tailieunhanh - Interest Rates and The Credit Crunch: New Formulas and Market Models

The excess demand thus drives up sales prices, which given an unchanged nominal income of private households leads to a revision of real consumption plans. The increase in sales prices in turn leads to a redistribution of real incomes from the household to the corporate sector. Thus profits in the business sectors increase which in the national accounting end up as retained profits and hence saving by the corporate sector. 6 In the end, again, aggregate saving equals aggregate investment, but the transmission channel is fundamentally different than in the textbook approach | Interest Rates and The Credit Crunch New Formulas and Market Models Fabio Mercurio QFR Bloomberg First version 12 November 2008 This version 5 February 2009 Abstract We start by describing the major changes that occurred in the quotes of market rates after the 2007 subprime mortgage crisis. We comment on their lost analogies and consistencies and hint on a possible simple way to formally reconcile them. We then show how to price interest rate swaps under the new market practice of using different curves for generating future LIBOR rates and for discounting cash flows. Straightforward modifications of the market formulas for caps and swaptions will also be derived. Finally we will introduce a new LIBOR market model which will be based on modeling the joint evolution of FRA rates and forward rates belonging to the discount curve. We will start by analyzing the basic lognormal case and then add stochastic volatility. The dynamics of FRA rates under different measures will be obtained and closed form formulas for caplets and swaptions derived in the lognormal and Heston 1993 cases. 1 Introduction Before the credit crunch of 2007 the interest rates quoted in the market showed typical consistencies that we learned on books. We knew that a floating rate bond where rates are set at the beginning of their application period and paid at the end is always worth par at inception irrespectively of the length of the underlying rate as soon as the payment schedule is re-adjusted accordingly . For instance Hull 2002 recites The floating-rate bond underlying the swap pays LIBOR. As a result the value of this bond equals the swap Stimulating discussions with Peter Carr Bjorn Flesaker and Antonio Castagna are gratefully acknowledged. The author also thanks Marco Bianchetti and Massimo Morini for their helpful comments and Paola Mosconi and Sabrina Dvorski for proofreading the article s first draft. Needless to say all errors are the author s responsibility. 1 2 principal. We also .

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