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Anonymous asked in Business & FinanceOther - Business & Finance · 1 decade ago

how to do financial modeling without programming?

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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

    Radon-Nikodym derivatives

    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 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

    Correlation trading

    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

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