An introduction to quantitative finance / Stephen Blyth

Includes bibliographical references and index.

Machine generated contents note: pt. 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 -- pt. 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. Summary -- 2.10. 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 fixed cashflows -- 3.6. Exercises -- 4. Interest rate swaps -- 4.1. Swap definition -- 4.2. Forward swap rate and swap value.
Contents note continued: 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 theorem -- 6.3. 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 -- pt. 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 theorem.
Contents note continued: 9.1. 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 function -- 11.2. Butterflies and risk-neutral density -- 11.3. Calls as spanning set -- 11.4. Implied volatility -- 11.5. Exercises -- pt. 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.
Contents note continued: 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 -- 14. Libor-in-arrears and constant maturity swap contracts -- 14.1. Libor-in-arrears -- 14.2. Libor-in-arrears convexity correction -- 14.3. Classic libor-in-arrears trade -- 14.4. Constant maturity swap contracts -- 14.5. Exercises -- 15. The Brace--Gatarek--Musiela framework -- 15.1. BGM volatility surface -- 15.2. Option price dependence on BGM volatility surface -- 15.3. Exercises -- pt. V TOWARDS CONTINUOUS TIME -- 16. Rough guide to continuous time -- 16.1. Brownian motion as random walk limit -- 16.2. Stochastic differential equations and geometric Brownian motion -- 16.3. Ito's lemma -- 16.4. Black-Scholes equation -- 16.5. Ito and change of numeraire.

"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 underlying financial asset - and the probabilistic tools that were developed to analyse them. The theory in the text is motivated by a desire to provide a suitably rigorous yet accessible foundation to tackle problems the author encountered whilst trading derivatives on Wall Street. The book combines an unusual blend of real-world derivatives trading experience and rigorous academic background. Probability provides the key tools for analysing and valuing derivatives. The price of a derivative is closely linked to the expected value of its pay-out, and suitably scaled derivative prices are martingales, fundamentally important objects in probability theory. The prerequisite for mastering the material is an introductory undergraduate course in probability. The book is otherwise self-contained and in particular requires no additional preparation or exposure to finance. It is suitable for a one-semester course, quickly exposing readers to powerful theory and substantive problems. The book may also appeal to students who have enjoyed probability and have a desire to see how it can be applied. Signposts are given throughout the text to more advanced topics and to different approaches for those looking to take the subject further."