Price a Commodity Storage Contract

The concept is simple: any trade agreement is as valuable as the price you can sell minus the price at which you are able to buy. Any cost incurred as part of executing this agreement is also deducted from the overall value. So, for example, if I can purchase a million MMBtu of natural gas in summer at $2/MMBtu, store this for four months, and ensure that I can sell the same quantity at $3/MMBtu without incurring any additional costs, the value of this contract would be ($3-$2) *1e6 = $1million.

If there are costs involved, such as having to pay the storage facility owner a fixed fee of $100K a month, then the 'value' of the contract, from my perspective, would drop by the overall rental amount to $600K. Another cost could be the injection/withdrawal cost, like having to pay the storage facility owner $10K per 1 million MMBtu for injection/withdrawal, then the price will further go down by $10K to $590K. Additionally, if I am supposed to foot a bill of $50K each time for transporting the gas to and from the facility, the cost of this contract would fall by another $100K. Think of the valuation as a fair estimate at which both the trading desk and the client would be happy to enter into the contract. 

 We will be creating a prototype pricing model that can go through further validation and testing before being put into production. Eventually, this model may be the basis for fully automated quoting to clients, but for now, the desk will use it with manual oversight to explore options with the client. 

To do this it would be ideal that the function is able to use the data created in previous project (Investigating and Analyzing Natural Gas Data) to price the contract. The client may want to choose multiple dates to inject and withdraw a set amount of gas, so the approach should generalize the explanation from before.

To do this it is of the highest importance to consider all the cash flows involved in the product.

The input parameters that should be taken into account for pricing are:

1. Injection dates. 

2. Withdrawal dates.

3. The prices at which the commodity can be purchased/sold on those dates.

4. The rate at which the gas can be injected/withdrawn.

5. The maximum volume that can be stored.

6. Storage costs.

We will write a function that takes these inputs and gives back the value of the contract. We can assume there is no transport delay and that interest rates are zero. Market holidays, weekends, and bank holidays need not be accounted for. We will test the code by selecting a few sample inputs.

First we will import the necessary toolset to accomplish this task!

from datetime import date
import math

def price_contract(in_dates, in_prices, out_dates, out_prices, rate, storage_cost_rate, total_vol, injection_withdrawal_cost_rate):
    volume = 0
    buy_cost = 0
    cash_in = 0
    last_date = min(min(in_dates), min(out_dates))

Ensure dates are in sequqence, processing code for each date is accurate, and Injection dates are correct, and then sum up cash flows!

all_dates = sorted(set(in_dates + out_dates))
    
    for i in range(len(all_dates)):
        # processing code for each date
        start_date = all_dates[i]

        if start_date in in_dates:
            # Inject on these dates and sum up cash flows
            if volume <= total_vol - rate:
                volume += rate

                # Cost to purchase gas
                buy_cost += rate * in_prices[in_dates.index(start_date)]
                # Injection cost
                injection_cost = rate * injection_withdrawal_cost_rate
                buy_cost += injection_cost
                print('Injected gas on %s at a price of %s'%(start_date, in_prices[in_dates.index(start_date)]))

            else:
                # We do not want to inject when rate is greater than total volume minus volume
                print('Injection is not possible on date %s as there is insufficient space in the storage facility'%start_date)
        elif start_date in out_dates:
            # Withdraw on these dates and sum cash flows
            if volume >= rate:
                volume -= rate
                cash_in += rate * out_prices[out_dates.index(start_date)]
                # Withdrawal cost
                withdrawal_cost = rate * injection_withdrawal_cost_rate
                cash_in -= withdrawal_cost
                print('Extracted gas on %s at a price of %s'%(start_date, out_prices[out_dates.index(start_date)]))
            else:
                # we cannot withdraw more gas than is actually stored
                print('Extraction is not possible on date %s as there is insufficient volume of gas stored'%start_date)
                
    store_cost = math.ceil((max(out_dates) - min(in_dates)).days // 30) * storage_cost_rate
    return cash_in - store_cost - buy_cost

Example usage of Price_contract() is as follows

in_dates = [date(2022, 1, 1), date(2022, 2, 1), date(2022, 2, 21), date(2022, 4, 1)] #injection dates
in_prices = [20, 21, 20.5, 22]# prices on the injection days
out_dates = [date(2022, 1, 27), date(2022, 2, 15), date(2022, 3, 20), date(2022, 6, 1)] # extraction dates
out_prices = [23, 19, 21, 25] # prices on the extraction days
rate = 100000  # rate of gas in cubic feet per day
storage_cost_rate = 10000  # total volume in cubic feet
injection_withdrawal_cost_rate = 0.0005  # $/cf
max_storage_volume = 500000 # maximum storage capacity of the storage facility
result = price_contract(in_dates, in_prices, out_dates, out_prices, rate, storage_cost_rate, max_storage_volume, injection_withdrawal_cost_rate)
print()
print(f"The value of the contract is: ${result}")

Output:()

Injected gas on 2022-01-01 at a price of 20

Extracted gas on 2022-01-27 at a price of 23

Injected gas on 2022-02-01 at a price of 21

Extracted gas on 2022-02-15 at a price of 19

Injected gas on 2022-02-21 at a price of 20.5

Extracted gas on 2022-03-20 at a price of 21

Injected gas on 2022-04-01 at a price of 22

Extracted gas on 2022-06-01 at a price of 25 T

The value of the contract is: $399600.0

## Explaining the Methodology Adopted for this Task ##

# The given Python code implements a function `price_contract` that calculates the profit or loss obtained by

# undertaking trades on given dates for a contract involving the buying, storing, and selling of natural gas the

# storage cost of the gas, the injection/withdrawal. The value of the contract is the profit or loss obtained by

# undertaking the trades on given dates. Play around with the parameters and you'll be able to see this.

# In the end the intent for this function returns the value of the contract.

#The function takes in eight inputs:

#- `in_dates`: A list of dates on which the gas is being injected into the storage facility.

#- `in_prices`: A list of prices of gas on each of the injection dates.

#- `out_dates`: A list of dates on which the gas is being withdrawn from the storage facility.

#- `out_prices`: A list of prices of gas on each of the withdrawal dates.

#- `rate`: The rate of gas in cubic feet per day.

#- `storage_cost_rate`: A fixed monthly fee to store the gas

#- `total_vol`: The total volume of gas in cubic feet that can be stored.

#- `injection_withdrawal_cost_rate`: The injection/withdrawal cost of gas in dollars per cubic foot.

# The function first ensures that all the dates are in sequence and sorted in ascending order. Then, it iterates

#over all the dates and calculates the cash flows on each date. If the current date is an injection date, it

#injects gas into the storage facility and calculates the cost to store the gas, the cost to purchase the gas,

#and the injection cost. If the current date is a withdrawal date, it withdraws gas from the storage facility and

#calculates the cash inflow from selling the gas, the cost to store the remaining gas, and the withdrawal cost.

# Finally, the function returns the net profit or loss by subtracting the storage cost and the cost to purchase

#the gas from the cash inflow from selling the gas.

# The example usage of the `price_contract` function calculates the profit or loss for a contract that involves

#injecting gas on four different dates and withdrawing gas on four different dates, each with a different price.

#The other inputs such as the rate of gas, the storage cost rate, the total volume, and the injection/withdrawal

#cost rate are also provided. The output is printed to the console using an f-string.