This module is developed from the recent research paper titled Time dependent Heston Model authored by E.Benhamou, E.Gobel and M.Miri. We know ,the heston stochastic volatility Model is :

Here X,ν ,ξ,θ,ρ are time dependent parameters. They represent stock price, volatility, volatility of volatility, long term volatility and correlation between two Brownian motion respectively. K is mean reversion parameter.

Traditional heston model calculation lacks of time dependent parameters. In that
paper, they have developed a way to compute heston model when the parameters are
time dependent. In this module, we have assumed the function of ξ, θ, ρ are piecewise
constant and equal respectively at each interval [i/4, i+1/4]:

Here is a figure of of how it looks if T (maturity) is set for 10. Number of pieces
are 100. So at each step these three parameters are calculated.

This module contains two parts. It can calculate option price and corresponding
implied volatility for vanilla put or call for constant heston parameter. The second
option gives you to calculate option price and implied volatility for piecewise
constant parameters. Here are the equations used to calculate the put option price
according to the paper. Put price =
For constant model the parameters are:
For piecewise constant Model the parameters:

Here,

This Module Implemented by S.M Ferdous & Md. Mizanur Rahman nur

## Financial Modules

### Projects

- Time dependent heston model
- Modeling and Pricing of Variance Swaps for Local Stochastic Volatilities with Delay and Jumps
- LIBOR Market Model with Stochastic Basis
- Series Expansion of SABR Joint Density
- Optimal Hedging of Variance Derivatives

### Pricing and Valuation

### Simulation

- NIG Process Simulation
- Variance Gamma Process Simulation
- Compound Poisson Process Simulation
- Multivariate Brownian Motion Generation
- Heavytailed Process Simulation using (Mixed Normal)