performOptimization

Function retrieving a martingale distribution Q and a physical distribution P s.t.

• Q prices financial instrument correctly

• The second moment of the pricing kernel by the bound $\alpha$

• The risk-neutral variance is higher than the physical expected variance

dbbpy

dbbpy.performOptimization(n, alpha, lambda_, omega_l, sp, strike, bid, ask, pFlag)

Parameters:

• n (int): The number of states considered

• alpha (float): A parameter limiting the second moment of the pricing kernel

• lambda (float): A parameter for the Tikhonov-type regularization

• omega_l (numpy.ndarray): A 1D numpy array of integers representing the disjunct state space partitions of interest

• sp (numpy.ndarray): A 1D numpy array of floats representing the spot prices in different states of the world

• strike (numpy.ndarray): A 1D numpy array of floats representing the strike prices of different options

• bid (numpy.ndarray): A 1D numpy array of floats representing the bid prices of different options

• ask (numpy.ndarray): A 1D numpy array of floats representing the ask prices of different options

• pflag (numpy.ndarray): A 1D numpy array of booleans indicating whether an option is a call (True) or a put (False) option

Output:

• (tuple): includes two elements:

  • P distribution: The recovered P distribution

  • Q distribution: The recovered Q distribution

rdbb