# Time Decay Arbitrage

Time Decay Arbitrage is a trading strategy that takes advantage of the time decay characteristic inherent in options pricing.

This strategy focuses on exploiting the difference in the rate of time decay (theta) between different options.

## Key Takeaways – Time Decay Arbitrage

Deterioration of Option Value

- Time decay accelerates as expiration approaches.
- Toward expiry, this significantly reduces the value of options (particularly those that are out-of-the-money).
Strategic Timing

- Exploit time decay by selling options with short expiration dates to capture premium as they lose value rapidly.
Risk Management

- Monitor positions closely to avoid substantial losses from sudden market movements against short-term options.

## Understanding Time Decay

Time decay, or theta, is a measure of the rate at which the price of an option decreases as it approaches its expiration date.

The value of an option diminishes over time (all else being equal).

This is due to the reduction in the time available for the underlying asset to move in the trader’s favor.

## Key Concepts

### Options Pricing

Options are financial derivatives that give the holder the right, but not the obligation, to buy or sell an underlying asset at a specified price (strike price) before a certain date (expiration date).

The price of an option is influenced by various factors, including the:

- underlying asset price
- strike price
- time to expiration
- volatility, and
- interest rates

### Theta

Theta represents the rate of decline in the value of an option due to the passage of time.

For example, atheta of -0.05 for an option means that the option’s price will theoretically decrease by $0.05 for every day that passes, all else being equal.

As expiration approaches, theta accelerates, which leads to a more rapid decline in the option’s value.

## Execution of Time Decay Arbitrage

### Identifying Opportunities

Traders look for opportunities where the time decay rates of similar options differ significantly.

This could involve comparing options with the same expiration date but different strike prices (vertical spreads) or options with different expiration dates (calendar spreads).

### Constructing the Arbitrage Position

To construct a time decay arbitrage position, a trader might simultaneously buy and sell options in such a way that the net theta is positive.

This means the position will benefit from the passage of time.

For instance, in a calendar spread, a trader could sell a near-term option and buy a longer-term option, capturing the differential in time decay.

## Risks and Considerations

### Volatility

Changes in volatility can impact the value of options and potentially offset the gains from time decay.

### Market Movements

Movements in the underlying asset can affect the profitability of a time decay arbitrage strategy.

If the underlying asset moves sharply, the value of the options can change in a way that outweighs the benefits from time decay.

### Transaction Costs

Frequent adjustments and the simultaneous buying and selling of options can incur substantial transaction costs.

Traders need to account for these costs when evaluating the potential profitability of their strategy.

## Example of Time Decay Arbitrage

### Calendar Spread

Consider a trader who notices that a one-month call option on a stock has a theta of -0.10, while a three-month call option on the same stock has a theta of -0.05.

The trader can sell the one-month call option and buy the three-month call option.

As time passes, the one-month option will decay faster than the three-month option, allowing the trader to potentially profit from the differential in time decay.

Let’s look at this example involving time decay arbitrage step by step.

## Trade Example: Calendar Spread

### Step 1: Identify Suitable Options

**Underlying Asset –**Assume we are dealing with stock XYZ, currently trading at $100.**Options –**Look at call options for stock XYZ.**Near-Term Call Option –**Expiring in 1 month, strike price $100.**Longer-Term Call Option –**Expiring in 3 months, strike price $100.

### Step 2: Analyze Theta Values

**Near-Term Call Option Theta:**-0.10 (indicates the option loses $0.10 per day).**Longer-Term Call Option Theta:**-0.05 (option loses $0.05 per day).

### Step 3: Determine Trade Quantities

**Quantity –**Decide to trade 10 contracts of each option. One options contract typically represents 100 shares.**Investment –**Be sure you have the capital to cover margin requirements and potential losses.

### Step 4: Execute the Trade

#### Sell Near-Term Call Options

- Sell 10 contracts of the 1-month $100 strike call options.
- Each contract loses value at a rate of $0.10 per day.
**Premium collected**: Assume each contract is trading at $2.00.- Total premium collected = $2.00 * 10 * 100 = $2,000.

#### Buy Longer-Term Call Options

- Buy 10 contracts of the 3-month $100 strike call options.
- Each contract loses value at a rate of $0.05 per day.
- Premium paid: Assume each contract is trading at $4.00.
- Total premium paid = $4.00 * 10 * 100 = $4,000.

### Step 5: Monitor and Manage the Position

#### Time Decay Benefit

The near-term options decay faster than the longer-term options.

The net daily decay benefit is:

- Daily decay of sold options = 10 contracts * 100 shares/contract * $0.10 = $100.
- Daily decay of bought options = 10 contracts * 100 shares/contract * $0.05 = $50.
- Net daily decay benefit = $100 – $50 = $50.

#### Adjustments

Monitor the position and adjust if necessary.

For instance, if volatility changes or the underlying stock price moves significantly, you might need to close or modify the trade.

### Step 6: Closing the Trade

#### Close Near-Term Options

- Buy back the 10 near-term contracts before expiration or at a desired profit point.
- Assume these options are now worth $0.50 each.
- Total cost to buy back = $0.50 * 10 * 100 = $500.

#### Close Longer-Term Options

- Sell the 10 longer-term contracts.
- Assume these options are now worth $3.50 each.
- Total premium received = $3.50 * 10 * 100 = $3,500.

### Step 7: Calculate Profit/Loss

**Premium collected (initial):**$2,000.**Premium paid (initial):**$4,000.**Cost to close near-term options:**$500.**Premium received for longer-term options:**$3,500.**Net profit/loss:**- Premium collected – Premium paid + Premium received for longer-term options – Cost to close near-term options.
- $2,000 – $4,000 + $3,500 – $500 = $1,000 profit.

### Note

The real profit from a time decay arbitrage strategy comes from careful timing and adjustments, trying to capture the decay differential more effectively and manage risks such as volatility changes.