Option Replication Using Put-Call Parity
50 questions available
Key Points
- Formula: S + P = B + C
- Mnemonic: Sip Pepsi = Be Cool
- Protective Put: Long Stock + Long Put
- Fiduciary Call: Long Bond + Long Call
- Applies only to European options
Key Points
- Synthetic Call: S + P - B
- Synthetic Put: B + C - S
- Synthetic Stock: B + C - P
- Synthetic Bond: S + P - C
- + means Long, - means Short
Key Points
- Spot price is replaced by PV of Forward Price
- Equation: PV(F) + P = PV(X) + C
- Used for options on forwards/futures
- Maintains the no-arbitrage condition
Key Points
- Equity = Call Option on Firm Assets
- Strike Price = Face Value of Debt
- Solvency Payoff (Equity): V_T - D
- Insolvency Payoff (Equity): 0
- Bondholders bear downside risk in insolvency
Questions
According to the Put-Call Parity equation, which portfolio is equivalent to a Fiduciary Call?
View answer and explanationWhat represents 'B' in the mnemonic 'Sip Pepsi = Be Cool' (S + P = B + C)?
View answer and explanationWhich of the following correctly describes a 'Protective Put'?
View answer and explanationIf you want to create a Synthetic Call option, which positions should you take?
View answer and explanationThe Put-Call Parity relationship applies strictly to which type of options?
View answer and explanationUsing the Put-Call Parity, what is the formula for a Synthetic Put?
View answer and explanationIn a synthetic position, what does a negative sign (-) typically indicate?
View answer and explanationCalculate the price of a European Call option if: Stock = 100, Put = 5, PV of Strike (Bond) = 90.
View answer and explanationCalculate the price of the underlying Stock if: Call = 12, Put = 7, PV of Strike = 50.
View answer and explanationWhat constitutes a 'Fiduciary Call'?
View answer and explanationIn Put-Call Forward Parity, the spot price (S) is replaced by which expression?
View answer and explanationIf a firm is considered insolvent (Value of Assets < Debt), what is the payoff to shareholders?
View answer and explanationViewed as an option, a firm's equity is equivalent to:
View answer and explanationWhat represents the 'Strike Price' in the analogy where Equity is a Call Option on the firm?
View answer and explanationIf risk-free rates (RFR) increase, what is the impact on the value of a Call Option based on the parity logic shown?
View answer and explanationCalculate the value of a Bond (PV of Strike) in a parity arbitrage scenario if: Stock = 50, Put = 3, Call = 8.
View answer and explanationA Synthetic Long Bond is created by:
View answer and explanationIf the market price of a Call is 10, but the synthetic call (S + P - B) is calculated at 12, what arbitrage action should be taken?
View answer and explanationIn the Put-Call Forward Parity equation, if the Forward Price is F, what is the formula for the Synthetic Call?
View answer and explanationWhat is the payoff to debtholders if a firm is insolvent (Value of Assets < Debt)?
View answer and explanationCalculate the PV of the Strike Price (Bond) if Strike = 105, RFR = 5 percent, and time to maturity = 1 year.
View answer and explanationIf Stock = 80, Strike = 80, RFR = 10 percent, Time = 1 year, and Call = 10, what is the Put price? (Assume X=80 is face value).
View answer and explanationA portfolio of Long Stock + Long Put is used to limit downside risk. This is known as:
View answer and explanationIdentify the incorrect rearrangement of the Put-Call Parity formula (S + P = B + C).
View answer and explanationIf a Put option is priced at 5, Stock is 50, PV of Strike is 48, and Call is priced at 6, does an arbitrage opportunity exist?
View answer and explanationIn the arbitrage scenario where S+P = 55 and B+C = 54, what is the correct strategy?
View answer and explanationA 'Synthetic Stock' position is constructed by:
View answer and explanationIf the Spot Price (S) is 100 and the Risk-Free Rate is 5 percent (T=1), what is the Forward Price (F) used in parity?
View answer and explanationIn the Merton corporate bond model, the value of the firm's debt is equal to:
View answer and explanationIf a Call is 10, Put is 10, and PV of Strike is 100, what must the Stock price be for parity to hold?
View answer and explanationWhich component in Put-Call Parity accounts for the time value of money related to the strike price?
View answer and explanationThe equation 'Stock + Put = Bond + Call' implies that:
View answer and explanationUsing Put-Call Forward Parity, if F = 105, X = 105, RFR = 5 percent (T=1), and C = 5, what is the value of P?
View answer and explanationIf Risk-Free Rate increases, what happens to the price of a Put option (holding other factors constant)?
View answer and explanationWhich position allows an investor to borrow money at the risk-free rate synthetically?
View answer and explanationCalculate C if S=50, P=2, X=50, RFR=0 percent (T=1).
View answer and explanationIn the firm value analogy, if a company has Assets of 100 and Debt of 80, the 'option' is:
View answer and explanationIf implied volatility increases, what generally happens to both Call and Put prices?
View answer and explanationTo create a 'Synthetic Short Put', what positions are required?
View answer and explanationWhich condition allows for the substitution of S with PV(F) in parity equations?
View answer and explanationIf the equation S + P = B + C is violated, what is the immediate implication?
View answer and explanationCalculate the Synthetic Call price if Forward Price = 105, Strike = 100, RFR = 5 percent (T=1), Put = 3.
View answer and explanationWhat is the primary reason American options might not fit the 'Sip Pepsi = Be Cool' formula exactly?
View answer and explanationFor a solvent firm, the value of Debt (D) plus the value of Equity (E) equals:
View answer and explanationWhen rearranging the formula to S = B + C - P, what does the term 'B' represent in an investment context?
View answer and explanationWhich strategy mimics owning the stock using derivatives?
View answer and explanationIf Spot = 100, Call = 5, Put = 5, and Strike = 100, what is the implied Risk-Free Rate?
View answer and explanationThe combination of a Long Call and a Short Put with the same strike and maturity creates a position similar to:
View answer and explanationPut-Call Parity is effectively an application of:
View answer and explanationIf a firm is solvent, shareholders receive:
View answer and explanation