Financial Derivatives in Theory and Practice

Philip Hunt is the author of Financial Derivatives in Theory and Practice, Revised Edition, published by Wiley. Joanne Kennedy is the author of Financial Derivatives in Theory and Practice, Revised Edition, published by Wiley.

• Preface to revised edition xvPreface xviiAcknowledgements xxiPart I: Theory 11Single-Period option pricing 32 Brownian Motion 193 Martingales3.5 Local martingales and semimartingales 563.5.1 The space cMloc563.5.2 Semimartingales 593.6 Supermartingales and the Doob—Meyer decomposition 614 StochasticIntegration634.1 Outline 634.2 Predictable processes 654.3 Stochastic integrals: the L2 theory 674.3.1 The simplest integral 684.3.2 The Hilbert space L2 (M) 694.3.3 The L2 integral 704.3.4 Modes of convergence to H • M 724.4 Properties of the stochastic integral 744.5 Extensionsvialocalization774.5.1 Continuous local martingales as integrators 774.5.2 Semimartingales as integrators 784.5.3 The end of the road! 804.6 Stochastic calculus: Itô’s formula 814.6.1 Integration by parts and Itô’s formula 814.6.2 Differential notation 834.6.3 Multidimensional version of Itô’s formula 854.6.4 Lévy’stheorem885 GirsanovandMartingaleRepresentation915.1 Equivalent probability measures and the Radon—Nikodým derivative 915.1.1 Basic results and properties 915.1.2 Equivalent and locally equivalent measures on a filtered space 955.1.3 Novikov’s condition 975.2 Girsanov’s theorem 995.2.1 Girsanov’s theorem for continuous semimartingales 995.2.2 Girsanov’s theorem for Brownian motion 1015.3 Martingale representation theorem 1055.3.1 The space I2 (M) and its orthogonal complement 1065.3.2 Martingale measures and the martingale representation theorem 1105.3.3 Extensions and the Brownian case 1116 Stochastic Differential Equations 1156.1 Introduction 1156.2 Formal definition of an SDE 1166.3 An aside on the canonical set-up 1176.4 Weak and strong solutions 1196.4.2 Strong solutions 1216.4.3 Tying together strong and weak 1246.5 Establishing existence and uniqueness:Itô theory 1256.5.1 Picard—Lindelöf iteration and ODEs 1266.5.2 A technical lemma 1276.5.3 Existence and uniqueness for Lipschitz coefficients 1306.6 Strong Markov property 1346.7 Martingale representation revisited 1397 Option Pricing in Continuous Time 1417.1 Asset price processes and trading strategies 1427.1.1 A model for asset prices 1427.1.2 Self-financing trading strategies 1447.2 Pricing European options 1467.2.1 Option value as a solution to a PDE 1477.2.2 Option pricing via an equivalent martingale measure 1497.3 Continuous time theory 1517.3.1 Information within the economy 1527.3.2 Units, numeraires and martingale measures 1537.3.3 Arbitrage and admissible strategies 1587.3.4 Derivative pricing in an arbitrage-free economy 1637.3.5 Completeness 1647.3.6 Pricing kernels 1737.4 Extensions 1767.4.1 General payout schedules 1767.4.2 Controlled derivative payouts 1787.4.3 More general asset price processes 1797.4.4 Infinite trading horizon 1808 Dynamic Term Structure Models 1838.1 Introduction 1838.2 An economy of pure discount bonds 1838.3 Modelling the term structure 1878.3.1 Pure discount bond models 1918.3.2 Pricing kernel approach 1918.3.3 Numeraire models 1928.3.4 Finite variation kernel models 1948.3.5 Absolutely continuous (FVK) models 1978.3.6 Short-rate models 1978.3.7 Heath—Jarrow—Morton models 2008.3.8 Flesaker—Hughston models 206References 423Index 427