# 🧮 JP Morgan Quantitative Research – Task 2

Price a Commodity Storage Contract

This repository contains my solution for Task 2 of the J.P. Morgan Quantitative Research Virtual Job Experience on Forage.
The objective is to develop a valuation tool that prices a physical commodity storage contract based on forecasted commodity prices.

This exercise demonstrates quantitative modeling, event-driven simulation, and financial engineering techniques commonly used in energy markets and commodities trading.

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📘 Abstract

Commodity storage contracts are widely used by energy traders to capture seasonal price spreads — buying natural gas when prices are low (summer) and selling it when prices are high (winter).

This project builds a simulation-based valuation model that calculates the Net Present Value (NPV) of a storage strategy while respecting real-world operational and physical constraints such as:

• Injection and withdrawal rate limits
• Maximum storage capacity
• Daily/monthly storage and transaction costs

The result is a transparent event-driven simulation that produces both the final valuation and a detailed transaction log, allowing traders and analysts to audit every cash flow.

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📊 Problem Statement

The client’s goal is to execute a seasonal arbitrage strategy using natural gas storage.
We must determine whether the proposed trading schedule is profitable, and by how much.

The model must:

1. Take all contract parameters as inputs (dates, volumes, costs).
2. Calculate cash flows associated with purchases, sales, and costs.
3. Enforce capacity and rate constraints.
4. Output the Net Present Value (NPV) and detailed event log.

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🧠 Quantitative Framework

1. Cash Flow Definition

For any time step t, the incremental cash flow is: [ CF_t = Q_t (P_t^{sell} - P_t^{buy}) - C_{storage,t} - C_{trans,t} - C_{oper,t} ]

Where:

• ( Q_t ): quantity injected or withdrawn at time t
• ( P_t^{buy}, P_t^{sell} ): forecasted buy/sell price at time t
• ( C_{storage,t} ): storage cost for inventory
• ( C_{trans,t}, C_{oper,t} ): transport and operational costs

The Net Present Value (NPV) is the discounted sum: [ NPV = \sum_{t=1}^{T} \frac{CF_t}{(1+r)^{t/365}} ] where ( r ) is the annual discount rate (can be set to 0 for simplicity).

2. Arbitrage Intuition

If the forward curve exhibits a seasonal spread, such that: [ \Delta P = P_{winter} - P_{summer} > 0 ] then storing volume ( Q ) yields an arbitrage gain: [ Profit = Q (\Delta P - C_{storage} - C_{trans}) ]

The simulation quantifies this gain dynamically, handling non-linear constraints and real-world costs.

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🧮 Model Design

Simulation Architecture

1. Input Layer

   • Takes forecasted price data (price_data) and schedule inputs.
   • Validates all date mappings and price availability.

2. Event Processing Layer

   • Iterates through all injection and withdrawal events chronologically.
   • For each event, it:
     • Reads the price on that date
     • Computes transaction cost or revenue
     • Applies storage cost since last event
     • Updates cumulative cash_flow and inventory

3. Output Layer

   • Returns final cash_flow and a detailed pandas DataFrame log of all events.
   • Each log entry includes date, price, action type, volume, and resulting balance.

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🧰 Function Description

price_storage_contract()

def price_storage_contract(
    injection_dates,
    withdrawal_dates,
    price_data,
    injection_rate,
    withdrawal_rate,
    max_storage,
    storage_cost_per_month,
    injection_cost,
    withdrawal_cost,
    transport_cost
)