風(fēng)險中性定價

內(nèi)容概要

　　Books are written for use， and the best compliment that the community in the field could have paid to the first edition of 1998 was to buy out the printrun， and that of the corrected printing， as happened. Meanwhile， the fast-developing field of mathematical finance had moved on， as had our thinking， and it seemed better to recognize this and undertake a thorough-going re-write for the second edition than to tinker with the existing text.

作者簡介

作者：（英國）賓漢姆（N.H.Bingham）

書籍目錄

Preface to the Second EditionPreface to the First Edition1.Derivative Background　1.1 Financial Markets and Instruments　　1.1.1 Derivative Instruments　　1.1.2 Underlying Securities　　1.1.3 Markets　　1.1.4 Types of Traders　　1.1.5 Modeling Assumptions　1.2 Arbitrage　1.3 Arbitrage Relationships　　1.3.1 Fundamental Determinants of Option Values　　1.3.2 Arbitrage Bounds　1.4 Single-period Market Models　　1.4.1 A Fundamental Example　　1.4.2 A Single-period Model　　1.4.3 A Few Financial-economic Considerations　Exercises2.Probability Background　2.1 Measure　2.2 Integral　2.3 Probability　2.4 Equivalent Measures and Radon-Nikodym Derivatives.　2.5 Conditional Expectation　2.6 Modes of Convergence　2.7 Convolution and Characteristic Functions　2.8 The Central Limit Theorem　2.9 Asset Return Distributions　2.10 Infinite Divisibility and the Levy-Khintchine Formula　2.11 Elliptically Contoured Distributions　2.12 Hyberbolic Distributions　Exercises3.Stochastic Processes in Discrete Time　3.1 Information and Filtrations　3.2 Discrete-parameter Stochastic Processes　3.3 Definition and Basic Properties of Martingales　3.4 Martingale Transforms　3.5 Stopping Times and Optional Stopping　3.6 The Snell Envelope and Optimal Stopping　3.7 Spaces of Martingales　3.8 Markov Chains　Exercises4.Mathematical Finance in Discrete Time　4.1 The Model　4.2 Existence of Equivalent Martingale Measures　　 4.2.1 The No-arbitrage Condition　　 4.2.2 Risk-Neutral Pricing　 4.3 Complete Markets: Uniqueness of EMMs　 4.4 The Fundamental Theorem of Asset Pricing: Risk-Neutral　　 Valuation　 4.5 The Cox-Ross-Rubinstein Model　　 4.5.1 Model Structure　　 4.5.2 Risk-neutral Pricing　　 4.5.3 Hedging　 4.6 Binomial Approximations　　 4.6.1 Model Structure　　 4.6.2 The Black-Scholes Option Pricing Formula　　 4.6.3 Further Limiting Models　 4.7 American Options　　 4.7.1 Theory　　 4.7.2 American Options in the CRR Model　 4.8 Further Contingent Claim Valuation in Discrete Time　　 4.8.1 Barrier Options　　 4.8.2 Lookback Options　　 4.8.3 A Three-period Example　 4.9 Multifactor Models　　 4.9.1 Extended Binomial Model　　 4.9.2 Multinomial Models　 Exercises5.Stochastic Processes in Continuous Time6.Mathematical Finance in Continuous Time7.Incomplete Markets8.Interest Rate Theory9.Credit RiskA.Hilbert SpaceB.Projections and Conditional ExpectationsC.The Separating Hyperplane TheoremBibliograpyIndex

章節(jié)摘錄

版權(quán)頁：插圖：The main focus of this book is the pricing of financial assets. Price formationin financial markets may be explained in an absolute manner in terms offundamentals, as, e.g. in the so-called rational expectation model, or, moremodestly, in a relative manner explaining the prices of some assets in termsof other given and observable asset prices. The second approach, which weadopt, is based on the concept of arbitrage. This remarkably simple concept is independent of beliefs and tastes （preferences） of the actors in the financialmarket. The basic assumption simply states that all participants in the mar-ket prefer more to less, and that any increase in consumption opportunitiesmust somehow be paid for. Underlying all arguments is the question: Is it possible for an investor to restructure his current portfolio （the assets currently owned） in such a way that he has to pay less today for his restructure dportfolio and still has the same （or a higher） return at a future date？ If suchan opportunity exists, the arbitrageur can consume the difference today andhas gained a free lunch.Following our relative pricing approach, we think of financial assets asspecific mixtures of some fundamental building blocks. A key observation willbe that the economics involved in the relative pricing lead to linearity of theprice formation. Consequently, if we are able to extract the prices of thesefundamental building blocks from the prices of the financial assets tradedin the market, we can create and price new assets simply by choosing newmixtures of the building blocks. It is this special feature of financial assetpricing that allows the use of modern martingale-based probability theory（and made the subject so special to us）.

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