CFA Level I Derivatives - Put-Call Parity

Summary

The video explains the concept of put-call parity for European options, focusing on protective puts and fiduciary calls. A protective put combines owning an asset with a long position in a put option to limit downside risk while keeping upside potential. A fiduciary call involves buying a call option and a risk-free bond to achieve a similar payoff. The two strategies are shown to yield identical results, leading to the put-call parity formula, which helps in pricing options and identifying arbitrage opportunities. The example illustrates this with specific figures and calculations.

Takeaways

• 📊 A protective put involves owning an asset and buying a put option to protect against potential downside risk.
• 💰 The protective put strategy allows the investor to limit downside risk while maintaining upside potential.
• 🔍 A fiduciary call involves buying a call option and a risk-free bond to create a position with similar payoffs to a protective put.
• 📈 Both protective put and fiduciary call strategies aim to protect against downside risk while participating in upside potential.
• 📝 Put-call parity is the relationship between the prices of a European put option, call option, and the underlying asset.
• 💡 Put-call parity can be expressed mathematically as: Asset Price + Put Price = Call Price + Present Value of Strike Price.
• 📉 The example illustrates put-call parity using an asset priced at $90, with a strike price of $100 and a 4% risk-free rate over three months.
• 💸 In the example, the difference between the put and call prices is calculated as $9.02, demonstrating the relationship under no arbitrage conditions.
• 🔑 Put-call parity helps in option pricing and identifying arbitrage opportunities in case of market mispricing.
• 📅 Arbitrage opportunities can arise when there is a mismatch between put and call prices, accounting for transaction costs.

Q & A

What is a protective put?

A protective put is a strategy where an investor holds a long position in an asset and buys a put option on the same asset. This combination provides downside protection, limiting losses while allowing for unlimited upside potential.

Why is a protective put called 'protective'?

It is called 'protective' because it protects the investor from downside risk. If the asset's value decreases below the strike price, the put option ensures the investor can still sell the asset at the strike price, thus limiting the potential loss.

What is a fiduciary call?

A fiduciary call is a strategy where an investor buys a call option and a risk-free bond with a face value equal to the call's strike price. The bond matures at the same time as the call option's expiration, providing protection if the call expires worthless.

What is the payoff structure of a protective put?

The payoff of a protective put depends on the underlying asset's price at expiration. If the asset's price (ST) is above the strike price (X), the put option expires worthless, and the investor keeps the asset. If the price is below X, the investor exercises the put and sells the asset at the strike price.

What is the payoff structure of a fiduciary call?

The payoff of a fiduciary call depends on the underlying asset's price at expiration. If the asset's price (ST) is above the strike price (X), the call option is exercised, and the investor uses the bond's value to buy the asset. If the price is below X, the call expires worthless, and the investor keeps the bond.

How do protective puts and fiduciary calls produce similar results?

Both strategies ensure the investor's ending position is either the asset's price (ST) if it's greater than the strike price (X), or X if the asset's price is lower. This means both strategies yield identical payoffs despite using different instruments.

What is put-call parity?

Put-call parity is a financial principle that defines the relationship between the price of a European call option and a European put option with the same strike price and expiration date. The formula is: S0 + P0 = C0 + PV(X), where S0 is the asset price, P0 is the put price, C0 is the call price, and PV(X) is the present value of the strike price.

How can put-call parity be used for option pricing?

Put-call parity helps determine the fair prices of options and identify arbitrage opportunities. By rearranging the put-call parity formula, investors can compute the price of one option if they know the price of the other, ensuring no arbitrage opportunities exist.

What example is used to illustrate put-call parity in the script?

The script uses an example where the underlying asset is priced at $90, the strike price is $100, the risk-free rate is 4%, and the options expire in three months. Based on this, the script calculates that the difference between the put and call prices should be $9.02.

How does put-call parity prevent arbitrage opportunities?

Put-call parity ensures that the relationship between the prices of puts and calls is maintained, preventing mispricing. If there is a significant discrepancy between the prices, arbitrage opportunities arise where investors can exploit the price differences for a risk-free profit.