chapter05 - Jarrow Turnbull Chatterjea Pricing Forwards(and...

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© Jarrow, Turnbull, Chatterjea Pricing Forwards (and Futures) Contracts Chapter 5 Page 1 AEM 421, Fall Chapter 5 Pricing Forwards (and Futures) Contracts 5.1 Introduction 5.2 Cash-and-Carry Model Assumptions 5.3 Cash-and-Carry Model No-Arbitrage Principle Revisiting a Forward Contract Intuition Behind Cash-and-Carry Model 5.4 Intuition 5.5 Miscellaneous Results 5.1 Introduction Take today’s Wall Street Journal, turn to the 3 rd Section on Money and Investing, and scan a few pages. Prices, prices, and prices! Shares and debts of more companies are traded, more indexes have proliferated, more mutual funds have been floated, and more derivatives have been created than ever before. The number of prices that get quoted in the Journal has more than doubled in the last two decades. And this is only for the exchange-traded contracts. Zillions more financial securities get traded in the over-the-counter markets that are tailored to client needs. What do you do when faced with such a vast array of prices? Do you sit down and memorize them? Of course you have to remember a few that they ask in job interviews like what was the price of Japanese Yen in terms of Swiss Francs at 3 am this morning. Jokes aside, barring a few key variables like the levels of Dow and the S&P 500, the inflation and the GDP growth rate, the long and the short term rates on U.S. Treasury bonds- there is little need to remember this stuff. It’s far better to understand a few key principles The need to find guidance in this jungle is greater than ever before. Finance tells you how to find order in this forest, and helps you see how the prices can be linked. Courses in Investments teach how to value stocks and price bonds. As this book deals with derivatives, we will see the order and linkages in the markets of forwards, futures, options and swaps. Because forwards and swaps are OTC instruments, we will not find their prices in the Wall Street Journal except as parts of informal stories. So the futures and the options help us develop pricing models and directly test our theory. A student once commented, “I don’t seem to understand how to price forwards and futures. I can price stocks easily from the discount rate, dividends, and growth rate. Forwards and futures seem too difficult to price. Such knee-jerk reactions can happen when seeing a derivative pricing model the first time. In reality, stocks are much harder to price. The constant growth dividend discount model looks easy because it is familiar; the hard part is finding good estimates for those inputs. Forwards on the other hand can be easily priced by the “no-arbitrage” principle and the simple property that securities can be carried from one period to another. We will see that such cash-and-carry model gives remarkably accurate answers in many frameworks.
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© Jarrow, Turnbull, Chatterjea Pricing Forwards (and Futures) Contracts Chapter 5 Page 2 AEM 421, Fall No-arbitrage principle suggests that in well functioning markets, opportunities to make riskless profits with no investments are extremely rare. As we have mentioned before, this
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