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Course Instructor : Lin Chen

drlinchen@post.harvard.edu

Part I Monte Carlo Simulations

1

Introduction

Monte Carlo toolkit

Linear congruential generators

Testing uniformity

The Chi test

Kolmogorov Smirnov test

Discrepancy

Monte Carlo integration

The sample mean method

The hit or miss method

2

Inverse transform method

Continuous variables

Generalized Pareto

Order statistics

Discrete variables

Geometric random variables

Composition method

Acceptance- rejection method

Beta and Gamma variates

Normal variates

3

Convolution method

Chi square

Gamma and Beta

Composition method

Hyperexponentials

Hypergeometric variates

Special properties method

Student’s t

Negative binomial (Pascal)

Inverse gamma

4

Simulating stochastic process

Discrete process

Binomial process

Homogenous Poisson process

Non homogenous Poisson process

Renewal process

Cox process

5

Continuous time process

Brownian motion

Fractional Brownian motion

Geometric Brownian motion

Multiple dimensions

Correlated geometric Brownian process

The regime switching volatility model

6

Stable process

Levy process

Self-similarity

Variance-Gamma

***

Mixture process

7

Hidden Markov model

Jump intensity process

Sampling from empirical distribution

Sampling from given joint distribution

Sampling from given marginals and correlation

Slice sampler

8

Markov Chains Monte Carlo sampling

Gibbs sampler

Metropolis sampling

Metropolis-Hasting sampling

Sampling for Bayesian inference

9

Simulating stochastic differential equations

Strong solution and weak solution

Discretization schemes

Euler discretization

Milstein scheme

Runge-Kutta scheme

Kloeden and Platen scheme

10

Brownian bridge

Various SDE processes

Regulated Brownian process

Jump-diffusion process

11

Variance reduction techniques:

Common variables (Variate recycling)

Control variates

Multiple controls

Nonlinear controls

12

Importance sampling

Antithetic variates

Conditional Monte Carlo

13

Stratified sampling

Optimal strata

Latin hypercube sampling

Moments matching

14

Quasi-Monte Carlo

Low discrepancy sequences (LDS)

Van de Corput sequence

Halton sequence

Faure sequence

Sobol sequence

QMC integration

Hybrid Monte Carlo method

Part II Equity and Equity Derivatives

15

Option pricing

Risk neutral valuation and option pricing

Variance reduction techniques in option pricing

Importance sampling

Moment matching

16

Greeks in Monte Carlo

Heaviside function and Dirac function

Malliavin calculus method

Optimal Malliavin weighting function

Option sensitivities

17

Stochastic volatility modeling

Parameter estimations: historical and market-implied

Affine models: pros and cons

LSV model: theoretical and practical issues

18

Stochastic volatility option pricing models

Heston model

Hull&White model

GARCH option pricing

Empirical martingale

19

Complete smile model?

Local volatility

Implied distribution

Independent returns

Implementing smile model

Path dependent features

20

Pricing American options

Valuing American options in a path-simulation model

Least square Monte Carlo simulation

Duality approach

21

Pricing high-dimensional American options

The random lattice method

Stochastic mesh method

MCMC approach

22

Exotic option pricing

Lookback option

Asian option

Spread products: Quanto options

23

Double barrier options

Conditional expectation and importance sampling

Using Brownian Bridge to reduce discretization bias

Rainbow option

Chooser option

Monte Carlo pricing of exotics under a Levy Model

Part III Term Structure Models and Interest Rate Derivatives

24

Equilibrium short rate models

Affine model

Vasicek model (OU process)

CIR model (Feller process)

25

Multifactor model

Longstaff&Schwartz model

Fong&Vasicek model

Chen model

26

Bond pricing and yield curves

Interest rate derivatives

Bond option pricing

Swap pricing

Interest rate exotics pricing

27

Arbitrage free interest rate models

Hull&White trinomial tree model

Calibration of HW model

Applications of HW model

Derivatives pricing

28

The BlackDermanToy term structure model

Calibration of BDT model

Black&Karasinski model

Calibrated to term structure and cap volatilities

29

The HJM model

Simulation and calibration of HJM model

Markovian HJM model

Multifactor generalization of HJM model

Stochastic volatility HJM model

30

BGM market model

Implementing BGM model

Pricing under BGM model

31

The random field model of the term structure

Simulating Gaussian random field

Simulating random filed model

Stochastic string model of the term structure

32

Nonparametric modeling of the term structure

Arbitrage opportunities in arbitrage-free models of bond pricing

Lattice models for pricing American interest rate claims

Part IV Latest Developments in Equity and Interest Rate Products

33

3rd generation volatility products

Understanding variance swaps

Options on quadratic payoffs: affine and quadratic models

Corridor variance swaps.

Variance swaps valuation

34

Almost stationary calibration

Forward start skews

Latest developments in CPPI

Equity swap valuation

35

Equity-IR hybrid structuring

Modeling long-term equity-interest rate correlation

Tail events in equity-IR behavior

Term structure of equity-IR covariance

IR-contingent equity options

Part V Copula Approach and Extreme value Theory

36

Copulas: a new approach to model dependence structure

Mathematical introduction

Sklar's representation lemma

The Frechet-Hoeding Bounds for joint distribution functions

Copulas and random variables

Dependence

37

Archimedean copulas

Multivariate Archimedean copulas

Elliptical Copulas

The Gaussian copula

The t-copula

Extreme value copulas

38

Survival copula

Threshold copula

Simulations from copula draws

Elliptic copulas

Archimedean copulas

Marshall and Olkin's method

39

Farlie-Gumbel-Morgenstern Family

Marshall-Olkin Family

Simulating from the empirical copula

Empirical copula

40

Estimation of the copula function

Non parametric estimation

Identification of an Archimedean copula

41

Parametric estimation

MLE method

IFM method

Canonical method

42

Application of the copula approach

Multivariate option pricing

Asset return modeling

43

Portfolio aggregation

Term structure model and yields correlation

Dependence patterns across financial markets

44

Extreme value Theory

Maximum domain of attraction

GPD and GEV

Mean excess plots

POT method

45

Estimation and simulation

Estimation of EVT models

Estimation of marginal parameters

Estimation of extremal copula parameters

EVT by simulations

46

Calculating value-at-Risk with Monte Carlo simulation

Using non-normal Monte Carlo simulation to compute value-at-Risk

Beyond VAR and Stress Testing

Expected shortfall

VaR and ES by the copula－EVT based approach

Portfolio VaR and ES analysis

Loss aggregation

Part VI Credit Risk Modeling and Credit Derivatives

47

Structural modeling of credit risk

Merton’s model

First-passage approach

Diffusion-jump model

Structural model in practice

MKV and CreditMetrics

48

Intensity-based credit risk modeling

Default as Poisson event

Time-varying intensities

Jump intensity process

Affine intensity model

General intensities and valuation

49

Simulating defaults

Copula-dependent default risk in intensity models

Latent variable model

Factor models

Mixture models

Join credit event

50

Modeling correlated defaults

Generating correlated default times

Default contagion models

Measuring financial contagion: a copula approach

Sequential defaults

Markov models of default interaction

51

Pricing credit derivatives

Defaultable bond pricing

Credit default swaps

CDS pricing

The Poisson model and default times

Sensitivity

52

Portfolio products

Pricing Nth-to-default contracts

Extreme events and multi-name credit derivatives

Heavy tailed hybrid approach

53

Collateralised Debt Obligations

Relationship to nth-to-default

Standard tranched CDO structures

Portfolio product pricing by simulation

CDO tranches

Complex CDO structures

Part VII Markov Chains Monte Carlo Sampling

54

Gibbs sampler

Random scan Gibbs sampler_

Systematic scan Gibbs sampler

55

Metropolis sampling

Metropolis-Hasting sampling

Hybrid MCMC algorithms

56

MCMC for Bayesian Inference

Principles of Bayesian inference

Sequential inference: Filtering

57

Generalized stochastic volatility models

Equity asset pricing models

Bayesian Credit Scoring

Web www.brar.cn

posted on 2006-10-27 18:16 金融工程部落 阅读(207) 评论(0) 编辑 收藏 引用 网摘