Create simulation-investigation.ipynb

simulation-investigation.ipynb

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+import pandas as pd
+import numpy as np
+import matplotlib.pyplot as plt
+import datetime as dt
+
+def get_price_data(n_samples, risk_free_rate, volatility, time_deltas, total_collateral):
+    price_data = np.zeros((n_samples, len(time_deltas)+1))
+    initial_price = total_collateral
+    price_data[:,0] = initial_price
+    for j in range(n_samples):
+        for i in range(0,len(time_deltas)):
+            price_data[j,i+1] = price_data[j,i]*np.exp((risk_free_rate-np.power(volatility, 2)/2)*time_deltas[i]+volatility*np.sqrt(time_deltas[i])*np.random.normal(0,1))
+
+    return price_data
+
+def lender_payoff(price_data_row, risk_free_rate, total_loan_amount, total_repayment_amount, convertible_coll_ratios, convertible_loan_ratios, time_deltas):
+    lender_total_payoff = 0
+    collateral_percent_left = 1
+    loan_percent_accounted_for = 0
+    time_left = np.sum(time_deltas)
+    is_repaid=False
+    for i in range(1,len(price_data_row)):
+        current_value = price_data_row[i]
+        if borrower_should_default(collateral_percent_left, loan_percent_accounted_for, current_value, total_repayment_amount, total_loan_amount):
+            lender_total_payoff += current_value*collateral_percent_left*np.exp(risk_free_rate*time_left)
+            break
+        else:
+            if lender_should_convert(current_value, convertible_coll_ratios[i-1], convertible_loan_ratios[i-1], total_loan_amount):
+                lender_total_payoff += current_value*convertible_coll_ratios[i-1]
+                collateral_percent_left -= convertible_coll_ratios[i-1]
+                loan_percent_accounted_for += convertible_loan_ratios[i-1]
+                time_left -= time_deltas[i-1]
+                if time_left <= 0:
+                    is_repaid=True
+                    break
+            else:
+                lender_total_payoff += total_loan_amount*convertible_loan_ratios[i-1]
+                collateral_percent_left -= convertible_coll_ratios[i-1]
+                loan_percent_accounted_for += convertible_loan_ratios[i-1]
+                time_left -= time_deltas[i-1]
+                if time_left <= 0:
+                    is_repaid=True
+                    break
+    if is_repaid:
+        lender_total_payoff += total_repayment_amount - total_loan_amount*loan_percent_accounted_for
+    return lender_total_payoff
+
+def borrower_should_default(collateral_percent_left, loan_percent_accounted_for, current_value, total_repayment_amount, total_loan_amount):
+    total_amount_still_owed = total_repayment_amount - loan_percent_accounted_for*total_loan_amount
+    total_collateral_left_current_value = collateral_percent_left*current_value
+    return total_amount_still_owed > total_collateral_left_current_value
+
+def lender_should_convert(current_value, convertible_collateral_percentage, convertible_loan_percentage, total_loan_amount):
+    return current_value*convertible_collateral_percentage > convertible_loan_percentage*total_loan_amount
+
+def get_average_payoffs(n_samples, risk_free_rate, volatility, total_collateral, total_loan_amount, total_repayment_amount, convertible_coll_ratios, convertible_loan_ratios, time_deltas):
+    price_data = get_price_data(n_samples, risk_free_rate, volatility, time_deltas, total_collateral)
+    lender_payoffs = np.zeros(n_samples)
+    for i in range(n_samples):
+        lender_payoffs[i] = lender_payoff(price_data[i,:], risk_free_rate, total_loan_amount, total_repayment_amount, convertible_coll_ratios, convertible_loan_ratios, time_deltas)
+    return np.average(lender_payoffs)
+
+def get_payoff_delta(n_samples, risk_free_rate, volatility, total_collateral, total_loan_amount, total_repayment_amount, convertible_coll_ratios, convertible_loan_ratios, time_deltas):
+    loan_payoff = get_average_payoffs(n_samples, risk_free_rate, volatility, total_collateral, total_loan_amount, total_repayment_amount, convertible_coll_ratios, convertible_loan_ratios, time_deltas)
+    risk_free_payoff = total_loan_amount*np.exp(risk_free_rate*np.sum(time_deltas))
+    return loan_payoff - risk_free_payoff
+
+def get_payoff_histogram(n_samples, risk_free_rate, volatility, total_collateral, total_loan_amount, total_repayment_amount, convertible_coll_ratios, convertible_loan_ratios, time_deltas):
+    price_data = get_price_data(n_samples, risk_free_rate, volatility, time_deltas, total_collateral)
+    lender_payoffs = np.zeros(n_samples)
+    for i in range(n_samples):
+        lender_payoffs[i] = lender_payoff(price_data[i,:], risk_free_rate, total_loan_amount, total_repayment_amount, convertible_coll_ratios, convertible_loan_ratios, time_deltas)
+    plt.hist(lender_payoffs, bins=50)
+    plt.show()
+
+# n_samples = 50000
+# risk_free_rate = 0.03
+# volatility = 0.75
+# total_collateral = 1000000 #(in USD)
+# total_loan_amount = 300000 #(in USD)
+# total_repayment_amount = 310000 #(in USD)
+# convertible_coll_ratio = [0.03,0.02,0.01,0.01] 
+# convertible_loan_ratio = [0.2,0.15,0.1,0.1]
+# time_deltas = [0.25,0.25,0.25,0.25] # in years
+
+print(get_payoff_delta(50000, 0.03, 0.75, 1000000, 300000, 310000, [0.03,0.02,0.01,0.01], [0.2,0.15,0.1,0.1], [0.25,0.25,0.25,0.25]))
+get_payoff_histogram(10000, 0.03, 0.75, 1000000, 300000, 310000, [0.03,0.02,0.01,0.01], [0.2,0.15,0.1,0.1], [0.25,0.25,0.25,0.25])