Interest-Rate ManagementWho gains all his ends did set the level too low. Although the history of trading on financial markets started a long and possibly not exactly definable time ago, most financial analysts agree that the core of mathematical finance dates back to the year 1973. Not only did the world's first option exchange open its doors in Chicago in that year but Black and Scholes published their pioneering paper [BS73] on the pricing and hedging of contingent claims. Since then their explicit pricing formula has become the market standard for pricing European stock op tions and related financial derivatives. In contrast to the equity market, no comparable model is accepted as standard for the interest-rate market as a whole. One of the reasons is that interest-rate derivatives usually depend on the change of a complete yield curve rather than only one single interest rate. This complicates the pricing of these products as well as the process of managing their market risk in an essential way. Consequently, a large number of interest-rate models have appeared in the literature using one or more factors to explain the potential changes of the yield curve. Beside the Black ([Bla76]) and the Heath-Jarrow-Morton model ([HJM92]) which are widely used in practice, the LIBOR and swap market models introduced by Brace, G~tarek, and Musiela [BGM97], Miltersen, Sandmann, and Son dermann [MSS97J, and Jamshidian [Jam98] are among the most promising ones. |
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assumption Black model bond with maturity call option caplet coherent risk measure contingent claim corresponding coupon bond coupon payments d₁ daycount convention defined denote discounted duration equivalent martingale measure EURIBOR F t,T f(to financial instrument financial market floating forward price function Furthermore futures contract futures price given Hence Hull-White model interest rates interest-rate derivatives interest-rate market Itô Itô's lemma key-rate buckets key-rate deltas LIBOR lower partial m-dimensional market model measurable stochastic process notional amount numéraire P₁ portfolio manager price process primary traded assets put option Q-martingale random variable risk factors risk management risk measure RL Tk Section short rate stochastic process swap rate swaption T₁ T₂ Ti+1 Tk+1 Tn+1 to,T trading strategy Treasury bill value at risk VaRo volatility Wiener process zero rates zero-coupon bond zero-coupon bond prices zero-rate curve
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Page viii - on an earlier draft of this book. I would also like to thank