Added framework for LSM and FD

Least-square Monte-Carlo, Finite difference method applied to Black-Scholes model

Author: martinzwm

FD.py

@@ -0,0 +1,21 @@
+class LSM(object):
+    def __init__(self, option_type, S0, strike, T, M, r, sigma, div):
+        """
+            Input:
+                option_type [string]: type of option (i.e. American, European, Asian)
+                S0 [float]: current value of stock
+                strike [float]: strike price
+                T [float]: expiration date
+                M [int]: number of mesh grid in time domain
+                r [float]: riskfree rate (i.e. similar to discount factor)
+                div [float]: dividend yield
+        """
+        self.parameters = {} # use appropriate date structure to keep track of parameters
+        raise NotImplementedError
+
+    def simulate():
+        """ Given current price, strike, T and other parameters of the option, find its valuation by solving PDE
+            Some reference: https://towardsdatascience.com/option-pricing-using-the-black-scholes-model-without-the-formula-e5c002771e2f
+            or https://github.com/wessle/option_pricer/blob/master/fin_diffs.py
+        """
+        raise NotImplementedError

LSM.py

@@ -0,0 +1,29 @@
+class LSM(object):
+    def __init__(self, option_type, S0, strike, T, M, r, sigma, div, N):
+        """
+            Input:
+                option_type [string]: type of option (i.e. American, European, Asian)
+                S0 [float]: current value of stock
+                strike [float]: strike price
+                T [float]: expiration date
+                M [int]: number of mesh grid in time domain
+                r [float]: riskfree rate (i.e. similar to discount factor)
+                div [float]: dividend yield
+                
+                N [int]: number of simulations
+
+            Some reference: https://github.com/jpcolino/IPython_notebooks/blob/master/Least%20Square%20Monte%20Carlo%20Implementation%20in%20a%20Python%20Class.ipynb
+            or https://cran.r-project.org/web/packages/LSMRealOptions/vignettes/LSMRealOptions.html#:~:text=The%20Least%2DSquares%20Monte%20Carlo,option%20at%20discrete%20observation%20points.
+        """
+        self.parameters = {} # use appropriate date structure to keep track of parameters
+        raise NotImplementedError
+
+    def train():
+        """ Given a trajectory object, find fitted parameters based on the trajectory.
+        """
+        raise NotImplementedError
+
+    def price():
+        """ Given current price, strike, and other parameters of option, find its valuation using the fitted parameters
+        """
+        raise NotImplemented