Heston stochastic volatility model- Library
Implementation for Heston stochastic volatility model. The model assumes that the volatility is stochastic and mean reverting.
Synoposis - Available functions
- heston_EuropeanCallPrice
- heston_EuropeanPutPrice
- heston_EuropeanCallPriceMC
- heston_EuropeanPutPriceMC
- heston_CalibrateLevMar
- heston_CalibrateDE
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. |
