Introduction to Quantitative Finance

The worlds of Wall Street and The City have always held a certain allure, but in recent years have left an indelible mark on the wider public consciousness and there has been a need to become more financially literate. The quantitative nature of complex financial transactions makes them a fascinating subject area for mathematicians of all types, whether for general interest or because of the enormous monetary rewards on offer. An Introduction to Quantitative Finance concerns financial derivatives - a derivative being a contract between two entities whose value derives from the price of an unde.

Cover; Contents; PART I: PRELIMINARIES; 1 Preliminaries; 1.1 Interest rates and compounding; 1.2 Zero coupon bonds and discounting; 1.3 Annuities; 1.4 Daycount conventions; 1.5 An abridged guide to stocks, bonds and FX; 1.6 Exercises; PART II: FORWARDS, SWAPS AND OPTIONS; 2 Forward contracts and forward prices; 2.1 Derivative contracts; 2.2 Forward contracts; 2.3 Forward on asset paying no income; 2.4 Forward on asset paying known income; 2.5 Review of assumptions; 2.6 Value of forward contract; 2.7 Forward on stock paying dividends and on currency; 2.8 Physical versus cash settlement

2.9 Summary2.10 Exercises; 3 Forward rates and libor; 3.1 Forward zero coupon bond prices; 3.2 Forward interest rates; 3.3 Libor; 3.4 Forward rate agreements and forward libor; 3.5 Valuing floating and flxed cashflows; 3.6 Exercises; 4 Interest rate swaps; 4.1 Swap definition; 4.2 Forward swap rate and swap value; 4.3 Spot-starting swaps; 4.4 Swaps as difference between bonds; 4.5 Exercises; 5 Futures contracts; 5.1 Futures definition; 5.2 Futures versus forward prices; 5.3 Futures on libor rates; 5.4 Exercises; 6 No-arbitrage principle; 6.1 Assumption of no-arbitrage

6.2 Monotonicity theorem6.3 Arbitrage violations; 6.4 Exercises; 7 Options; 7.1 Option definitions; 7.2 Put-call parity; 7.3 Bounds on call prices; 7.4 Call and put spreads; 7.5 Butterflies and convexity of option prices; 7.6 Digital options; 7.7 Options on forward contracts; 7.8 Exercises; PART III: REPLICATION, RISK-NEUTRALITY AND THE FUNDAMENTAL THEOREM; 8 Replication and risk-neutrality on the binomial tree; 8.1 Hedging and replication in the two-state world; 8.2 Risk-neutral probabilities; 8.3 Multiple time steps; 8.4 General no-arbitrage condition; 8.5 Exercises

9 Martingales, numeraires and the fundamental theorem9.1 Definition of martingales; 9.2 Numeraires and fundamental theorem; 9.3 Change of numeraire on binomial tree; 9.4 Fundamental theorem: a pragmatic example; 9.5 Fundamental theorem: summary; 9.6 Exercises; 10 Continuous-time limit and Black-Scholes formula; 10.1 Lognormal limit; 10.2 Risk-neutral limit; 10.3 Black-Scholes formula; 10.4 Properties of Black-Scholes formula; 10.5 Delta and vega; 10.6 Incorporating random interest rates; 10.7 Exercises; 11 Option price and probability duality

11.1 Digitals and cumulative distribution function11.2 Butterflies and risk-neutral density; 11.3 Calls as spanning set; 11.4 Implied volatility; 11.5 Exercises; PART IV: INTEREST RATE OPTIONS; 12 Caps, floors and swaptions; 12.1 Caplets; 12.2 Caplet valuation and forward numeraire; 12.3 Swaptions and swap numeraire; 12.4 Summary; 12.5 Exercises; 13 Cancellable swaps and Bermudan swaptions; 13.1 European cancellable swaps; 13.2 Callable bonds; 13.3 Bermudan swaptions; 13.4 Bermudan swaption exercise criteria; 13.5 Bermudan cancellable swaps and callable bonds; 13.6 Exercises

Includes bibliographies and index.

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