陈琳博士的金融工程课大纲
(更多请见http://www.brar.cn)
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
NIG
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
posted on 2006-10-27 18:16
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