### Heston stochastic volatility model- Library

Implementation for Heston stochastic volatility model. The model assumes that the volatility is stochastic and mean reverting.

##### heston_EuropeanCallPrice

Description : Calculates the option price for European call using the Heston closed form solution.

Input parameters

Input variable Example Description
Spot 100.00 Underlying spot price
Strike 100.00 Strike price
TimeToMaturity 1.5 Time to maturity (in Years)
InterestRate 0.05 Risk free interest rate - Dividend yield
rho -0.3 Correlation between volatility and spot
kappa 3.0 Mean reversion speed
theta 0.1 Long run variance
lambda 0.0 Market price of volatility risk. Use 0.0 for variable reduction.
sigma 0.20 Volatility of variance
v 0.10 Current variance
##### heston_EuropeanPutPrice

Description : Calculates the option price for European put. This formula uses put call parity to arrive at the put price from the Heston closed form solution for European call.

Input parameters

Input variable Example Description
Spot 100.00 Underlying spot price
Strike 100.00 Strike price
TimeToMaturity 1.5 Time to maturity (in Years)
InterestRate 0.05 Risk free interest rate - Dividend yield
rho -0.3 Correlation between volatility and spot
kappa 3.0 Mean reversion speed
theta 0.1 Long run variance
lambda 0.0 Market price of volatility risk. Use 0.0 for variable reduction.
sigma 0.20 Volatility of variance
v 0.10 Current variance
##### heston_EuropeanCallPriceMC

Description : Calculates the option price for European call through Monte Carlo simulations. The volatility assumed to be stochastic as in Heston model. Pseudo random used for standard normal gaussian variables

Input parameters

Input variable Example Description
Spot 100.00 Underlying spot price
Strike 100.00 Strike price
TimeToMaturity 1.5 Time to maturity (in Years)
InterestRate 0.05 Risk free interest rate - Dividend yield
rho -0.3 Correlation between volatility and spot
kappa 3.0 Mean reversion speed
theta 0.1 Long run variance
lambda 0.0 Market price of volatility risk. Use 0.0 for variable reduction.
sigma 0.20 Volatility of variance
v 0.10 Current variance
nSimulations 15000 Number of simulations
nTimeSteps 300 Number of time steps
##### heston_EuropeanPutPriceMC

Description : Calculates the option price for European put through Monte Carlo simulations. The volatility assumed to be stochastic as in Heston model. Pseudo random used for standard normal gaussian variables

Input parameters

Input variable Example Description
Spot 100.00 Underlying spot price
Strike 100.00 Strike price
TimeToMaturity 1.5 Time to maturity (in Years)
InterestRate 0.05 Risk free interest rate - Dividend yield
rho -0.3 Correlation between volatility and spot
kappa 3.0 Mean reversion speed
theta 0.1 Long run variance
lambda 0.0 Market price of volatility risk. Use 0.0 for variable reduction.
sigma 0.20 Volatility of variance
v 0.10 Current variance
nSimulations 15000 Number of simulations
nTimeSteps 300 Number of time steps
##### heston_CalibrateLevMar

Description : Calibrates the model using Levenberg–Marquardt non linear minimization technique. Requires an initial guess parameter array. This is a local minimizer and hence should be used only when a good guess is known. Ideally use the function within the VBA macro as the algorithm could take several minutes to complete

Order of parameters - Initial volatility (v) , Long term volatility (theta) , Mean reversion speed (kappa) , Volatility of volatility (sigma) and Correlation between volatility and spot (rho)

Input parameters

Input variable Description
lowerBound Lower bound for the parameters. Passed as array of decimals.
upperbound Upper bound for the parameters. Passed as array of decimals.
initialGuess Initial guess for the parameters. Passed as array of decimals.
strikeArray Observation table - strikes. Passed as array of decimals.
maturityArray Observation table - option maturities (in Years). Passed as array of decimals.
callTypeArray Observation table - option type (1 for call 0 for put). Passed as array of numbers.
observedPriceArray Observation table - observed option prices. Passed as array of decimals.
currentSpot Current spot price.
interestRateArray Discount rates = Risk free rate - dividend yield. Passed as array.
weights Weights for the observation data
maxIterations Maximum number of trials.
##### heston_CalibrateDE

Description : Calibrates the model using Differential evolution non linear minimization technique. This is a global minimizer and hence does not need an initial guess. Ideally use the function within the VBA macro as the algorithm could take several minutes to complete

Order of parameters - Initial volatility (v) , Long term volatility (theta) , Mean reversion speed (kappa) , Volatility of volatility (sigma) and Correlation between volatility and spot (rho)

Input parameters

variable Description
lowerBound Lower bound for the parameters. Passed as array of decimals.
upperbound Upper bound for the parameters. Passed as array of decimals.
strikeArray Observation table - strikes. Passed as array of decimals.
maturityArray Observation table - option maturities (in Years). Passed as array of decimals.
callTypeArray Observation table - option type (1 for call 0 for put). Passed as array of numbers.
observedPriceArray Observation table - observed option prices. Passed as array of decimals.
currentSpot Current spot price.
interestRateArray Discount rates = Risk free rate - dividend yield. Passed as array.
weights Weights for the observation data
maxIterations Maximum number of trials.