    • 'rho': A numeric scalar or vector representing the correlation coefficient between the asset price and volatility.
    • 'sigma': A numeric scalar or vector representing the volatility of volatility.

mode (optional) is an integeralscalar or vector indicating the output mode:

  • 0 (default): NPV (net present value) only.
  • 1: NPV and Greeks (delta, gamma, theta, vega and rho) in a nested tuple.
  • 2: NPV and Greeks (delta, gamma, theta, vega and rho) in an ordered dictionary.

Details

Calculate vanilla option prices using specified methods.

Return value:

  • When mode=0, return a FLOATING scalar or vector indicating the NPV.
  • When mode=1, return a tuple with two tuple elements, NPV and Greeks (delta, gamma, theta, vega and rho).
  • When mode=2, return an ordered dictionary with keys 'npv', 'delta', 'gamma', 'theta', 'vega', and 'rho'.

Examples

settlement = 1998.05.17
maturity = 1999.05.17
valDay = 1998.05.15
spot = 36
strike = 40
riskFree = 0.06
dividend = 0
volatility = 0.2
isCall = false
style = 'european'
basis = 3
calendar = 'CCFX'

vanillaOption(settlement, maturity, valDay, spot, strike, riskFree, dividend, volatility, isCall, style, basis, calendar, mode=2)

/* output:
npv->3.844299590004929
delta->-0.550451634430198
gamma->0.054964980970804
theta->-0.005058800993712
vega->14.246923067632348
rho->-23.660558429492027
*/