Problem 1 - A Course in Financial Calculus

Question

What view about the market is reflected in each of the following strategies? (a) Bullish vertical spread: Buy one European call and sell a second one with the same expiry date, but a larger strike price. (b) Bearish vertical spread: Buy one European call and sell a second one with the same expiry date but a smaller strike price. (c) Strip: Buy one European call and two European puts with the same exercise date and strike price. (d) Strap: Buy two European calls and one European put with the same exercise date and strike price. (e) Strangle. Buy a European call and a European put with the same expiry date but different strike prices (consider all possible cases).

Step-by-Step Solution

Answer

(a) Market expected to rise moderately. (b) Market expected to fall or stay neutral. (c) Market expected to fall. (d) Market expected to rise. (e) Market expected to move significantly in any direction.

Step 1: Bullish Vertical Spread Analysis

A bullish vertical spread involves buying a European call option and selling another with the same expiry date but a higher strike price. This strategy is used when the market is expected to rise moderately. It limits the profits (due to the sold high-strike call) but also limits the initial investment, lowering the break-even point.

Step 2: Bearish Vertical Spread Analysis

A bearish vertical spread entails buying a European call option and selling another with the same expiry date but a lower strike price. This strategy reflects an expectation that the market will decrease or remain neutral. It limits the potential loss while also capping the profit, making it suitable when the market is slightly bearish.

Step 3: Strip Strategy Analysis

A strip strategy involves buying one European call option and two European put options with the same expiration and strike price. This strategy is neutral to slightly bearish since the investor anticipates a downward movement in the market. It provides more weight on the downside due to the additional put.

Step 4: Strap Strategy Analysis

A strap consists of buying two European call options and one European put option with the same expiration and strike price. This strategy indicates a bullish view as it expects an upward market movement. The extra call reflects a stronger anticipation of an upward market move compared to the downside protection from the single put.

Step 5: Strangle Strategy Analysis

A strangle involves buying a call and a put with the same expiration date but different strike prices. This strategy is used when an investor expects a significant market move in either direction but is unsure which direction. The call protects against significant upward movement, while the put protects against downward movement.

Key Concepts

Bullish Vertical Spread

A bullish vertical spread is a nifty options trading strategy primarily used when you anticipate a moderate increase in the underlying asset's price. Here, you purchase one European call option and sell another with the same expiration date but a higher strike price.

This approach not only limits your potential profit to the difference between the two strike prices (minus the net premium paid) but also reduces the initial investment needed. This makes it particularly appealing if you're slightly optimistic about the market's direction.

• Benefits: Low initial investment.
• Cons: Capped profits due to the higher strike call sold.

Ultimately, by employing a bullish vertical spread, you're positioning yourself to benefit from a moderate upward trend while minimizing risks and costs.

Bearish Vertical Spread

In contrast to the bullish vertical spread, the bearish vertical spread reflects expectations of a slight decline or neutral movement in the market. This strategy requires buying one European call option and selling another with the same expiration date but a lower strike price.

• Allows you to define a limited risk-reward ratio.
• Useful in slightly bearish conditions.

Your potential loss is capped by the premium difference between the options, whereas the profit is limited to the difference in strike prices, minus the net premium. This strategy can help hedge against less dramatic market downturns while providing limited upside in case of unexpected market stability.

Strip Strategy

A strip strategy seeks to profit from a downward market motion, particularly when there's possibility of significant declines. In this setup, you buy one European call option and two European put options, with identical strike prices and expiration dates.

The additional put option emphasizes the expectation of a decline, offering heavier protection.

• Heavily weighted towards downside protection.
• Limited losses if the market unexpectedly rises.

This neutral to bearish strategy is advantageous if you anticipate market turbulence with a potential downward slide, but want some upside exposure.

Strap Strategy

The strap strategy leans bullish, preparing for potential substantial price upticks. It involves buying two European call options and one European put option, all with the same exercise price and expiration date.

The two calls compared to the one put reflect a confidence in upward movements and a conservative downside hedging.

• A bullish outlook with the extra call option.
• Balanced with the downside safety of a single put option.

This strategy is particularly helpful if you expect major rallies, yet still plan for protection against possible downward retreats.

Strangle Strategy

A strangle strategy is perfect when you expect significant volatility but are uncertain about the direction. It involves purchasing a European call and a European put option, both having the same expiration date but differing strike prices.

The key here is to stay flexible and profit from any major market moves.

• Profitable in scenarios of extreme market fluctuations.
• Minimized risk if market direction is unclear.

Investors use the strangle strategy when they want to take advantage of the extreme price swings, offering coverage for sudden shifts upwards as well as downturns.