# Futures options and swaps book

Spot markets allow the purchase and sale of an asset today. By contrast a forward contract specifies the price at which an asset can be purchased or sold at some future date. Although a futures options and swaps book contract is classified as a derivative in many markets it is difficult to distinguish between the underlying and the forward contract. Large trading volumes in OTC forwards can in fact make them more significant than spot markets. A forward contract does not require upfront payment.

It is simply the purchase or sale of an asset at some future date at a fixed price the forward futures options and swaps book. Therefore the assumption is that the forward price reflects the value of this asset on this date. If this assumption is based on a market view, characterising a forward contract as a derivative is misleading.

The primary reason for the classification of a forward contract as a derivative is that in many cases its price can be derived through a no-arbitrage argument that relates the forward price of an asset to its spot price. For assets like oil this is not possible; given the spot price of a barrel of oil it is not possible to construct an arbitrage argument that relates it to the forward price.

In the oil markets forwards or futures are effectively the underlying and cannot be understood as derivatives. In these markets the forward price of oil is similar in nature to the price of a stock: In financial futures options and swaps book forwards can be determined through a no-arbitrage argument. If today one euro can be exchanged for 1. In the absence of arbitrage opportunities the net cashflow of this trade should be zero and therefore.

Another example is a forward contract on a zero coupon one year bondone year from now. Therefore the net cashflow in one year is. Futures contracts, like forward contracts, specify the delivery of an asset at some future date. Futures contracts, unlike forward contracts. There three requirements in practice are not unique to futures contracts. The best way to understand them is by looking at a specific futures contract. The specifications of the contract are very strict and require the delivery of "no.

The contract size can be in multiples of 5, bushels of corn. Futures can be purchased for delivery of corn in months December, March, May, July and September only. Trading this contract ceases on the business day nearest to the 15th calendar date of the delivery month. Delivery takes place two business days after the 15th calendar date of the delivery month.

If the buyer does not post this amount of money in her account with the exchange, her order cannot be executed. For this contract the maintenance margin is the same; during the life of this futures contract the balance of the account cannot go below this level; if for any reason the balance of the account falls below the maintenance margin, the buyer of this contract will receive a margin call.

On the date on which the trade was executed the mark-to-market of the futures contract is zero. The mark-to-market of the Jul corn futures is. The account is like a normal deposit account and earns interest on its balance. The clearing house acts as counterparty in the transaction between the corn producer and the buyer and makes sure payments are made and corn is delivered to the warehouse nominated by the buyer.

This set of equations can be solved recursively. Therefore the forward price must be equal to the futures price. Since in practise the actual value of the interest rate is not known assume that we can lock in a forward rate. We conclude that when the futures contract is a function of the interest rate the futures price will not be equal to the forward price.

Another exception occurs when the futures price can change by large amounts from one date to the next. In this case on the date when this large price change occurs the error in the notional locked in at the forward rate is large enough to magnify the error in our estimate of the change in the mark-to-market.

Fortunately, most exchanges limit the maximum change in the futures price that can occur from one date to the next. But if such large price moves are possible then, even if the futures price is not a function of the interest rate, the assumption that it is equal to the forward price is wrong. In general, the relation between the futures and the forward price cannot be derived through a futures options and swaps book arbitarge strategy unless interest rates have a futures options and swaps book term-structure.

The derivation of the relation between the futures and the futures options and swaps book price of an asset is one of the first applications of dynamic hedging [Black ]. A Swap is an agreement to exchange a sequence of cash futures options and swaps book over a period of time in the future in same or different currencies. Mainly used for hedging various interest rate exposures, they are very popular and highly liquid instruments.

Some of the very popular swap types are. For example, you pay fixed 5. For example, if a company has a fixed rate USD 10 mio loan at 5. Note in this case no initial Exchange of notional takes place unless the Fx fixing date and the swap start date fall in the future. In this case, company wants to lockin the cost from the spread widening or narrowing. At the moment, this company has a net profir of 40 bps. To explain the use of this type of swap, consider a US company operating in Japan.

To fund their Japanese growth, they need JPY 10 bio. As futures options and swaps book company might be new in the Japanese market with out a well known reputation among the Japanese investors, this can be an expensive option. Added on top of this, the company might not have appropriate Debt issuance program in Japan and they might lack sophesticated treasury operation in Japan.

Although this option solves the first problem, it introduces two new risks to the company. If the JPY rates come down, the return on the investment in Japan might go down and this introduces a interest rate risk component.

First exposure in the above can be hedged using long dated FX forward contracts but this introduces futures options and swaps book new risk where the implied rate from the Fx Spot and the Fx Frward is futures options and swaps book fixed rate but the JPY invest ment returns a floating rate. Although futures options and swaps book are several alternatives to hedge both the exposures effectively with out introducing new risks, the easiest and the most cost effective alternative would be to use a Float-Float swap in different currencies.

For example, you pay JPY 1. Primarily used as hedging instruments, against varying interest payments. The base concept is quite easy to follow; futures options and swaps book swap a fixed rate for a floating rate or vice-versa. In essence, the company has hedged it's risk against a sudden rate increase, as it is locked in a fixed rate over time.

Swaps may be terminated with one party paying it's counterpart a certain fee, which may have been determined at time of initial agreement or may be based on future payments if interest rates were to remain constant.

An option is a financial instrument that gives the holder to purchase or sale the stated number of shares at pre determined price exercise price within or on certain future date. It can be defined as a contract between two investors i. Each option comes with an "Exercise Date". European options may only be futures options and swaps book on the exercise date, whereas American options may be exercised at any time up till the exercise date.

Due to the put-call parity, it is possible to create artificial call or put options if the other is not available. Put options may also be used as a hedging instrument, against possible decline in value of the underlying stock.

While stocks with high volatility modified duration are high risk, options whose underlying stock futures options and swaps book high volatility are actually better. They provide a possibility of a higher payout if the stock goes up in proportion to its volatility and the same amount of loss.

In this case, the underlying asset on which the option is written is a forward contract. A market exists in which forward contracts are traded. We do not impose the martingale property on the s. Lets price this option blindly the actuarial approach. This approach requires that the price of the option is given by taking the expectation of its payoff under the 'true' distribution of the forward price.

The expectation has the following simple solution. In the same way the price of a put is given by. This transparent approach, first proposed by Emanuel Derman and Nassim Taleb [2]generates the arbitrage-free option price without the need for unrealistic assumptions about the viability of dynamic hedging.

The only assumption we made was regarding the 'true' probability distribution function of the forward price. The growth of the financial sector has resulted in products which are covered under the broad term "exotic derivatives".

These derivatives are often written on indices which are derived from traded prices but which themselves are not traded. Depending on investor preferences an index **futures options and swaps book** be a function of more than one asset prices and can be determined from the value of these asset prices from a single or a series of observations. Exotic derivatives can either be priced using analytic methods or numerical techniques. The framework used to price all exotic derivatives is based on the Black-Scholes option pricing theory, in which dynamic hedging is used to obtain an arbitrage-free equation for the option price.

Although we can always obtain a p. However, there exists a large range of exotics where an analytic solution is possible. An option on the product of two asset prices has an analytic solution. Therefore the last equation gives rise to the following p.

Theoretically, the price of an option or option premium consists of two elements: The price of an option consists of five things: Since the first four can be read from the markets, the only unknown factor in the price of the option futures options and swaps book volatility. From Wikibooks, open books for an open world. Retrieved from futures options and swaps book https: Views Read Edit View history.

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Dispatched from the UK in 2 business days When will my order arrive? Home Futures options and swaps book Us Help Free delivery worldwide. Futures, Options, and Swaps. Description A new and updated edition of the most readable, comprehensive text available on derivatives markets. Utilizes an even more applied approach than previous editions Provides an excellent balance between introductory and advanced topics Extensively updated to incorporate and explicate development in the field including the areas of electronic trading platforms, globalization of markets, hedge funds, financial scandals involving derivatives, and government regulation Revised to include over 50 text boxes with applied vignettes on topical issues, product profiles, and historical anecdotes futures options and swaps book more.

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Back cover copy Written in an accessible, non-technical style, Futures options and swaps book, Options, and Swaps is the most comprehensive text on derivatives markets available. As the only book to utilize such a reader-friendly, instructive approach, students will find the material readily futures options and swaps book without a professor's guidance, thereby freeing instructors to cover only the vital topics, or to teach futures options and swaps book more technical course.

This fifth edition has been extensively revised to address the most recent developments in this rapidly evolving field. New and updated information reflects current conditions in a variety of areas, including electronic trading platforms, **futures options and swaps book** of markets, hedge funds, financial scandals involving derivatives, and government regulation.

Also new to this edition are text boxes containing anecdotes or vignettes related to topics discussed more formally in the text, and product profiles to describe some of the more successful contracts around the world and to highlight innovative or unusual features of traded contracts. The treatment in this text emphasizes financial derivatives, but it does not neglect traditional commodity futures. An accompanying website can be found online at www. The website also includes more than 80 exercises designed to enhance the understanding of option pricing principles and applications.

Table of contents Preface. Option Payoffs and Option Strategies. Bounds on Option Prices. Option Sensitivities and Option Hedging. The Options Approach to Corporate Securities. Economic Analysis and Pricing. Review Text "This is a revision of an already excellent textbook that has a very clear way of explaining the often difficult concepts that the student needs to understand in this very technical subject area.

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