We are now entering the world of derivatives. Derivatives are contracts whose value depends on the value of other securities, commodities, rates, or even derivatives themselves; hence their name. They are nowadays traded as highly sophisticated risk transfer instruments in organized markets like the Chicago Board Options Exchange (CBOE) or in secondary over the counter markets (OTC). Valuation of derivatives is at the heart of quantitative finance, and can sometimes be a very challenging task. This chapter is only a gentle warm-up for the techniques to be discussed in the sequel.

Forward and Future Contracts

Forwards and futures are contracts, which enable an agent to lock in a future price for an arbitrary underlying today. An underlying can be a security, a commodity, an exchange rate, or in principle everything that can be traded. The difference between forward and future contracts is the way they are traded and settled. Forwards are individually “over the counter” (OTC) brokered contracts. Settlement is at expiry or shortly after, usually but not necessarily in cash. A future is a standardized contract that is traded in an organized market. Both sides of the future can be contracted independently with a clearing house as counterparty. To reduce the default risk for the clearing house, the agent has to provide collateral and to agree to daily settlement payments via a margin account. By this procedure, the value of an open contract is reset every day. In a world where the risk-free interest rate is either constant, or a deterministic function of time, forward and future prices have to coincide. In reality, where interest rates themselves are stochastic, both prices diverge because of the different settlement policies. Until further notice, we will assume that the risk-free interest rate is deterministic.

Why would anyone enter into a forward or future contract at all? Let's look at the following example.

Example 11.1

Assume A is a large food retail chain, say in Germany, and B is an agricultural producer in Spain. A would like to buy 50 tons of tomatoes from B next year. B is willing to sell the requested quantity to A, but both operate under a fair amount of risk and effort. The underlying commodity, the 50 tons of tomatoes, does not even exist today.

Proper design and analysis of the elements of a structure, machine or installation is critical to its rigidity, safety, cost and reliability. With methods and materials of fabrication, construction and manufacturing changing rapidly, a lot of attention to design and analysis is required so that the system is robust yet cost effective. Further, ‘principles of mechanics’ is a foundation subject and its importance to several engineering disciplines cannot be overemphasized. A sound understanding of this subject is extremely useful during the analysis of complex problems in core engineering subjects. The subject deals with a variety of materials, in different geometries and loading configurations subjected to various types of loads. During this course, the learner needs to be presented cases similar to those encountered in real engineering problem-situations. This helps the student develop faculties to choose the right approach to analyze problems, situations and arrive at a correct solution.

Due to the importance of engineering mechanics and its applications in many engineering disciplines, it is a part of common engineering curricula. The contents of this volume have been developed to match the syllabi of major universities. This treatise is organized to provide the basic concepts in the initial chapters; advancing to subsequent application of these concepts to a variety of situations encountered in engineering problem solving. The architecture of the volume makes it a self-sufficient introduction to the subject. The book begins with an introduction to basic building blocks of this subject, such as units, system of units of force and force systems. Representation, interaction and concatenation of forces in the Cartesian space are also dealt with. Concept of planar forces is developed through concurrent and non-concurrent forces in chapters 2 and 3. These chapters demonstrate articulation of forces and force systems to resolve forces, to work out resultants, and equilibrium conditions through free body diagrams. The concept and articulation of moments and couples is developed through forces and force systems. Forces and moments are further related to real applications by introducing beams and loading of beams.

Apart from applied and incident forces as dealt with in the beginning, friction and related aspects are introduced in chapters 4 and 5. Forces induced due to friction, their estimation and articulation is presented in these chapters.