GBE PS2
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"""
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Problem Set 2 - Problem 3
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Put Option Analysis
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"""
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import numpy as np
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import matplotlib.pyplot as plt
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print("="*80)
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print("PROBLEM 3: PUT OPTION ANALYSIS")
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print("="*80)
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print()
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# Given data
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amount_eur = 1000 # EUR
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option_fee_chf = 75 # CHF
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R_3m_EUR = 0.013 # 1.3%
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R_3m_CHF = 0.005 # 0.5%
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E_spot = 0.95 # CHF/EUR
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print("GIVEN INFORMATION:")
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print("-" * 80)
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print(f"Put option to SELL: {amount_eur:,} EUR")
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print(f"Option fee: {option_fee_chf} CHF (paid at signing)")
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print(f"3-month EUR interest rate: R_3m_EUR = {R_3m_EUR:.3f} ({R_3m_EUR*100:.1f}%)")
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print(f"3-month CHF interest rate: R_3m_CHF = {R_3m_CHF:.3f} ({R_3m_CHF*100:.1f}%)")
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print(f"Spot exchange rate: E_CHF/EUR = {E_spot:.2f}")
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print()
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# Part 1: Calculate expected exchange rate
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print("="*80)
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print("PART 1: EXPECTED EXCHANGE RATE FROM INTEREST PARITY")
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print("="*80)
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print()
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print("Interest Parity Condition (Uncovered Interest Parity):")
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print(" E_e / E_spot = (1 + R_CHF) / (1 + R_EUR)")
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print()
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print("Solving for expected exchange rate E_e:")
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print(" E_e = E_spot × (1 + R_CHF) / (1 + R_EUR)")
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print()
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E_expected = E_spot * (1 + R_3m_CHF) / (1 + R_3m_EUR)
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print(f"Calculation:")
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print(f" E_e = {E_spot:.2f} × (1 + {R_3m_CHF:.3f}) / (1 + {R_3m_EUR:.3f})")
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print(f" E_e = {E_spot:.2f} × {1 + R_3m_CHF:.4f} / {1 + R_3m_EUR:.4f}")
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print(f" E_e = {E_spot:.2f} × {(1 + R_3m_CHF) / (1 + R_3m_EUR):.6f}")
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print(f" E_e = {E_expected:.6f}")
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print()
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print(f"✓ ANSWER: E_e_CHF/EUR = {E_expected:.4f} CHF per EUR")
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print()
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print("Interpretation:")
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print(f" • The expected exchange rate ({E_expected:.4f}) is LOWER than spot ({E_spot:.2f})")
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print(f" • This means the CHF is expected to APPRECIATE relative to EUR")
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print(f" • This makes sense: CHF has lower interest rate than EUR")
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print(f" • By interest parity, lower interest rate currency appreciates")
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print()
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# Strike price equals expected exchange rate
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X = E_expected
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print(f"Strike Price: X = E_e = {X:.4f} CHF/EUR")
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print()
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# Part 2: Exercise decision when E = 0.93
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print("="*80)
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print("PART 2: SCENARIO WITH E_CHF/EUR = 0.93 AFTER 3 MONTHS")
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print("="*80)
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print()
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E_future_1 = 0.93
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print(f"After 3 months: E_CHF/EUR = {E_future_1:.2f}")
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print(f"Strike price: X = {X:.4f}")
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print()
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print("EXERCISE DECISION:")
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print("-" * 80)
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print()
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print("Put option gives the RIGHT (not obligation) to SELL EUR at strike price X")
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print()
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print(f" • If we exercise: Sell 1,000 EUR at X = {X:.4f} CHF/EUR")
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print(f" → Receive: {amount_eur:,} × {X:.4f} = {amount_eur * X:.2f} CHF")
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print()
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print(f" • If we don't exercise: Sell 1,000 EUR at market rate E = {E_future_1:.2f}")
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print(f" → Receive: {amount_eur:,} × {E_future_1:.2f} = {amount_eur * E_future_1:.2f} CHF")
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print()
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if X > E_future_1:
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exercise_1 = True
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print(f"Since X ({X:.4f}) > E ({E_future_1:.2f}), we SHOULD EXERCISE the option!")
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print(f"We can sell EUR at a better rate than the market offers.")
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else:
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exercise_1 = False
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print(f"Since X ({X:.4f}) ≤ E ({E_future_1:.2f}), we should NOT exercise.")
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print(f"The market rate is better than the strike price.")
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print()
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print("PAYOFF AND PROFIT:")
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print("-" * 80)
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print()
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if exercise_1:
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payoff_1 = amount_eur * (X - E_future_1)
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print("Payoff (intrinsic value at expiration):")
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print(f" Payoff = Amount × max(X - E, 0)")
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print(f" Payoff = {amount_eur:,} × max({X:.4f} - {E_future_1:.2f}, 0)")
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print(f" Payoff = {amount_eur:,} × {X - E_future_1:.4f}")
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print(f" Payoff = {payoff_1:.2f} CHF")
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else:
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payoff_1 = 0
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print("Payoff (intrinsic value at expiration):")
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print(f" Payoff = Amount × max(X - E, 0)")
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print(f" Payoff = {amount_eur:,} × max({X:.4f} - {E_future_1:.2f}, 0)")
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print(f" Payoff = 0 CHF (option expires worthless)")
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print()
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# Calculate profit (accounting for option premium with interest)
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option_cost_future = option_fee_chf * (1 + R_3m_CHF)
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profit_1 = payoff_1 - option_cost_future
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print("Profit (payoff minus cost of option with interest):")
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print(f" Option fee paid upfront: {option_fee_chf} CHF")
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print(f" Future value of option fee: {option_fee_chf} × (1 + {R_3m_CHF:.3f}) = {option_cost_future:.2f} CHF")
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print(f" Profit = Payoff - FV(Option Fee)")
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print(f" Profit = {payoff_1:.2f} - {option_cost_future:.2f}")
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print(f" Profit = {profit_1:.2f} CHF")
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print()
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if profit_1 > 0:
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print(f"✓ The option generates a POSITIVE profit of {profit_1:.2f} CHF")
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elif profit_1 < 0:
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print(f"✗ The option generates a NEGATIVE profit (loss) of {abs(profit_1):.2f} CHF")
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else:
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print("○ The option breaks even (zero profit)")
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print()
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print(f"✓ ANSWER PART 2:")
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print(f" • Exercise decision: {'YES, exercise the option' if exercise_1 else 'NO, let it expire'}")
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print(f" • Payoff: {payoff_1:.2f} CHF")
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print(f" • Profit: {profit_1:.2f} CHF")
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print()
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# Part 3: Exercise decision when E = 0.98
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print("="*80)
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print("PART 3: SCENARIO WITH E_CHF/EUR = 0.98 AFTER 3 MONTHS")
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print("="*80)
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print()
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E_future_2 = 0.98
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print(f"After 3 months: E_CHF/EUR = {E_future_2:.2f}")
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print(f"Strike price: X = {X:.4f}")
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print()
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print("EXERCISE DECISION:")
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print("-" * 80)
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print()
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print("Put option gives the RIGHT (not obligation) to SELL EUR at strike price X")
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print()
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print(f" • If we exercise: Sell 1,000 EUR at X = {X:.4f} CHF/EUR")
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print(f" → Receive: {amount_eur:,} × {X:.4f} = {amount_eur * X:.2f} CHF")
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print()
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print(f" • If we don't exercise: Sell 1,000 EUR at market rate E = {E_future_2:.2f}")
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print(f" → Receive: {amount_eur:,} × {E_future_2:.2f} = {amount_eur * E_future_2:.2f} CHF")
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print()
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if X > E_future_2:
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exercise_2 = True
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print(f"Since X ({X:.4f}) > E ({E_future_2:.2f}), we SHOULD EXERCISE the option!")
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print(f"We can sell EUR at a better rate than the market offers.")
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else:
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exercise_2 = False
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print(f"Since X ({X:.4f}) ≤ E ({E_future_2:.2f}), we should NOT exercise.")
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print(f"The market rate is better than the strike price.")
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print()
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print("PAYOFF AND PROFIT:")
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print("-" * 80)
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print()
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if exercise_2:
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payoff_2 = amount_eur * (X - E_future_2)
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print("Payoff (intrinsic value at expiration):")
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print(f" Payoff = Amount × max(X - E, 0)")
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print(f" Payoff = {amount_eur:,} × max({X:.4f} - {E_future_2:.2f}, 0)")
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print(f" Payoff = {amount_eur:,} × {X - E_future_2:.4f}")
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print(f" Payoff = {payoff_2:.2f} CHF")
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else:
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payoff_2 = 0
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print("Payoff (intrinsic value at expiration):")
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print(f" Payoff = Amount × max(X - E, 0)")
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print(f" Payoff = {amount_eur:,} × max({X:.4f} - {E_future_2:.2f}, 0)")
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print(f" Payoff = 0 CHF (option expires worthless)")
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print()
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profit_2 = payoff_2 - option_cost_future
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print("Profit (payoff minus cost of option with interest):")
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print(f" Option fee paid upfront: {option_fee_chf} CHF")
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print(f" Future value of option fee: {option_fee_chf} × (1 + {R_3m_CHF:.3f}) = {option_cost_future:.2f} CHF")
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print(f" Profit = Payoff - FV(Option Fee)")
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print(f" Profit = {payoff_2:.2f} - {option_cost_future:.2f}")
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print(f" Profit = {profit_2:.2f} CHF")
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print()
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if profit_2 > 0:
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print(f"✓ The option generates a POSITIVE profit of {profit_2:.2f} CHF")
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elif profit_2 < 0:
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print(f"✗ The option generates a NEGATIVE profit (loss) of {abs(profit_2):.2f} CHF")
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else:
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print("○ The option breaks even (zero profit)")
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print()
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print(f"✓ ANSWER PART 3:")
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print(f" • Exercise decision: {'YES, exercise the option' if exercise_2 else 'NO, let it expire'}")
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print(f" • Payoff: {payoff_2:.2f} CHF")
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print(f" • Profit: {profit_2:.2f} CHF")
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print()
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# Create graphs
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print("="*80)
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print("GENERATING PAYOFF AND PROFIT DIAGRAMS")
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print("="*80)
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print()
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# Generate exchange rate range
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E_range = np.linspace(0.85, 1.05, 200)
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# Calculate payoff and profit for each exchange rate
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payoffs = amount_eur * np.maximum(X - E_range, 0)
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profits = payoffs - option_cost_future
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# Create figure with two subplots
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fig, (ax1, ax2) = plt.subplots(2, 1, figsize=(12, 10))
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# Plot 1: Payoff diagram
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ax1.plot(E_range, payoffs, 'b-', linewidth=2.5, label='Payoff')
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ax1.axhline(y=0, color='k', linestyle='-', linewidth=0.5)
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ax1.axvline(x=X, color='r', linestyle='--', linewidth=1.5, alpha=0.7, label=f'Strike Price (X = {X:.4f})')
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# Mark the two scenarios on payoff diagram
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ax1.plot(E_future_1, payoff_1, 'go', markersize=12, label=f'Scenario 1: E = {E_future_1:.2f}', zorder=5)
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ax1.plot(E_future_2, payoff_2, 'mo', markersize=12, label=f'Scenario 2: E = {E_future_2:.2f}', zorder=5)
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# Add annotations
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ax1.annotate(f'Payoff = {payoff_1:.2f} CHF',
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xy=(E_future_1, payoff_1), xytext=(E_future_1-0.03, payoff_1+50),
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fontsize=10, ha='right',
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bbox=dict(boxstyle='round,pad=0.5', facecolor='green', alpha=0.3),
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arrowprops=dict(arrowstyle='->', connectionstyle='arc3,rad=0', color='green'))
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ax1.annotate(f'Payoff = {payoff_2:.2f} CHF',
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xy=(E_future_2, payoff_2), xytext=(E_future_2+0.03, payoff_2+50),
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fontsize=10, ha='left',
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bbox=dict(boxstyle='round,pad=0.5', facecolor='magenta', alpha=0.3),
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arrowprops=dict(arrowstyle='->', connectionstyle='arc3,rad=0', color='magenta'))
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ax1.set_xlabel('Spot Exchange Rate at Maturity (E_CHF/EUR)', fontsize=11, fontweight='bold')
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ax1.set_ylabel('Payoff (CHF)', fontsize=11, fontweight='bold')
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ax1.set_title('Put Option PAYOFF Diagram\n(Intrinsic Value at Expiration)', fontsize=13, fontweight='bold')
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ax1.grid(True, alpha=0.3)
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ax1.legend(loc='upper right', fontsize=10)
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ax1.set_xlim([0.85, 1.05])
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# Plot 2: Profit diagram
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ax2.plot(E_range, profits, 'r-', linewidth=2.5, label='Profit')
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ax2.axhline(y=0, color='k', linestyle='-', linewidth=0.5)
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ax2.axvline(x=X, color='r', linestyle='--', linewidth=1.5, alpha=0.7, label=f'Strike Price (X = {X:.4f})')
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ax2.axhline(y=-option_cost_future, color='orange', linestyle=':', linewidth=2,
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label=f'Maximum Loss = -{option_cost_future:.2f} CHF')
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# Mark the two scenarios on profit diagram
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ax2.plot(E_future_1, profit_1, 'go', markersize=12, label=f'Scenario 1: E = {E_future_1:.2f}', zorder=5)
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ax2.plot(E_future_2, profit_2, 'mo', markersize=12, label=f'Scenario 2: E = {E_future_2:.2f}', zorder=5)
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# Add annotations
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ax2.annotate(f'Profit = {profit_1:.2f} CHF',
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xy=(E_future_1, profit_1), xytext=(E_future_1-0.03, profit_1+20),
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fontsize=10, ha='right',
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bbox=dict(boxstyle='round,pad=0.5', facecolor='green', alpha=0.3),
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arrowprops=dict(arrowstyle='->', connectionstyle='arc3,rad=0', color='green'))
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ax2.annotate(f'Profit = {profit_2:.2f} CHF',
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xy=(E_future_2, profit_2), xytext=(E_future_2+0.03, profit_2-30),
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fontsize=10, ha='left',
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bbox=dict(boxstyle='round,pad=0.5', facecolor='magenta', alpha=0.3),
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arrowprops=dict(arrowstyle='->', connectionstyle='arc3,rad=0', color='magenta'))
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ax2.set_xlabel('Spot Exchange Rate at Maturity (E_CHF/EUR)', fontsize=11, fontweight='bold')
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ax2.set_ylabel('Profit (CHF)', fontsize=11, fontweight='bold')
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ax2.set_title('Put Option PROFIT Diagram\n(Payoff - Cost of Option)', fontsize=13, fontweight='bold')
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ax2.grid(True, alpha=0.3)
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ax2.legend(loc='upper right', fontsize=10)
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ax2.set_xlim([0.85, 1.05])
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plt.tight_layout()
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plt.savefig('/home/quinta/Documents/Atlas/Global Business Environment /Problem Set 2/problem3_put_option_diagrams.png',
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dpi=300, bbox_inches='tight')
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print("✓ Graphs saved as 'problem3_put_option_diagrams.png'")
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plt.show()
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print()
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print("="*80)
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print("SUMMARY OF ALL ANSWERS")
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print("="*80)
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print()
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print(f"PART 1: Expected Exchange Rate")
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print(f" E_e_CHF/EUR = {E_expected:.4f}")
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print()
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print(f"PART 2: Scenario E = {E_future_1:.2f}")
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print(f" • Exercise: {'YES' if exercise_1 else 'NO'}")
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print(f" • Payoff: {payoff_1:.2f} CHF")
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print(f" • Profit: {profit_1:.2f} CHF")
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print()
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print(f"PART 3: Scenario E = {E_future_2:.2f}")
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print(f" • Exercise: {'YES' if exercise_2 else 'NO'}")
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print(f" • Payoff: {payoff_2:.2f} CHF")
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print(f" • Profit: {profit_2:.2f} CHF")
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print()
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print("="*80)
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