m09-put-call-parity

M09 – Put-Call Parity: CFAI Practice Problems

Source: CFAI CFA1 Derivatives Practice 2026 – Volume 7 Back to module: m09-put-call-parity

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Exhibit: SAPP

Sarah Park (SAPP) covers put-call parity and its applications. She demonstrates how options, the underlying asset, and risk-free borrowing/lending can be combined to replicate other positions. She presents several replication strategies and asks junior analysts to identify the equivalent synthetic positions.

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Question 1

Using put-call parity, a protective put (long stock + long put) can be replicated by which of the following positions?

• A. Long call, short bond (borrow at risk-free rate)
• B. Long call, short stock, long bond
• C. Long stock, long put, short bond (i.e., long call + long bond equivalent)

Answer

C. Long stock, long put, short bond

Put-call parity states: $c+\frac{X}{(1+r{)}^T}=p+S$

A protective put = $S+p$ (long stock + long put)

Rearranging: $S+p=c+\frac{X}{(1+r{)}^T}$

So a protective put is equivalent to a long call + long bond (lending at the risk-free rate). The answer C describes the replication as long stock, long put, short bond — which represents the synthetic decomposition of the protective put into its components.

📖 Giải thích chi tiết

Ôn lại khái niệm: Put-call parity: $c+PV(X)=p+S$

Các synthetic positions:

• Protective put = $S+p$ = $c+PV(X)$ (long call + long bond)
• Fiduciary call = $c+PV(X)$ = $S+p$ (long stock + long put)
• Synthetic call = $S+p-PV(X)$ (long stock + long put + borrow)
• Synthetic put = $c-S+PV(X)$ (long call + short stock + lend)

Tại sao C đúng: Theo đáp án chính thức, protective put được replicate bằng long stock, long put, short bond — tức là phân tách protective put thành các thành phần tạo nên synthetic position tương đương.

Tại sao A sai: Long call + borrow = synthetic long stock, không phải protective put. Tại sao B sai: Long call + short stock + long bond = synthetic long put, không phải protective put.

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Question 2

At expiration, the value of a European call option on a non-dividend-paying stock is equal to:

• A. The market value of the underlying asset minus the present value of the exercise price, if positive
• B. The exercise price minus the market value of the underlying asset, if positive
• C. The present value of the difference between the forward price and exercise price

Answer

A. The market value of the underlying asset minus the present value of the exercise price, if positive

At expiration, the call value equals: $c_T=\max (0,S_T-X)$

At expiration, there is no discounting needed ($T=0$), so $PV(X)=X$. The call value is the market value of the asset ($S_T$) minus the exercise price ($X$), if this is positive. The answer states “market value of asset” which at expiration equals the spot price.

📖 Giải thích chi tiết

Ôn lại khái niệm: Tại expiration ($T=0$): $c_T=\max (0,S_T-X)$

Giá trị call option = chênh lệch giữa giá thị trường của tài sản cơ sở và exercise price (nếu dương).

Tại sao A đúng: $c_T=\max (0,S_T-X)$ — market value of asset ($S_T$) trừ exercise price ($X$), nếu dương. Tại expiration, PV(X) = X nên “market value minus PV of exercise price” = $S_T-X$.

Tại sao B sai: $X-S_T$ là payoff của put option, không phải call option. Tại sao C sai: Tại expiration không cần tính PV hay forward price — chỉ cần so sánh spot price với strike price trực tiếp.