
Explore forwards in the derivatives market, including over-the-counter trading, forward pricing, and hedging foreign exchange risk with customized, nonstandardized contracts.
Explore forward contracts, futures, and options, and how hedgers, speculators, and arbitrageurs use pricing and hedging strategies. Understand American vs European styles, strike prices, expiration, and counterparty risk.
Explore how forwards and futures hedge against price movements with long and short payoffs. See payoff examples and hedging concepts using rice, gold, and dollars.
analyze how forward hedging converts euro payments to dollars using a 1.24 forward rate, compare hedged and unhedged outcomes at different spot rates, and discuss derivatives risk, arbitrage strategies.
Examine how forwards relate to interest rates and bond pricing, and learn to derive spot and forward rates via bootstrapping, including discrete and continuous compounding.
Compute the effective annual rate from continuous compounding and demonstrate it with an 8.5% rate on a $5,000 balance after eight years.
Present values of a coupon bond arise by discounting each cash flow with spot rates, treating it as a series of zero coupon bonds under continuous compounding.
Master bootstrapping to construct the spot curve by treating Treasury bonds as zero coupon components, deriving six-month and one-year spot rates with continuous compounding.
Derive forward rates from the spot curve using bootstrapping and apply them to pricing and hedging forward rate agreements, with concrete calculations and the spot curve–forward curve relationship.
Derive forward rate agreement payoff formulas for continuous and quarterly compounding, applying them to fixed-for-floating payments and example calculations.
Explore durations and convexity to improve bond price estimates as yields move, and apply forward rates and term-structure theories to pricing, hedging, and arbitrage in interest rate markets.
Determine forward prices using the cost of carrying, linking storage costs to consuming assets, and note that forwards are private and customized while futures are exchange-traded with delivery options.
Learn how forward prices arise from the spot price using continuous compounding at the risk-free rate. Use this relationship to spot arbitrage opportunities when forward diverges from cost of borrowing.
Compute forward prices with no interim cash flows by discounting known cash flows and adjusting the spot price for the cost of carry.
Compute the six-month stock index forward price using a 1.5% dividend yield and 4.5% rate (1025.26), and show the long forward value after inception as S0 e^{-qT} - K e^{-rT}.
Explore forward pricing and no-arbitrage, comparing forwards with futures and applying carry-cost and dividend adjustments to price assets and bonds.
Learn to price a 120-day forward with a short stock position using dividend discounting and the cost of carry, and compare forward contracts to futures.
Learn how commodity forwards price from expected spot prices and carrying costs. Understand the forward curve and synthetic forwards built from a long forward and a zero-coupon bond.
Learn how forward prices reflect the present value of expected spot prices under a risk-free rate, including a risk premium bias. Explore cash-and-carry arbitrage and electricity’s non-storability.
Explore cash-and-carry arbitrage by exploiting overpriced gold futures: buy spot gold at $900, borrow at 7%, short the futures at $975, and lock in a risk-free $10 profit.
Explains reverse cash-and-carry arbitrage when futures are underpriced, using gold with spot $900 and one-year futures $950, and locks in a $15 riskless profit with long futures and short gold.
Lease rates adjust commodity forward prices by subtracting the lease rate from the risk-free rate, like dividends, enabling no-arbitrage pricing in forward contracts.
Explain forward pricing with lease and risk-free rates using a soybeans arbitrage example, and define contango and backwardation by comparing lease rates to the risk-free rate.
Explore how storage costs push forward prices above spot prices in commodity forwards, through carry markets and cash-and-carry strategies, including continuous compounding and convenience yield.
Explore how forward prices relate to spot prices, storage costs, and convenience yields within a continuous-compounding framework. Learn no-arbitrage cash-and-carry bounds and how lease rates alter forward pricing.
Explore how commodity characteristics shape forward pricing, including storage costs, lease rates, and convenience yields, with examples from gold, corn, natural gas, and oil.
Understand crack spreads from crude oil to gasoline and heating oil, and apply strip or stack hedges, while analyzing forward price, basis risk, and contango.
Examine foreign exchange risk from globalization and currency mismatches, and learn hedging with forward contracts, managing net exposure, and the four trading activities banks use in foreign exchange.
Explore foreign exchange risk through a CHF/USD one-year case, calculating spot-rate impacts, portfolio weighted returns, alpha gains, and how currency movements affect bank margins and arbitrage strategies.
Balance sheet hedging aligns USD and CHF assets and liabilities by matching currency and maturity, then evaluates borrowings, conversions, and net returns under exchange rate movements.
Explore off balance sheet hedging using forward contracts to lock in future exchange rates, convert risk into a contingent balance sheet item, and secure a known return.
Explore interest rate parity in foreign exchange risk by linking forward and spot rates to domestic and foreign rates to prevent arbitrage. Use direct quotes and examples like NZD/CHF.
Explore how interest rate parity and forward contracts enable hedging and arbitrage across multi-currency asset-liability portfolios, using real rates, inflation expectations, and diversification to manage currency risk.
Introduction:
This course is designed to provide an in-depth exploration of forward contracts and their role in the financial markets. Forward contracts are vital tools used in hedging and managing risk across various assets, including commodities, interest rates, and foreign exchange. Students will learn about the pricing, computation, and practical applications of forwards in managing financial risks. The course also covers advanced topics such as the relationship between forwards and interest rates, market compounding, forward rate agreements (FRA), and foreign exchange risks.
Section 1: Introduction to Forwards
In this section, students will be introduced to the concept of forward contracts and their place in the world of derivatives. The lectures cover the basics of forwards, their usage, and the structural differences that set them apart from other financial instruments. By the end of this section, learners will have a clear understanding of what forward contracts are, how they are created, and their role in hedging and risk management strategies.
Section 2: Relationship Between Forwards and Interest Rates
This section delves into the intricate connection between forward contracts and interest rates. Beginning with payoff profiles of forward contracts, learners will be introduced to key concepts such as compounding, spot rates, bond pricing, and bootstrapping. Through practical examples, the course illustrates how forward rate agreements work and how they are influenced by duration and convexity. This section equips students with the knowledge to analyze forward contracts in the context of interest rate movements and market conditions.
Section 3: Determination of Forward Price
Here, students will explore the methods used to determine the price of forward contracts. The section discusses pricing scenarios with and without interim cash flows, as well as special cases like stock index forwards. Through detailed explanations and real-world examples, learners will gain a deep understanding of how forward prices are set and the factors that influence them, preparing them for practical applications in financial markets.
Section 4: Computation of Forwards
In this section, the computation of forward contracts is explored in greater detail, particularly with a focus on commodities. Students will learn about cash-and-carry arbitrage, lease rates, and storage costs, which are vital components when pricing commodity forwards. Various scenarios, such as overpriced or underpriced futures, are discussed, showing learners how to identify and exploit arbitrage opportunities. This section provides practical insights into how forwards work in commodity markets and how to compute their fair value.
Section 5: Foreign Exchange Risk and Computation of Forwards
The final section focuses on foreign exchange (FX) risk management using forward contracts. Students will learn about FX risk, on-balance-sheet and off-balance-sheet hedging techniques, and the principle of interest rate parity. Practical examples of FX forward contracts and their use in hedging foreign exchange exposure are provided. By the end of this section, learners will understand how to compute and apply forwards in managing FX risk, ensuring better risk management strategies in international finance.
Conclusion:
Upon completing this course, students will have mastered the fundamental and advanced concepts of forward contracts, their pricing, and computation. They will have gained practical skills in managing interest rate, commodity, and foreign exchange risks using forward derivatives. This course is essential for professionals in finance looking to deepen their understanding of forward contracts and their role in modern financial markets.