vanillaOption
Syntax
vanillaOption(settlement, maturity, evalDate, spot, strike, riskFree,
divYield, volatility, isCall, style, basis, calendar, [method=`BS], [kwargs],
[mode=0])
Arguments
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 scalar or vector indicating the day-count basis. It can be:
- 0: US (NASD) 30/360
- 1: actual/actual
- 2: actual/360
- 3: actual/365
- 4: 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
*/