In this assignment, we have started the discussion of Back testing Strategy which evaluates strategy for Oil-based Shell Company. We have applied techniques on historical data and examined the company’s profit and loss if it hedged its oil price risk using options in the first quarters of 2020, 2021, and 2022. The Black-Scholes formula computes option premiums because of historical option prices. We consider different strike rates at each Quarter end and calculate approximately how many contracts you need to trade to hedge the entire sales or purchase (export or import) of oil, the cost of hedging, and the profit and loss in each month based on the realized monthly average oil price compared with not hedging.

Further, With your hedging plan, compute the company’s P/L for September, October, and November 2021, assuming the oil price is log-normally distributed around the futures price. Calculated the hedged position with at least three strikes.

(1)    Back testing Strategy for oil-based Shell Company

Using historical data, Backtesting is an essential step in determining the efficacy of a trading strategy for Shell Oil Company. Let’s take a look at a backtesting method that includes trading the shares of a Shell Oil Company. We’ll lay out the fundamentals of Backtesting, containing:

Step 1: Specify Your Trading Approach

Shell Oil Company Choose a trading approach (trend following, mean reversion, breakout, etc.) and stick to it. Here, we’ll look at a primary trend-following method. Establish when Shell Oil Company is appropriate to enter and leave the plan (Ni & Zhang, 2005). One strategy involves using moving averages (such as the 50-day and 200-day averages) to determine when to enter and quit a trade.

Step 2: Acquiring Data

Collect the oil company’s stock price history. This data is essential to trading volumes and daily/weekly open, high, low, and closing prices (Olorunnimbe & Viktor, 2022). Ensure the data is error-free and covers a long enough time frame to properly test the approach.

Step 3: Establish Limits

The first step is to set the limits of your trading strategy. These settings could include the look-back time of the moving averages and any extra filters or criteria for a system based on them.

Step 4: Formulate the Trading Strategy in Code

Use the available historical data to design the trading strategy in a language such as Python. Run a simulated version of the trading method to provide buy/sell/hold trading signals according to the preset parameters.

Step 5 Consider Slippage and Transaction Fees

Consider how brokerage fees and taxes, for example, will affect the total profitability of the plan. Consider slippage, the deviation between the forecasted and actual price, since Shell Oil Company represents actual trading conditions.

Step 6: Measures of Success

Select useful performance indicators to measure the strategy’s success. Standard measures consist of the cumulative returns that measure the overall percentage gain or loss during the time frame of the backtest.

• Cumulative returns normalized to an annualized rate constitute annualized returns.
• A strategy’s risk-adjusted return may be evaluated using the Sharpe ratio.
• The maximum drawdown is the maximum decrease from the equity curve’s peak to its trough.
• The percentage of successful deals relative to the total number of trades (Suhonen et al., 2017)

Step 7: Testing Beyond the Sample Size

Separate the backtesting data from the out-of-sample data in the historical data. Make adjustments to the strategy and fine-tune its parameters throughout the backtesting phase.

To observe how well the optimized strategy performs on out-of-sample data representing future market circumstances, you should implement it (Alexander, 2000).

Stage 8: Handling Dangers

Use position size and stop-loss orders, two risk management tools, to reduce losses.

Step 9: Analyse and refine

Backtest findings should be analyzed, including metrics and the strategy’s general behavior. Recognize where the approach may be lacking and consider how to strengthen it.

Step 10: practice trading on paper or in a real account

Test the strategy in a simulated or paper trading environment to ensure Shell Oil Company performs as expected before putting Shell Oil Company into action in the actual market.

Step 11: Constantly Checking and Making Changes

Once the plan has been implemented, Shell Oil Company should be tracked continuously to make any necessary adjustments in response to shifting market circumstances or fresh data (Cornelius et al., 2005).Backtesting is not a guarantee of future performance, but Shell Oil Company does reveal how successful a trading strategy for an oil firm was in the past. Before making any major trading choices, you should always proceed with care and even seek advice from financial specialists. (Huang et al., 2021)

(2)    Black Scholes formula to calculate the option premium

Let’s figure out how much the company would have made or lost if Shell Oil Company had bought options to protect itself from changes in the price of oil in the first quarters of 2020, 2021, and 2022. Since we don’t have real-time data, I’ll give you an example based on some theories. (Meisner & Labuszewski, 1984)

Assumptions:

• Each month, 100,000 barrels of oil are at risk because of changes in the price of oil.
• We will look at at-the-money (ATM) call options with two whole-dollar strikes: $55 and $57.
• The daily price information for WTI, one month before the trading day, shows that the price changes by 30% annually. (Chesney & Scott, 1989)

Step 1: Figure out the cost of the option.

 Let’s use the Black-Scholes method to determine the option premium for each ATM call option based on the estimated Volatility, target price, time to expiry (quarterly), and risk-free interest rate. For ease, let’s say the risk-free interest rate is 1%.

Step 2: Figure out how many contracts you need.

• For each strike price, figure out how many call option contracts the company needs to buy to cover its risk of 100,000 barrels per month.
• The size of each option deal is 1,000 barrels.

Step 3: Figure out the cost of hedging.

• Multiply the number of contracts you found in Step 2 by the option premium to get the total cost of hedging for each strike price.

Step 4: Figure out your profit and loss

• At the end of each month in the quarter, compare the average price of oil paid with the strike price of the options used to protect against price changes.
• Figure out each month’s profit or loss based on the difference between the actual price of oil and the strike price, considering the number of contracts.

Let’s pretend that the following statistics about WTI crude oil prices in the first quarters are accurate:

The first three months of 2020, from January to March:

The average price of oil that was sold was $28.34 per barrel

The first three months of 2021, from January to March:

The average price of oil that was sold was $61.45 per barrel

The first three months of 2022, from January to March:

• The average price of oil that was sold was $97.90 per barrel

Now, let’s figure out the numbers:

Step 1: Figure out the cost of the option.

Using the Black-Scholes method, here’s how to figure out the option premium for each strike price:

Excel File is attached separately

Step 2: Figure out how many contracts you need.

• For each strike price, figure out how many call option contracts the company needs to buy to cover its risk of 100,000 barrels per month.

Step 3: Figure out the cost of hedging.

Multiply the number of contracts you found in Step 2 by the option premium to get the total cost of hedging for each strike price.

Step 4: Figure out your profit and loss

For each quarter, figure out the profit or loss by dividing the difference between the average price of oil sold and the strike price by the number of contracts.

Let’s look at the possible outcomes:

First three months of 2020:

• The premium for the strike price of an option is $30: Each barrel costs $1.06
• The premium for the strike price of an option is $33 per barrel at $0.68.

Let’s say the company uses the following number of contracts to cover all of its risks:

• 40 contracts (40,000 barrels) for a strike price of $55.
• 60 contracts (60,000 barrels) for a strike price of $57.

The total cost of the hedge would be:

• For a strike price of $30, 40 contracts times $1.06 equals $42,400
• For a strike price of $33, 60 contracts times $0.68 equals $40,800

Gains and losses:

• The average price of oil that was sold was $50 28.34 per barrel
• Strike Price $30: ($30 – $28.34) * 40,000 barrels equals a profit of $66,400
• For a Strike Price of $33: ($33 – $28.34) * 60,000 barrels equals a profit of $279,600

 Profit as a whole: $346,600

First three months of 2021:

• The premium for the strike price of an option is $64: Each barrel costs $2.67
• The premium for the strike price of an option is $1.73 per barrel at $67.00

Let’s say the company uses the following number of contracts to cover all of its risks:

• 25 contracts (25,000 barrels) for a strike price of $64.
• 35 contracts (35,000 barrels) for a strike price of $67.

The total cost of the hedge would be:

• For a strike price of $64, 25 contracts times $2.67 equals $66,750
• For a strike price of $67, 25 contracts times $1.73 equals $43,250

Gains and losses:

• The average price of oil that was sold was $61.45 per barrel
• Strike Price $64: ($64 – $61.45) * 25,000 barrels equals a profit of $63,750
• For a Strike Price of $67: ($67 – $61.45) * 35,000 barrels equals a profit of $194,250
• Profit as a whole: $258,000

First three months of 2022:

• The premium for the strike price of an option is $100: Each barrel costs $5.03
• The premium for the strike price of an option is $3.88 per barrel at $103.

Let’s say the company uses the following number of contracts to cover all of its risks:

• 15 contracts (15,000 barrels) for a strike price of $100.
• 25 contracts (25,000 barrels) for a strike price of $103.

The total cost of the hedge would be:

• 15 contracts times $5.03 equals $ 75,450 for a strike price of $100.
• For a strike price of $3.88, 25 futures times $3.88 equals $97,000

Gains and losses:

• The average price of oil that was sold was $97.90 per barrel
• Strike Price $100: ($100 – $97.90 * 25,000 barrels equals a profit of $52,500
• For a Strike Price of $103: ($103 – $97.90) * 35,000 barrels equals a profit of $178,500
• Profit as a whole: $231,000

( c )-  Assuming the oil price is log-normally distributed.

To figure out the company’s profit and loss (P/L) for September, October, and November of 2021, we need to know more about the company’s oil market situation. We need to know, in particular, if they have bought or sold oil futures and options contracts and how many of each they have. Assuming that the company has these positions:

• Futures contracts for September 2021 were bought for $75.03.
• Futures contracts for October 2021 were purchased for $83.57 each.
• Futures contracts for November 2021 were sold for $66.18 each.
• Contracts for options for September 2021 were purchased for $77.50.
• Options contracts for October 2021 were purchased for $85.05 each.
• Contracts for options for November 2021 were sold for $67.85.

We also need to know the oil’s monthly payment price. Let’s say the following are the final prices:

$80 in September 2021

$78 in October 2021

$70 in November 2021

Now, let’s figure out how much money we made and lost each month:

In September 2021:

Settlement price minus Futures price.= $80.00 – $75.03 = 4.97 dollars per barrel

Settlement price – Options price = Options P/L.= $80.00 – $77.50 = 2.50 dollars per barrel

Profit and loss for September 2021:

= (Futures Profit/Loss + Options Profit/Loss) * Number of contracts

= ($4.97 + $2.50) * 30,000 = $74,100

In October 2021:

Settlement price minus Futures price. = $78.00 – $83.57 = -5.57 dollars a barrel

Settlement price – Options price = Options P/L. = $78.00 – $85.05 = -7.05 dollars a barrel

For October 2021, the total P/L is:

= (Futures Profit/Loss + Options Profit/Loss) * Number of contracts

= (-$5.57 – $7.05) * 30,000= – $378,600

In November 2021:

Futures P/L: Futures price minus Settlement price

= $66.18 – $70.00

= -3.82 dollars a barrel.

Options P/L = Option price – Settlement price

= $67.85 – $70.00

= -2.15 dollars a barrel

For November 2021, the total P/L is:

= (Futures Profit/Loss + Options Profit/Loss) * Number of contracts

= (-$3.82 – $2.15) * 30,000= -$179,100

(d)- Calculate the P/L of the hedged position if the oil price is realized at P05, P16, P50, P84, and P95 of the distribution

To determine the P/L (Profit/Loss) of the hedged position, we’ll need to look at the different possibilities based on the chance distribution of the oil price and the rates for September, October, and November 2021. Let’s go through each step:

Step 1: Figure out the profit and loss for each case.

The oil price has the following chance distribution:

• P 5%, Oil Price: $5
• P 16%, Oil Price: $16
• P 50%, Oil Price: $50
• P 84%, Oil Price: $84
• P 95%, Oil Price: $95

Now, let’s figure out the P/L for each situation based on each month’s future rates and options rates:

In September 2021:

• The rate in the future: $75.03
• The rate for the call option: $77.50
• The rate for a put option: $67.85

In October 2021:

• $83.57 in the future
• The rate for a call option: $85.05
• The rate for a put option: $67.85

In November of 2021:

• $66.18 per month.
• The rate for a call option: $85.05
• The rate for a put option: $67.85

Step 2: Use hedges to figure out P/L for each situation.

We’ll figure out the P/L for each chance situation for both call option hedging and put option hedging.

Hedging a Call Option:

Call Option P/L = Maximum (Oil Rate – Call Option Rate, 0)

Future Rate – Call Option Rate + Call Option P/L = Hedged P/L

Hedging a Put Option:

Put Option P/L = Maximum (Put Option Rate – Oil Rate, 0)

Hedged P/L = Future Rate plus Put Option Rate minus Put Option P/L

Step 3: Figure out the average weighted P/L

Lastly, we’ll figure out the weighted average P/L for each situation, considering how likely each one is.

Let’s figure out these numbers for each case:

• If the chance is 5%:

Call Option P/L: Max(5, -77.50, 0) = 0 (Since the Call Option is not used, the P/L is 0)

Put Option Payoff: Max(67.85 – 5, 0) = 62.85

Weighted P/L = 5% x (66.18 + 67.85 – 62.85) = 5% x (71.18) = 3.559

• If the chance is 16%:

Call Option Payoff: Max(16 – 85.05, 0) = 0

Put Option P/L: Maximum (67.85 – 16.0) = 51.85

Weighted P/L = 16% x (83.57 + 67.85 – 51.85) = 16% x (99.57) = 15.9312

• If the chance is 50%:

Call Option Payoff: Max(50 – 85.05, 0) = 0

Put Option Payoff: Max(67.85 – 50, 0) = 17.85

Weighted P/L = 50% x (66.18 + 67.85 – 17.85) = 50% x (116.18 – 116.18) = 58.09

• If the chance is 84%:

Call Option Payoff: Max(84 – 85.05, 0) = 0

Put Option P/L: Max(67.85 – 84, 0) = 0 (Since the Put Option is not used, the P/L is 0)

Weighted P/L = 84% x (83.57 + 67.85) = 84% x 151.42 = 127.2288

If the chance is 95%:

Call Option Payoff: Max(95 – 85.05, 0) = 9.95

Put Option P/L: Maximum(67.85 – 95, 0) = 0

Weighted P/L = 95% x (75.03 – 85.05 + 9.95) = 95% x -0.07 = -0.0665

Step 4: Figure out the total P/L:

Overall P/L = the sum of all the weighted P/L numbers

Overall P/L = 3.559 + 15.9312 + 58.09 + 127.2288 – 0.0665 = 204.7425

Considering the given chance distribution and rates, the total P/L of the hedged stake is about $204.74.

Step 5: Making sense of the results

The total P/L of an investment covered is about $204.74. This means that, based on the chance distribution of oil prices and the trading approach that uses call-and-put options, the trade is projected to make a profit of about $204.74.

Using call options to protect against oil prices going up above the strike price of the call option and putting options to protect against oil prices going down below the strike price of the set option was the hedging method. The goal of the approach is to limit possible losses while leaving room for potential gains as long as oil prices stay within a specific range.

How to figure out what each probability scenario means:

If the chance is 5%:

In this situation, the weighted P/L of the hedged stake was about $3.56. The put option was used, and a $62.85 gain was made to compensate for the future rate loss.

If the chance is 16%:

In this case, the hedged trade led to a weighted profit/loss of about $15.93. In a situation similar to the last one, the put option was used, which gave a gain of $51.85 to make up for the loss in the future rate.

If the chance is 50%:

The weighted P/L for this situation was about $58.09. The put option was used, and a $17.85 profit was made to make up for the loss in the future rate.

If the chance is 84%:

In this situation, the weighted P/L of the hedged investment was about $127.23. Since neither the buy or put option was used, the benefit was equal to the sum of the future rates for October and November 2021.

If the chance is 95%:

Last, the overall weighted P/L in this situation was about -$0.07. A slight loss of $0.0665 was made when the call option was used.

Step 6: Managing risks and thinking about what to do next

This study’s hedging approach helped reduce possible losses and gave an excellent total P/L. But it’s important to remember that all purchases come with risks, and the natural movement of oil prices may differ from what was predicted.

When using hedging tactics, keeping an eye on the market, changing stocks if needed, and reevaluating your risk tolerance and financial goals are essential. Also, it’s important to consider when the choices will expire because their prices can change significantly over time.

Conclusion:

Backtesting, the Black-Scholes method, hedging techniques, and oil options are all related to financial markets, notably risk management and oil trading choices. Oil market risk management requires hedging methods like oil options. Hedging protects against price fluctuations by offsetting holdings. Oil traders and organizations utilize options contracts to hedge oil price swings. The Black-Scholes model calculates the fair value of these options depending on market parameters such as underlying asset price, Volatility, and time to expiry. Traders and corporations may assess their hedging strategies’ strengths and flaws through Backtesting. Backtesting helps refine and optimize hedging methods for better future judgments. Oil option pricing and valuation use the Black-Scholes formula. It lets traders and investors determine these options’ fair market value using market characteristics. Market players may use the Black-Scholes method to evaluate whether an oil option is overvalued or underpriced, which is essential for trading choices. The technique also helps traders predict market moves by analyzing Implied Volatility. Options let traders predict oil prices without buying the commodity. Oil options may lock in future costs and shield hedgers from price fluctuations. Hedging methods and oil options allow market players to manage risk and position themselves in the oil market. Backtesting, the Black-Scholes algorithm, hedging methods, and oil options help oil traders manage risk and make educated trading choices. They help market players understand the energy market and hedge against price volatility.

References

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