Initial file. To be corrected i.e. decide the data type

.gitignore

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+*.aux
+*.bbl
+*.blg
+*.log
+*.maf
+*.toc
+*.mtc*
+*.out
+*backup
+
+*.sty
+*.pdf
+*~

no_jumps.py

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+#! /usr/bin/python3 
+
+import time
+#import sys
+
+import numpy as np
+import numpy.matlib
+from copy import deepcopy
+
+t=time.time()
+
+#%%
+def cost_f(x,y,cost_b,cost_s):
+
+    cost = np.zeros( (len(x), len(y) ) )
+
+    for i in range(len(y)):
+        if y[i] <= 0 :
+            cost[:,i] = (1+cost_b) * y[i] * np.exp(x)
+        else:
+            cost[:,i] = (1-cost_s) * y[i] * np.exp(x)
+
+    return cost     # np.longfloat(np.transpose(cost))
+
+
+
+def cost_opt(x,y,cost_b,cost_s,K):
+
+    cost = np.zeros( (len(x),len(y)) )
+
+    for i in range(len(x)):
+        for j in range(len(y)):
+
+            if y[j] < 0 and np.exp(x[i]) <= K :
+                cost[i][j] = (1+cost_b) * y[j] * np.exp(x[i])
+
+            elif y[j] >= 0 and np.exp(x[i]) <= K : 
+                cost[i][j] = (1-cost_s) * y[j] * np.exp(x[i])
+
+            elif y[j]-1 >= 0 and np.exp(x[i]) > K :
+                cost[i][j] = ( (1-cost_s) * (y[j]-1) * np.exp(x[i]) ) + K
+
+            elif y[j]-1 < 0 and np.exp(x[i]) > K :
+                cost[i][j] = ( (1+cost_b) * (y[j]-1) * np.exp(x[i]) ) + K
+
+    return np.longfloat(cost)
+
+def cost_opt2(x,y,cost_b,cost_s,K):
+
+    cost = np.zeros( (len(x),len(y)) )
+
+    for i in range(len(x)):
+        for j in range(len(y)):
+            cost[i,j] = cost_f([x[i]],[y[j]],cost_b,cost_s) if (np.exp(x[i]) <= K) else cost_f([x[i]],[y[j]-1],cost_b,cost_s) + K
+    return cost
+
+
+#%%    
+
+
+r = 0.1                   # interest rate
+mu = 0.1                  # drift coefficient
+sig = 0.25                # diffusion coefficient
+
+
+S0 = 15.0                  # current price
+x0 = np.log(S0)           # current log-price
+
+K = 15.0                   # strike
+T = 1.0                  # year
+
+cost_b = 0.0             # (lambda in the paper) BUY cost  
+cost_s = 0.0             # (mu in the paper)  SELL cost
+gamma = 0.01              # risk avversion coefficient
+
+#%%
+#def trans_cost_NJ( T=1, S0=15, K=15, r=0.1, mu=0.1, sig=0.25, cost=0.005, gamma=0.1, N=800  ):
+
+N = 2000          # time steps even!!!
+#cost1 = cost2 = cost
+
+dt = T/N
+T_vec = np.linspace(0,T,N+1)
+delta = np.exp(-r*(T-T_vec))        # discount factor
+
+dx = sig * np.sqrt(dt)
+
+
+M = int(np.floor(N/2))
+dy = dx
+y = np.longfloat(np.linspace(-M*dy,M*dy,2*M+1))       
+N_y = len(y)
+med = np.where(y == 0)[0].item()
+
+
+
+F = lambda x,l,N: np.exp( gamma * (1+cost_b)*np.exp(x)*l / delta[N] )  
+
+G = lambda x,m,N: np.exp( -gamma * (1-cost_s)*np.exp(x)*m / delta[N] )
+
+#%%
+
+for TYPE in range(2):
+
+    x = np.array( [x0 + (mu-0.5*sig**2)*dt*N + (2*i-N)*dx for i in range(N+1) ] , dtype=np.float128 )
+
+    ############# Boundary conditions ##############
+
+    # Terminal
+    if TYPE == 0:
+        Q = np.exp( np.longfloat( -gamma * np.longfloat( cost_f(x,y,cost_b,cost_s)) ))
+    else:
+        Q = np.exp( np.longfloat( -gamma * np.longfloat( cost_opt(x,y,cost_b,cost_s,K)) ))
+
+
+    for k in range(N-1,-1,-1):
+
+        ###  expectation term
+        Q_new = ( Q[:-1,:] + Q[1:,:] ) / 2
+
+        ### create the logprice vector at time k
+        x = np.array( [x0 + (mu-0.5*sig**2)*dt*k + (2*i-k)*dx for i in range(k+1) ] , dtype=np.float128)
+
+
+        ### buy term
+        Buy = np.longfloat(deepcopy(Q_new))
+        Buy[:,:-1] = np.longfloat( np.matlib.repmat(F(x,dy,k),N_y-1,1).transpose() ) * np.longfloat( Q_new[:,1:] ) 
+
+        ### sell term
+        Sell = np.longfloat(deepcopy(Q_new))
+        Sell[:,1:] = np.matlib.repmat(G(x,dy,k),N_y-1,1).transpose() * np.longfloat( Q_new[:,:-1] )
+
+        ### update the Q(:,:,k) 
+        Q = np.minimum( np.minimum(Buy,Sell) , Q_new )
+
+    if (TYPE == 0):
+        Q_no = Q[0,med]
+    else:
+        Q_yes = Q[0,med]
+
+
+price = (delta[0] / gamma) * np.log( Q_yes / Q_no )
+#return price
+elapsed=time.time()-t
+
+print("price: %.15f" %price )
+print("time: %.15f" %elapsed )