The CFA Standards require analysts to act with diligence, transparency, and fairness. When applying put–call parity, which assumes no arbitrage and frictionless markets, professionals must disclose how the value was derived, including relevant inputs (such as stock price, risk-free rate, and time to maturity). This helps clients make informed decisions and ensures consistency with ethical responsibilities around full and fair communication.

A fiduciary call replicates the payoff of owning the underlying asset by combining a long European call with a risk-free bond. The CFA Standards require professionals to communicate all relevant information, including the structure, assumptions, and possible outcomes. This transparency ensures clients understand that if the option expires in the money, the strategy provides the asset’s market value, while if it expires out of the money, only the bond’s face value is received.

We use the put–call parity formula:

p = c + X (1 + r) ^{-T} -S _{0}

• p = put price (what we’re solving for)

• c = 18.40 = call option price

• X =145 = strike price

• r = 0.05 = risk-free interest rate (5%)

• T = 0.5 = time to maturity in years (6 months)

• S _{0} = 150.00 = current stock price

Step 1: Calculate the present value of the strike using X (1 + r) ^{-T}

X ( 1 + r) ^{-T} = 145 × ( 1 + 0.05 ) ^{-.5} = 141.51

Step 2: Plug into the formula

p = 18.40 + 141.51 - 150.00 = 9.91

Put–call parity shows that a portfolio consisting of a long call, short put, and a long position in a risk-free bond replicates the payoff of directly owning the underlying asset. According to the CFA Standards, professionals must communicate such strategies in a clear and understandable manner so clients can make informed decisions. Transparency and clarity are essential—even when using sophisticated instruments like options.

According to the put–call parity relationship:

p _{0} = C _{0} - S _{0} + \frac{X}{(1 + r)^{T}}

This means the payoff of a long put can be replicated by combining a long call, short stock, and a long position in a risk-free bond. This equivalence holds for European-style options and assumes no arbitrage. Each component offsets or mimics the behavior of the actual put, making this structure a perfect replication.

If the actual put price is higher than this theoretical value, it is overpriced. To exploit this arbitrage:

• Sell the put (it's overpriced)

• Sell the stock short (receive proceeds)

• Buy a call (to limit upside risk)

• Invest in a risk-free bond (to lock in the discounted strike)

This creates a synthetic put using the call, bond, and short stock. Since the real put is overpriced, you’re selling high and replicating the same payoff for less — locking in an arbitrage profit at no risk.

A protective put with forward contract consists of three components:

1. A long put option

2. A long forward contract on the asset

3. A risk-free bond maturing at the forward price

If the put expires out of the money, it has no value, but the investor still receives the asset via the forward contract and already holds the bond to pay for it. Therefore, the overall position ends up being equivalent to owning the underlying asset, which means the payoff is equal to its market value at expiration.

In structural models of firm value, equity is viewed as a call option on the firms assets, with the strike price equal to the face value of debt (D). Conversely, debtholders payoff is:

This is equivalent to holding the firms value and being short a put option on that value. As leverage increases, the firms asset risk rises, making the put option more valuable, which hurts debtholders. Therefore, they face more downside risk, while shareholders benefit from the increased upside potential of their implicit call.

A fiduciary call is a portfolio consisting of:

• A long European call option, and

• A risk-free bond that pays the strike price at expiration.

According to put–call–forward parity, this has the same payoff as a synthetic protective put, which consists of:

• A long European put,

• A long forward contract, and

• A long risk-free bond (equal to the forward price discounted back).

This equivalence reflects the fundamental pricing relationships in options and forwards, ensuring no arbitrage. Therefore, the fiduciary call is equivalent to:
long put + long forward + long bond.