Introduction to Option Strategies

Option strategies represent combinations of options and underlying assets that are designed to achieve specific investment objectives, including speculation, hedging, and income generation. Understanding option strategies is essential for comprehending how market participants use options to manage risk and enhance returns in various market conditions. Option strategies can be classified based on their market outlook, risk profile, and the number of options involved. The versatility of options enables investors to construct positions that profit from rising markets, falling markets, range-bound markets, and volatile markets.

The selection of an option strategy depends on the investor’s market view, risk tolerance, and investment objectives. Investors with a bullish outlook may use strategies such as buying calls or selling puts. Investors with a bearish outlook may use strategies such as buying puts or selling calls. Investors with a neutral outlook may use strategies such as covered calls or cash-secured puts. Investors with a volatility outlook may use strategies such as straddles or strangles. The choice of strategy should reflect the investor’s expectations for the underlying asset’s price movement and the level of volatility.

Option strategies can be classified as directional strategies, which profit from price movements in a specific direction; non-directional strategies, which profit from the passage of time or changes in volatility; and combination strategies, which combine multiple options to achieve specific payoff profiles. Directional strategies include long calls, long puts, and bull and bear spreads. Non-directional strategies include covered calls, cash-secured puts, and iron condors. Combination strategies include straddles, strangles, and butterflies. Each strategy has its own risk-return profile and is appropriate for different market conditions.

The payoff profiles of option strategies are determined by the payoffs of the individual options at expiration. The net payoff of a strategy is the sum of the payoffs of the individual options, adjusted for the premiums paid or received. Understanding the payoff profiles of option strategies is essential for evaluating the potential outcomes and risks associated with each strategy. The payoff profiles can be represented graphically, showing the relationship between the underlying price and the strategy’s profit or loss at expiration.

Protective Puts

A protective put strategy involves purchasing a put option to protect a long position in the underlying asset against downside risk. Understanding protective puts is essential for comprehending how investors can hedge their existing positions while retaining the potential for upside appreciation. Protective puts provide insurance against price declines, limiting the investor’s loss to a known amount while allowing participation in any upside.

The protective put strategy is implemented by purchasing a put option on the same underlying asset that the investor owns. The put option provides the right to sell the underlying asset at the strike price, establishing a floor for the investor’s loss. If the underlying price falls below the strike price, the investor can exercise the put option and sell the asset at the strike price, limiting the loss. If the underlying price rises, the investor can participate in the appreciation, with the put option expiring worthless.

Example of a Protective Put:

Suppose an investor owns 100 shares of Company ABC stock, currently trading at $50 per share. The investor is concerned about a potential decline but does not want to sell the shares. To protect the position, the investor purchases a put option with a strike price of $45 for a premium of $2 per share.

• Cost of the put option: $2 × 100 = $200

• Effective purchase price of the stock: $50 per share

• Breakeven point: $50 + $2 = $52 per share (stock appreciation must cover the premium)

• Maximum loss: ($50 – $45 + $2) × 100 = ($7) × 100 = $700

Scenarios:

Formula for Protective Put Payoff:

Payoff = S_T – S_0 – P + Max(K – S_T, 0)

Where:

• S_T = The price of the underlying asset at expiration

• S_0 = The initial price of the underlying asset

• P = The premium paid for the put option

• K = The strike price of the put option

Formula for Protective Put Maximum Loss:

Maximum Loss = S_0 – K + P

Where:

• S_0 = The initial price of the underlying asset

• K = The strike price of the put option

• P = The premium paid for the put option

Formula for Protective Put Breakeven Point:

Breakeven = S_0 + P

Where:

• S_0 = The initial price of the underlying asset

• P = The premium paid for the put option

Covered Calls

A covered call strategy involves selling call options against a long position in the underlying asset, generating income from the option premium while potentially limiting upside appreciation. Understanding covered calls is essential for comprehending how investors can generate income from their existing positions and enhance returns in range-bound or slightly bullish markets. Covered calls are one of the most commonly used option strategies, particularly in equity markets.

The covered call strategy is implemented by owning the underlying asset and selling call options on the same asset. The call option gives the buyer the right to purchase the underlying asset at the strike price, and the seller receives a premium for assuming this obligation. If the underlying price remains below the strike price at expiration, the call option expires worthless and the investor keeps the premium. If the underlying price rises above the strike price, the investor may be required to sell the underlying asset at the strike price, limiting the upside appreciation.

Example of a Covered Call:

Suppose an investor owns 100 shares of Company XYZ stock, currently trading at $50 per share. The investor wants to generate additional income from the position and is willing to sell the shares at $55. The investor sells a call option with a strike price of $55 for a premium of $3 per share.

• Premium received: $3 × 100 = $300

• Effective sale price if called: $55 + $3 = $58 per share

• Breakeven point: $50 – $3 = $47 per share

• Maximum profit: ($55 – $50 + $3) × 100 = $8 × 100 = $800

Scenarios:

Formula for Covered Call Payoff:

Payoff = (S_T – S_0) + C – Max(S_T – K, 0)

Where:

• S_T = The price of the underlying asset at expiration

• S_0 = The initial price of the underlying asset

• C = The premium received from selling the call option

• K = The strike price of the call option

Formula for Covered Call Maximum Profit:

Maximum Profit = K – S_0 + C

Where:

• K = The strike price of the call option

• S_0 = The initial price of the underlying asset

• C = The premium received from selling the call option

Formula for Covered Call Breakeven Point:

Breakeven = S_0 – C

Where:

• S_0 = The initial price of the underlying asset

• C = The premium received from selling the call option

Bull Call Spreads

A bull call spread involves purchasing a call option at a lower strike price and selling a call option at a higher strike price, reducing the cost of the position while limiting the upside potential. Understanding bull call spreads is essential for comprehending how investors can profit from moderate price increases with limited risk. Bull call spreads are a popular strategy for investors who are moderately bullish and want to reduce the cost of their option positions.

The bull call spread is implemented by buying a call option at a lower strike price and selling a call option at a higher strike price, both with the same expiration date. The premium received from selling the higher strike call reduces the net cost of the position. The maximum profit is limited to the difference between the strike prices minus the net premium paid. The maximum loss is limited to the net premium paid.

Example of a Bull Call Spread:

Suppose an investor is moderately bullish on Company ABC stock, currently trading at $50. The investor buys a call option with a strike price of $50 for a premium of $4 per share and sells a call option with a strike price of $55 for a premium of $2 per share.

• Premium paid: $4 per share

• Premium received: $2 per share

• Net premium paid: $4 – $2 = $2 per share

• Maximum profit: ($55 – $50 – $2) = $3 per share

• Maximum loss: $2 per share

• Breakeven: $50 + $2 = $52 per share

Scenarios:

Wait, the above table has an error. Let me recalculate properly.

Correct Scenarios for Bull Call Spread:

Wait, I need to be more careful. The payoff for the short call is the premium received minus the maximum of zero and (S_T – K). Let me recalculate properly.

Correct Calculation for Bull Call Spread:

Long call: Buy K=$50, Premium = $4
Short call: Sell K=$55, Premium = $2
Net premium = $4 – $2 = $2

Formula for Bull Call Spread Payoff:

Payoff = Max(S_T – K_L, 0) – Max(S_T – K_H, 0) – (C_L – C_H)

Where:

• S_T = The price of the underlying asset at expiration

• K_L = The lower strike price (long call)

• K_H = The higher strike price (short call)

• C_L = The premium paid for the lower strike call

• C_H = The premium received for the higher strike call

Formula for Bull Call Spread Maximum Profit:

Maximum Profit = K_H – K_L – (C_L – C_H)

Where:

• K_H = The higher strike price

• K_L = The lower strike price

• C_L = The premium paid for the lower strike call

• C_H = The premium received for the higher strike call

Formula for Bull Call Spread Maximum Loss:

Maximum Loss = C_L – C_H

Formula for Bull Call Spread Breakeven Point:

Breakeven = K_L + (C_L – C_H)

Bear Put Spreads

A bear put spread involves purchasing a put option at a higher strike price and selling a put option at a lower strike price, reducing the cost of the position while limiting the profit potential. Understanding bear put spreads is essential for comprehending how investors can profit from moderate price decreases with limited risk. Bear put spreads are a popular strategy for investors who are moderately bearish and want to reduce the cost of their option positions.

The bear put spread is implemented by buying a put option at a higher strike price and selling a put option at a lower strike price, both with the same expiration date. The premium received from selling the lower strike put reduces the net cost of the position. The maximum profit is limited to the difference between the strike prices minus the net premium paid. The maximum loss is limited to the net premium paid.

Example of a Bear Put Spread:

Suppose an investor is moderately bearish on Company XYZ stock, currently trading at $50. The investor buys a put option with a strike price of $55 for a premium of $6 per share and sells a put option with a strike price of $50 for a premium of $3 per share.

• Premium paid: $6 per share

• Premium received: $3 per share

• Net premium paid: $6 – $3 = $3 per share

• Maximum profit: ($55 – $50 – $3) = $2 per share

• Maximum loss: $3 per share

• Breakeven: $55 – $3 = $52 per share

Scenarios:

Formula for Bear Put Spread Payoff:

Payoff = Max(K_H – S_T, 0) – Max(K_L – S_T, 0) – (P_H – P_L)

Where:

• S_T = The price of the underlying asset at expiration

• K_H = The higher strike price (long put)

• K_L = The lower strike price (short put)

• P_H = The premium paid for the higher strike put

• P_L = The premium received for the lower strike put

Formula for Bear Put Spread Maximum Profit:

Maximum Profit = K_H – K_L – (P_H – P_L)

Where:

• K_H = The higher strike price

• K_L = The lower strike price

• P_H = The premium paid for the higher strike put

• P_L = The premium received for the lower strike put

Formula for Bear Put Spread Maximum Loss:

Maximum Loss = P_H – P_L

Formula for Bear Put Spread Breakeven Point:

Breakeven = K_H – (P_H – P_L)

Straddles

A straddle involves purchasing a call option and a put option with the same strike price and expiration date, profiting from significant price movements in either direction. Understanding straddles is essential for comprehending how investors can profit from volatility without taking a directional view. Straddles are a popular strategy for investors who expect a significant price movement but are uncertain about the direction.

The straddle is implemented by buying a call option and a put option with the same strike price and expiration date. The cost of the straddle is the sum of the premiums paid for the call and put options. The straddle profits if the underlying price moves significantly in either direction, with the profit from one option offsetting the loss from the other. The maximum loss is limited to the total premium paid.

Example of a Straddle:

Suppose an investor expects significant volatility in Company ABC stock, currently trading at $100. The investor buys a call option with a strike price of $100 for a premium of $5 per share and buys a put option with a strike price of $100 for a premium of $5 per share.

• Total premium paid: $5 + $5 = $10 per share

• Maximum loss: $10 per share

• Breakeven points: $100 – $10 = $90 and $100 + $10 = $110

Scenarios:

Formula for Straddle Payoff:

Payoff = Max(S_T – K, 0) + Max(K – S_T, 0) – (C + P)

Where:

• S_T = The price of the underlying asset at expiration

• K = The strike price of the options

• C = The premium paid for the call option

• P = The premium paid for the put option

Formula for Straddle Breakeven Points:

Upper Breakeven = K + (C + P)
Lower Breakeven = K – (C + P)

Where:

• K = The strike price of the options

• C = The premium paid for the call option

• P = The premium paid for the put option

Strangles

A strangle involves purchasing a call option at a higher strike price and a put option at a lower strike price, profiting from significant price movements in either direction at a lower cost than a straddle. Understanding strangles is essential for comprehending how investors can profit from volatility while reducing the cost of the position. Strangles are a popular strategy for investors who expect a significant price movement but want to reduce the cost of their volatility positions.

The strangle is implemented by buying a call option at a higher strike price and buying a put option at a lower strike price, with the same expiration date. The cost of the strangle is the sum of the premiums paid for the call and put options. The strangle profits if the underlying price moves significantly beyond the strike prices, with the profit from one option offsetting the loss from the other. The maximum loss is limited to the total premium paid.

Example of a Strangle:

Suppose an investor expects significant volatility in Company XYZ stock, currently trading at $100. The investor buys a call option with a strike price of $105 for a premium of $3 per share and buys a put option with a strike price of $95 for a premium of $3 per share.

• Total premium paid: $3 + $3 = $6 per share

• Maximum loss: $6 per share

• Breakeven points: $95 – $6 = $89 and $105 + $6 = $111

Scenarios:

Formula for Strangle Payoff:

Payoff = Max(S_T – K_C, 0) + Max(K_P – S_T, 0) – (C + P)

Where:

• S_T = The price of the underlying asset at expiration

• K_C = The strike price of the call option

• K_P = The strike price of the put option

• C = The premium paid for the call option

• P = The premium paid for the put option

Formula for Strangle Breakeven Points:

Upper Breakeven = K_C + (C + P)
Lower Breakeven = K_P – (C + P)

Where:

• K_C = The strike price of the call option

• K_P = The strike price of the put option

• C = The premium paid for the call option

• P = The premium paid for the put option

Introduction to Swaps

Swaps represent agreements between two parties to exchange cash flows or other financial instruments over a specified period, providing a mechanism for managing interest rate, currency, and other risks. Understanding swaps is essential for comprehending one of the most important and widely used derivative instruments in financial markets. Swaps are primarily traded over the counter, with customized terms negotiated directly between the parties.

Swaps can be classified based on the type of cash flows being exchanged. Interest rate swaps involve the exchange of fixed-rate payments for floating-rate payments, enabling parties to manage their interest rate exposure. Currency swaps involve the exchange of cash flows in different currencies, enabling parties to manage their currency exposure. Credit default swaps involve the exchange of credit protection payments for contingent payments in the event of default, enabling parties to manage their credit exposure. Each type of swap serves different risk management purposes and has its own characteristics.

The fundamental principle of swaps is the exchange of cash flows based on a notional principal amount. The notional principal is the reference amount used to calculate the cash flows but is not exchanged between the parties. The cash flows are typically calculated as the notional principal multiplied by the interest rate or exchange rate, and are exchanged at specified intervals. The exchange of cash flows enables each party to achieve its desired risk exposure without directly altering its underlying positions.

Swaps provide various benefits for market participants, including the ability to manage risks efficiently, the ability to access markets that may otherwise be unavailable, and the ability to reduce funding costs. Companies use swaps to manage their interest rate and currency exposures, converting fixed-rate debt to floating-rate debt or vice versa. Financial institutions use swaps to manage their balance sheet risks and to generate income. Investors use swaps to gain exposure to different asset classes and to hedge their portfolio risks.

Interest Rate Swaps

Interest rate swaps represent agreements to exchange fixed-rate interest payments for floating-rate interest payments, enabling parties to manage their exposure to interest rate fluctuations. Understanding interest rate swaps is essential for comprehending the most common type of swap and its applications in risk management. Interest rate swaps are widely used by corporations, financial institutions, and investors to manage interest rate risk and to achieve their desired interest rate exposure.

In a plain vanilla interest rate swap, one party agrees to pay a fixed interest rate on a notional principal amount, while the other party agrees to pay a floating interest rate on the same notional principal. The fixed rate is typically based on the swap rate, which is the fixed rate that makes the present value of the fixed payments equal to the present value of the floating payments at the inception of the swap. The floating rate is typically based on a reference rate such as the Secured Overnight Financing Rate or the Euro Short-Term Rate.

Example of an Interest Rate Swap:

Suppose Company A has a $10 million loan with a floating interest rate of SOFR + 2%. Company A expects interest rates to rise and wants to lock in a fixed rate. Company B has a $10 million loan with a fixed interest rate of 6%. Company B expects interest rates to fall and wants to switch to a floating rate. The two companies enter into an interest rate swap.

• Notional principal: $10 million

• Fixed rate: 5% (paid by Company A, received by Company B)

• Floating rate: SOFR (paid by Company B, received by Company A)

• Payment frequency: Annual

Cash Flows if SOFR = 4%:

• Company A pays fixed: 5% × $10,000,000 = $500,000

• Company B pays floating: 4% × $10,000,000 = $400,000

• Net payment from Company A to Company B: $500,000 – $400,000 = $100,000

Company A’s Effective Interest Rate:

• Original loan: SOFR + 2% = 4% + 2% = 6%

• Swap: Pay fixed 5%, receive floating 4%

• Net payment: 5% – 4% = 1%

• Effective rate: 6% – 1% = 5% (fixed)

Company B’s Effective Interest Rate:

• Original loan: 6% fixed

• Swap: Pay floating 4%, receive fixed 5%

• Net receipt: 5% – 4% = 1%

• Effective rate: 6% – 1% = 5% (floating)

Cash Flows if SOFR = 3%:

• Company A pays fixed: 5% × $10,000,000 = $500,000

• Company B pays floating: 3% × $10,000,000 = $300,000

• Net payment from Company A to Company B: $500,000 – $300,000 = $200,000

Company A’s Effective Interest Rate:

• Original loan: SOFR + 2% = 3% + 2% = 5%

• Swap: Pay fixed 5%, receive floating 3%

• Net payment: 5% – 3% = 2%

• Effective rate: 5% – 2% = 3% (fixed)

Wait, this is incorrect. Let me correct the calculation for the interest rate swap.

Correct Calculation for Interest Rate Swap:

Net Payment = (Fixed Rate – Floating Rate) × Notional Principal

If Fixed Rate > Floating Rate, Company A pays Company B the difference.
If Floating Rate > Fixed Rate, Company B pays Company A the difference.

When SOFR = 4%:

• Fixed Rate = 5%, Floating Rate = 4%

• Difference = 5% – 4% = 1%

• Company A pays Company B: 1% × $10,000,000 = $100,000

Company A’s Effective Interest Rate:

• Original loan: SOFR + 2% = 4% + 2% = 6% (floating)

• Swap: Pay fixed 5%, receive floating 4%

• Net swap payment: 5% – 4% = 1% (payment)

• Effective rate: 6% + 1% – 0% = 7%? No, let me rethink.

Company A’s original loan payment: SOFR + 2% = 4% + 2% = 6% of $10,000,000 = $600,000
Company A’s swap payment: 5% of $10,000,000 = $500,000 (pay fixed)
Company A’s swap receipt: 4% of $10,000,000 = $400,000 (receive floating)
Net swap payment: $500,000 – $400,000 = $100,000
Total payment: $600,000 + $100,000 = $700,000
Effective rate: $700,000 / $10,000,000 = 7%? That doesn’t seem right.

Actually, I need to recalculate this more carefully. Let me think about this differently.

Company A wants to convert its floating rate loan (SOFR + 2%) into a fixed rate loan.
Company A enters into a swap where it pays fixed (5%) and receives floating (SOFR).

Company A’s Effective Rate:

Original loan: (SOFR + 2%)
Swap: Pay Fixed (5%) – Receive SOFR
Net rate: (SOFR + 2%) + Fixed(5%) – SOFR = 2% + 5% = 7%

So Company A’s effective rate is 7% fixed, regardless of what SOFR does.

When SOFR = 4%:

• Original loan: 4% + 2% = 6%

• Swap: Pay 5%, Receive 4%

• Net: 6% + 5% – 4% = 7%

When SOFR = 3%:

• Original loan: 3% + 2% = 5%

• Swap: Pay 5%, Receive 3%

• Net: 5% + 5% – 3% = 7%

So Company A has successfully converted its floating rate loan into a fixed rate loan of 7%.

Similarly, Company B has a fixed rate loan of 6% and wants to convert it to a floating rate loan.
Company B enters into a swap where it pays floating (SOFR) and receives fixed (5%).

Company B’s Effective Rate:

Original loan: 6% (fixed)
Swap: Pay SOFR – Receive Fixed (5%)
Net rate: 6% + SOFR – 5% = SOFR + 1%

When SOFR = 4%:

• Original loan: 6%

• Swap: Pay 4%, Receive 5%

• Net: 6% + 4% – 5% = 5%

When SOFR = 3%:

• Original loan: 6%

• Swap: Pay 3%, Receive 5%

• Net: 6% + 3% – 5% = 4%

So Company B has successfully converted its fixed rate loan into a floating rate loan of SOFR + 1%.

Formula for Interest Rate Swap Net Payment:

Net Payment = (Fixed Rate – Floating Rate) × Notional Principal

If Fixed Rate > Floating Rate, the fixed-rate payer pays the floating-rate payer.
If Floating Rate > Fixed Rate, the floating-rate payer pays the fixed-rate payer.

Formula for Effective Rate After Swap:

For a party converting from floating to fixed:
Effective Rate = Floating Index + Spread + (Fixed Rate – Floating Index) = Fixed Rate + Spread

For a party converting from fixed to floating:
Effective Rate = Fixed Rate + (Floating Index – Fixed Rate) = Floating Index

Currency Swaps and Their Applications

Currency swaps represent agreements to exchange cash flows in different currencies, enabling parties to manage their currency exposure and to access funding in different currencies. Understanding currency swaps is essential for comprehending how international businesses and financial institutions manage currency risk and optimize their funding costs. Currency swaps are widely used by multinational corporations and financial institutions to manage their cross-border exposures.

In a currency swap, the parties exchange principal amounts in different currencies at the inception of the swap and re-exchange them at maturity. The parties also exchange interest payments in the respective currencies, with the interest rates reflecting the prevailing rates in each currency. The exchange of principal amounts enables the parties to access funding in currencies that may not be directly available to them.

Example of a Currency Swap:

Suppose a US company needs €10 million for its European operations, and a European company needs $12 million for its US operations. The US company can borrow dollars at 5% and euros at 7%, while the European company can borrow euros at 4% and dollars at 6%. The two companies can benefit from a currency swap.

Without Swap:

• US company borrows euros at 7%, paying €700,000 annually on €10 million

• European company borrows dollars at 6%, paying $720,000 annually on $12 million

• Total interest cost: €700,000 + $720,000

With Swap:

• US company borrows dollars at 5%, paying $600,000 annually on $12 million

• European company borrows euros at 4%, paying €400,000 annually on €10 million

• The companies swap currencies, with the US company providing euros to the European company and the European company providing dollars to the US company.

• US company pays: $600,000 (dollar loan) + €400,000 (swap payment in euros)

• European company pays: €400,000 (euro loan) + $600,000 (swap payment in dollars)

Savings from the Swap:

US company: Original cost €700,000 vs Swap cost €400,000 = €300,000 savings
European company: Original cost $720,000 vs Swap cost $600,000 = $120,000 savings

Formula for Currency Swap Payments:

The cash flows in a currency swap are calculated as:

Dollar Payment = Notional Dollars × Dollar Interest Rate
Euro Payment = Notional Euros × Euro Interest Rate

The exchange of payments is typically based on the prevailing exchange rates at the time of the swap’s inception.

Basic Derivative Pricing Principles and the No-Arbitrage Condition

Basic derivative pricing principles are founded on the concept of no-arbitrage, which holds that there should be no opportunities for riskless profit in efficient markets. Understanding the no-arbitrage condition is essential for comprehending how derivatives are priced and how market participants ensure that prices remain consistent across related markets. The no-arbitrage condition is the foundation of modern derivative pricing theory.

The no-arbitrage condition requires that the price of a derivative be determined by the price of its underlying asset and the cost of carry, with no opportunity for riskless profit. If the derivative price deviates from its no-arbitrage value, arbitrageurs will step in to exploit the price difference, buying the undervalued asset and selling the overvalued asset until prices converge. This arbitrage activity ensures that derivative prices remain consistent with the prices of the underlying assets.

The No-Arbitrage Condition for Forward Contracts:

For a forward contract on a non-income-producing asset, the no-arbitrage condition requires that:

F = S × e^(rT)

Where:

• F = The forward price

• S = The spot price of the underlying asset

• r = The risk-free interest rate

• T = The time to maturity

If F > S × e^(rT), arbitrageurs can buy the underlying asset at the spot price and sell the forward contract, earning a riskless profit. If F < S × e^(rT), arbitrageurs can short the underlying asset and buy the forward contract, earning a riskless profit.

The No-Arbitrage Condition for Options:

For options, the no-arbitrage condition is captured by the put-call parity relationship, which holds for European options on the same underlying asset with the same strike price and expiration date.

C + K × e^(-rT) = P + S

Where:

• C = The price of a call option

• P = The price of a put option

• K = The strike price

• S = The spot price of the underlying asset

• r = The risk-free interest rate

• T = The time to expiration

If this relationship is violated, arbitrageurs can construct riskless positions to profit from the mispricing.

Example of Put-Call Parity Arbitrage:

Suppose the following prices exist for options on Company ABC stock:

• Call price (C) = $5

• Put price (P) = $4

• Stock price (S) = $100

• Strike price (K) = $105

• Risk-free rate (r) = 5%

• Time to expiration (T) = 1 year

Check Put-Call Parity:

Left side: C + K × e^(-rT) = 5 + 105 × e^(-0.05) = 5 + 105 × 0.9512 = 5 + 99.88 = 104.88
Right side: P + S = 4 + 100 = 104

The parity is violated because 104.88 > 104.

Arbitrage Strategy:

1. Buy the put option for $4

2. Buy the stock for $100

3. Sell the call option for $5

4. Net cost: 4 + 100 – 5 = $99

At Expiration:

Regardless of the stock price at expiration, the net cash flow is $105.

Profit Calculation:

• Initial investment: $99

• Cash received at expiration: $105

• Risk-free profit: $105 – $99 = $6 (present value of $6)

This arbitrage opportunity will be exploited by arbitrageurs, driving prices back to parity.