SLVCTMCApproximation

This package focuses on pricing a variety of path-dependent options through various Stochastic Volatility Models (hence the SLV in the name), which are approximated using a Continuous time Markov Process with at most countable state space. This approach is non-standard, where the standard approach is using a discrete time approximation of these stochastic local volatility models. The Stochastic Local Volatilities of interest are:

• [ ] Heston Model
• [ ] 3/2 Model
• [ ] Jump Diffusions - ABCJ/SLVJ or Bates
• [ ] SABR Model

Calculate the generator matrix Q for the Price and Volatility process

After calculating the generator matrix Q for the Volatility process, we can calculate the generator matrix Q for the Price and Volatility process. 
The Price and Volatility process is given by the following SDEs in the Heston model:

$$dS(t) = μS(t)dt + sqrt((1 - ρ^2)v(t))S(t)dW1(t) + ρ* sqrt(v(t))S(t)dW2(t)$$
$$dv(t) = (ν - ϱv(t))dt + κ*sqrt(v(t))dW2(t)$$

where W1(t) and W2(t) are independent Brownian motions.

Consider a volatility process of the following form:
dv(t) = μ(t)dt + σ(t)dW(t) 

The volatility process can be approximated using the following birth-death markov chain, with the following bounded finite states 

TODO List

• [x] Calculate the generator matrix Q for the Volatility process
• [ ] Calculate the generator matrix Q for the Price and Volatility process
• [ ] Write unit tests for the models
• [ ] Update documentation