隨機波動金融市場衍生品 [Derivatives in Financial Markets with Stochasic Volatility] 下載 mobi epub pdf 電子書 2026

內容簡介

This book addresses problems in financial mathematics of pricing and hedging derivative securities in an environment of uncertain and changing market volatility. These problems are important to investors ranging from large trading institutions to pension funds. The authors present mathematical and statistical tools that exploit the "bursty" nature of market volatility. The mathematics is introduced through examples and illustrated with simulations, and the approach described is validated and tested on market data.
The material is suitable for a one-semester course for graduate students who have been exposed to methods of stochastic modeling and arbitrage pricing theory in finance. It is easily accessible to derivatives practitioners in the inancial engineering industry.

內頁插圖

目錄

Introduction
1 The Black-Scholes Theory of Derivative Pricing
1.1 Market Model
1.1.1 Brownian Motion
1.1.2 Stochastic Integrals
1.1.3 Risky Asset Price Model
1.1.4 Itos Formula
1.1.5 Lognormal Risky Asset Price
1.2 Derivative Contracts
1.2.1 European Call and Put Options
1.2.2 American Options
1.2.3 Other Exotic Options
1.3 Replicating Strategies
1.3.1 Replicating Self-Financing Portfolios
1.3.2 The Black-Scholes Partial Differential Equation
1.3.3 Pricing to Hedge
1.3.4 The Black-Scholes Formula
1.4 Risk-Neutral Pricing
1.4.1 Equivalent Martingale Measure
1.4.2 Self-Financing Portfolios
1.4.3 Risk-Neutral Valuation
1.4.4 Using the Markov Property
1.5 Risk-Neutral Expectations and Partial Differential Equations
1.5.1 Infinitesimal Generators and Associated Martingales
1.5.2 Conditional Expectations and Parabolic Partial Differential Equations
1.5.3 Application to the Black-Scholes Partial Differential Equation
1.5.4 American Options and Free Boundary Problems
1.5.5 Path-Dependent Derivatives
1.6 Complete Market

2 Introduction to Stochastic Volatility Models
2.1 Implied Volatility and the Smile Curve
2.1.1 Interpretation of the Smile Curve
2.1.2 What Data to Use
2.2 Implied Deterministic Volatility
2.2.1 Time-Dependent Volatility
2.2.2 Level-Dependent Volatility
2.2.3 Short-Time Tight Fit versus Long-Time Rough Fit
2.3 Stochastic Volatility Models
2.3.1 Mean-Reverting Stochastic Volatility Models
2.3.2 Stock-Price Distribution under Stochastic Volatility
2.4 Derivative Pricing
2.5 Pricing with Equivalent Martingale Measures
2.6 Implied Volatility as a Function of Moneyness
2.7 Market Price of Volatility Risk and Data
2.8 Special Case： Uncorrelated Volatility
2.8.1 Hull-White Formula
2.8.2 Stochastic Volatility Implies Smile
2.8.3 Remark on Correlated Volatility
2.9 Summary and Conclusions

3 Scales in Mean-Reverting Stochastic Volatility
3.1 Scaling in Simple Models
3.2 Models of Clustering
3.2.1 Example： Markov Chain
3.2.2 Example： Another Jump Process
3.2.3 Example： Ornstein-Uhlenbeck Process
3.2.4 Summary
3.3 Convergence to Black-Scholes under Fast Mean-Reverting Volatility
3.4 Scales in the Returns Process
3.4.1 The Returns Process
3.4.2 Returns Process with Jump Volatility
3.4.3 Returns Process with OU Volatility
3.4.4 S&P; 500 Returns Process

4 Tools for Estimating the Rate of Mean Reversion
4.1 Model and Data
4.1.1 Mean-Reverting Stochastic Volatility
4.1.2 Discrete Data
4.2 Variogram Analysis
4.2.1 Computation of the Variogram
4.2.2 Comparison and Sensitivity Analysis with Simulated Data
4.2.3 The Day Effect
4.3 Spectral Analysis

5 Asymptotics for Pricing European Derivatives
5.1 Preliminaries
5.1.l The Rescaled Stochastic Volatility Model
5.1.2 The Rescaled Pricing Equation
5.1.3 The Operator Notation
5.2 The Formal Expansion
5.2.1 The Diverging Terms
5.2.2 Poisson Equations
5.2.3 The Zero-Order Term
5.2.4 The First Correction
5.2.5 Universal Market Group Parameters
5.2.6 Probabilistic Interpretation of the Source Term
5.2.7 Put-Call Parity
5.2.8 The Skew Effect
5.3 Implied Volatilities and Calibration
5.4 Accuracy of the Approximation
5.5 Region of Validity

6 Implementation and Stability
6.1 Step-by-Step Procedure
6.2 Comments about the Method
6.3 Dividends
6.4 The Second Correction

7 Hedging Strategies
7.1 Black-Scholes Delta Hedging
7.1.1 The Strategy and Its Cost
7.1.2 Averaging Effect
7.2 Mean Self-Financing Hedging Strategy
7.3 Staying Close to the Price

8 Application to Exotic Derivatives
8. l European Binary Options
8.2 Barrier Options
8.3 Asian Options

9 Application to American Derivatives
9.1 American Problem under Stochastic Volatility
9.2 Stochastic Volatility Correction for an American Put
9.2.1 Expansions
9.2.2 First Approximation
9.2.3 The Stochastic Volatility Correction
9.2.4 Uncorrelated Volatility
9.2.5 Probabilistic Representation
9.3 Numerical Computation
9.3.1 Solution of the Black-Scholes Problem
9.3.2 Computation of the Correction

10 Generalizations
10.1 Portfolio Optimization under Stochastic Volatility
10.1.1 Constant Volatility Merton Problem
10.1.2 Stochastic Volatility Merton Problem
10.1.3 A Practical Solution
10.2 Periodic Day Effect
10.3 Other Markovian Volatility Models
10.3.1 Markovian Jump Volatility Models
10.3.2 Pricing and Asymptotics
10.4 Martingale Approach
10.4.1 Main Argument
10.4.2 Decomposition Result
10.4.3 Comparison with the PDE Approach
10.5 Non-Markovian Models of Volatility
10.5.1 Setting： An Example
10.5.2 Asymptotics in the Non-Markovian Case
10.6 Multidimensional Models

11 Applications to Interest-Rate Models
11.1 Bond Pricing in the Vasicek Model
11.1.1 Review of the Constant Volatility Vasicek Model
11.1.2 Stochastic Volatility Vasicek Models
11.2 Bond Option Pricing
11.2.1 The Constant Volatility Case
11.2.2 Correction for Stochastic Volatility
11.2.3 Implications
11.3 Asymptotics around the CIR Model
11.4 Illustration from Data
11.4.1 Variogram Analysis
11.4.2 Yield Curve Fitting
Bibliography
Index

精彩書摘

The Black-Scholes model rests upon a number of assumptions that are，to some extent.“counterfactual.”Among these are continuity ofthe stock. price process it does not iump），the ability to hedge continuously without transaction costs，inde-pendent Gaussian returns. and constant volatility.We shall focus here on relaxing the last assumption by allowing volatility to vary randomly，for the following rea-son：a well. known discrepancy between Black-Scholes-predicted European op-tion prices and market-traded options prices，the smile curve，can be accounted for by stochastic volatility models. That iS.this modification of the Black-Scholes theory has a posteriori success in one area where the classical model fails.In fact.modeling volatility as a stochastic process iS motivated a priori by em-pirical studies of stock.price returns in which estimated volatility iS observed to exhibit“random”characteristics.Additionally，the effects of transaction costs show up. under many models，as uncertainty in the volatility；fat-tailed returns distributions can be simulated by stochastic volatility；and market‘jump”phe-nomena are often best modeled as volatility iump processes.Stochastic volatility modeling therefore iS not iust a simple fix to one particular Biacl（Scholes as-sumption but rather a powerful modification that describes a much more complex market.We cite literature that explores possible causes of stochastic volatility in the notes at the end Of this chapter. In Chapter 1，we introduced the notation and tools for pricing and hedging deriv-ative securities ander a constant volatility lognormal model（1.2）.This iS the sim-plest example of pricing in a complete market.However，pricing in a market with stochastic volatility is an incomplete markets problem.a distinction that（as we shall explain）has far-reaching consequences-particularly for the hedging prob-lem and the problem of parameter estimation. It iS the latter inverse problem that iS the biggest mathematical and practical challenge introduced by such models，and also perhaps the one that benefits most from the asymptotic methods of Chapter 5.

前言/序言

《金融市場隨機波動下的投資策略與風險管理》 在瞬息萬變的現代金融世界中，市場價格的波動是恒定的主題，而波動率本身並非靜止不變，它也隨著時間推移而呈現齣復雜的變化規律。這種“波動的波動”現象，即隨機波動，構成瞭金融市場中最深層的動力之一，對各類資産的定價、投資組閤的構建以及風險的度量都産生瞭至關重要的影響。本書旨在深入探討在隨機波動背景下，投資者如何製定有效的投資策略，以及如何進行係統性的風險管理。 本書的篇幅將聚焦於以下幾個核心領域，力求為讀者提供一套全麵而實用的分析框架和操作指南： 第一部分：隨機波動模型理論與實證分析 我們將從隨機波動模型的基本概念入手，介紹經典的隨機波動模型（如 the GARCH family models）及其演變。重點將放在理解這些模型的數學結構，包括均值方程、方差方程以及條件分布的設定。理論講解將與實際數據分析緊密結閤，通過案例分析展示如何使用統計軟件對真實市場數據進行模型擬閤和參數估計，評估模型的擬閤優劣，以及如何進行模型診斷和選擇。此外，本書還將介紹一些非參數方法和機器學習方法在捕捉隨機波動特性上的應用，為讀者提供更廣闊的視野。 第二部分：隨機波動下的資産定價與投資組閤優化 理解隨機波動對於準確評估金融資産的內在價值至關重要。本書將深入研究隨機波動模型如何影響資産定價，特彆是在股票、債券、外匯以及商品等不同資産類彆上的應用。我們將探討隨機波動對期權定價的影響，例如Black-Scholes模型在隨機波動下的修正和擴展。 在投資組閤優化方麵，本書將重點闡述如何將隨機波動納入投資組閤的構建過程中。傳統的均值-方差優化模型在隨機波動環境下會失效，因此，我們將介紹基於隨機波動模型進行投資組閤優化的新方法，包括如何衡量和管理組閤的波動率風險，如何構建能夠有效對衝波動率風險的投資組閤，以及如何根據市場動態調整投資組閤的資産配置。我們將重點關注風險預算、條件在險價值（CVaR）等風險度量指標，以及在隨機波動下的優化應用。 第三部分：隨機波動下的風險管理技術與工具 風險管理是金融實踐的核心，而隨機波動更是風險管理中不可迴避的挑戰。本書將詳細介紹如何在隨機波動的市場環境中識彆、度量和管理各類風險。 市場風險管理： 我們將深入分析隨機波動對市場風險度量的影響，如在險價值（VaR）和條件在險價值（CVaR）的計算。本書將探討如何在存在隨機波動時，更準確地估計這些風險指標，以及如何利用這些指標來指導交易和投資決策。 信用風險管理： 盡管本書側重於市場波動，但我們也將觸及隨機波動對信用風險的間接影響，例如在經濟下行或市場劇烈波動時，企業違約概率的增加。 流動性風險管理： 在市場波動加劇時，流動性往往會枯竭。本書將探討隨機波動如何影響市場流動性，以及如何在流動性風險顯著的市場環境下進行有效的風險管理。 操作風險與閤規風險： 雖然不是本書的重點，但我們將簡要提及在市場劇烈波動期間，操作風險和閤規風險也可能被放大，需要投資者保持高度警惕。 第四部分：實際應用案例與交易策略 理論與實踐相結閤是本書的一大特色。我們將通過多個精心挑選的實際應用案例，展示隨機波動模型和風險管理工具在不同市場環境下的應用效果。這些案例將涵蓋： 高頻交易中的波動率套利策略： 分析如何在短期市場波動中捕捉交易機會。 宏觀經濟事件對波動率的影響與應對： 探討突發事件（如地緣政治衝突、疫情）如何引發市場劇烈波動，以及投資者如何進行風險對衝。 量化對衝基金的波動率交易策略： 剖析一些利用波動率産品（如VIX期貨期權）進行交易的策略。 養老金和保險公司在不確定市場下的資産配置： 討論如何在長期投資中考慮隨機波動對收益和風險的影響。 第五部分：前沿研究與未來展望 本書的最後部分將對當前金融學界在隨機波動研究領域的最新進展進行梳理，例如高階矩模型、非綫性隨機波動模型、以及與高頻數據相結閤的波動率建模方法。我們將討論這些前沿研究的潛在應用價值，並展望隨機波動研究的未來發展方嚮，例如機器學習與深度學習在波動率預測和風險管理中的深度融閤，以及更精細化的微觀結構模型對波動率形成機製的揭示。 本書適閤於金融機構的風險管理人員、投資經理、量化分析師、對衝基金經理，以及對金融市場波動性有深入研究需求的學術界研究人員和研究生。通過閱讀本書，您將能夠更深刻地理解金融市場的內在運行機製，掌握在不確定性環境中進行投資決策和風險管理的先進方法，從而在復雜多變的金融市場中遊刃有餘，實現穩健的投資迴報。