The underlined algorithms have been already implemented.

### 1 Standard European Options in the Black-Scholes Model

#### 1.1 Call, Put, CallSpread, Digit

##### 1.1.1 Analytic
• Black-Scholes Type Formula The general version of the Black-Scholes formula used to price European options on stocks paying a continuos dividend yields 
• Stochastic expansion for the pricing of call options with discrete dividends. 

##### 1.1.2 Tree
• Cox Ross Rubinstein Binomial Binomial algorithm with the Cox-Ross-Rubinstein stock price parameters and probabilities 
• Extended Cox Ross Rubinstein Binomial Two steps backward CRR scheme, for a better accuracy of the Greeks 
• Hull White Binomial Binomial algorithm with the Hull-White stock price parameters and probabilities modified to account for dividends 
• Euler Binomial Stock price parameters and probabilities obtained from the discretization of the Wiener process
• Kamrad Ritchken Trinomial Trinomial tree with a stretch parameter λ 
• Third Moment Trinomial tree with matching first three moments
• LnThird Moment Trinomial tree with matching first four moments giving a o(h2) order of accuracy
• Figlewski Gao AMM Trinomial tree with Adaptive Mesh Model
• Moment and Matching Strike Algorithm Binomial tree with Moment and Matching Strike Algorithm
• Efficient pricing of derivatives on assets with discrete dividends
• Pricing American barrier options with discrete dividends by binomial trees

##### 1.1.3 Finite-Difference
• Gauss Method For a given time step the elliptic problem is solved by the direct method of Gauss for tridiagonal matrix 
• Explicit Method Direct explicit scheme 
• Iterative Sor Method For a given time step the elliptic problem is solved by the iterative method Sor(Successive Overrelaxation) 
• Multigrid Method For a given time step the elliptic problem is solved by a FMG Multigrid algorithm 
• Adaptative Finite Element Method Adaptative time step and space varies to improve precision. 
• Localization of the Black-Scholes equation using transparent boundary conditions

##### 1.1.4 Montecarlo
• Monte Carlo Standard
• Quasi Montecarlo Low discrepancy sequences(Faure, SquareRoot, VanDerCorput,
Sobol, Niedereitter, Owen’s Randomization Technique) , , , , 
• Variance Reduction Various reduction variance methods(Antithetic Methdod, Stratified Sampling, Control Variate,Moment Matching, Importance Function, Newton,Malliavin Calculus for Digital Options) ,, 

### 2 Standard American Options in the Black-Scholes Model

#### 2.1 Call, Put, CallSpread, Digit

##### 2.1.1 Tree
• Cox Ross Rubinstein Binomial Binomial algorithm with the Cox-Ross-Rubinstein stock price parameters and probabilities 
• Extended Cox Ross Rubinstein Binomial Two steps backward CRR scheme, for a better accuracy of the Greeks 
• Hull White Binomial Binomial algorithm with the Hull-White stock price parameters and probabilities modified to account for dividends 
• Euler Binomial Stock price parameters and probabilities obtained from the discretization of the Wiener motion process
• Kamrad Ritchken Trinomial Trinomial tree with a stretch parameter λ 
• Third Moment Trinomial tree with matching first three moments
• Breen Accelerated Binomial The Breen accelerated method approximates the Geske-Johnson option pricing formula 
• Broadie-Detemple BBSR Binomial Black-Scholes modification of binomial algorithm with Richardson extrapolation 
• LnThird Moment Trinomial tree with matching first four moments giving a o(h2) order of accuracy
• Figlewski Gao AMM Trinomial tree with Adaptive Mesh Model
• Moment and Matching Strike Algorithm Binomial tree with Moment and Matching Strike Algorithm

##### 2.1.2 Finite-Difference
• Brennan-Schwartz Algorithm The Brennan-Schwartz algorithm solves the linear complementarity problem ,
• Splitting Gauss Method The obstacle problem is splitted in two steps. Theta-method finite difference algorithm 
• Splitting Explicit Method The obstacle problem is splitted in two steps. Explicit finite-difference algorithm 
• Iterative Psor Method Projected SOR algorithm is used to solve large-scale linear complementarity problem 
• Cryer’s Algorithm Pivoting method to solve directly linear complementarity problem 
• Finite Element Method Finite Element Method
• Achdou Pironneau Method Finite difference Crank-Nicholson scheme coupled, within each timestep, with an iterative algorithm to locate the free boundary. This method is inspired from 

##### 2.1.3 Montecarlo
• Barraquand-Martineau Algorithm Stratification method. 
• Broadie-Glassermann Algorithm Approximation of dynamical programming using a stochastic mesh method. 
• Tsitsiklis-VanRoy Algorithm Approximation of dynamical programming using regression method.,
• Longstaff-Schwartz Algorithm Estimation of optimal stopping time using regression method.
• Pages-Bally Algorithm Approximation of dynamical programming using quantization method. 
• Broadie-Glassermann Algorithm Simulation algorithm for estimating the prices of American option with exercise opprtunities in a finite set of times. 
• Rogers Algorithm Method based on martingale Lagrangian. 
• Lions Regnier Algorithm Method based on Malliavin Calculus. 
• Barty Roy Strugarek Algorithm Stochastic algorithm.
• Pricing and Hedging American-Style Options: A Simple Simulation-Based Approach

##### 2.1.4 Approximation
• MacMillan Approximation Quadratic method based on exact solutions to approximations of the partial differential equation 
• Whaley Approximation Quadratic method based on exact solutions to approximations of the partial differential equation 
• Bjerksund-Stensland Approximation The approximation is based on an exercise strategy corresponding to a flat exercise boundary 
• Ho-Stapleton-Subrahmanyam Approximation 2-points approximation formula with exponential extrapolation 
• Bunch-Johnson Approximation 2-points Geske-Johnson approximation formula 
• Carr Approximation Randomization and the American Put 
• Ju Approximation Pricing an American Option by approximating Its Early Exercise Boundary as a Multipiece Exponential Function 
• Broadie-Detemple LBA and LUBA Methods Approximation methods based on lower and upper bounds 

### 3 Barrier European Options in the Black-Scholes Model

#### 3.1 Call, Put In-Out/Down-Up, Parisian

##### 3.1.1 Analytic
• Reiner-Rubinstein Formula Black-Scholes type formula 
• Labart-Lelong Method Laplace transform method for Parisian option
• Static Hedging of Standard Options.

##### 3.1.2 Trees
• Derman Kani Ergener Bardhan Algorithm Interpolation scheme for improving the pricing error of a binomial method 
• Ritchken Trinomial Algorithm Choosing the strech parameter λ of the Kamrad-Ritchken method such that the barrier is hit exactly 
• Rogers-Stapleton Method Tree with random time steps corresponding to hitting times 

##### 3.1.3 Finite-Difference
• Gauss Method Finite-difference algorithm with an interpolation scheme
• Finite Element Method Finite Element Method 

##### 3.1.4 Montecarlo
• Baldi-Caramellino-Iovino Method Large deviations technique 

#### 3.2 Discrete Barrier Option

##### 3.2.1 Approximation
• Broadie-Glassermann-Kou Method A continuity correction for discrete barrier options 
• Fusai-Abrahams-Sgarra Method Analitycal Solution for Discrete Barrier Options 
• Finite Difference Finite-difference algorithm.
• Tree Cheuk-Vorst algorithm .

##### 3.2.2 Montecarlo
• Variance Reduction Reduction variance methods

### 4 Barrier American Options

#### 4.1 Call, Put In-Out/Down-Up

##### 4.1.1 Trees
• Derman Kani Ergener Bardhan Algorithm Interpolation scheme for improving the pricing error of a binomial method 
• Ritchken Trinomial Algorithm Choosing the strech parameter λ of the Kamrad-Ritchken method such that the barrier is hit exactly 

##### 4.1.2 Finite-Difference
• Psor Method Psor Finite-difference algorithm with interpolation scheme 
• Cryer’s Algorithm Pivoting method to solve directly linear complementarity problem algorithm with interpolation scheme 
• Finite Element Method Finite Element Method 

### 5 Double Barrier European Options In/Out, Parisian in the Black-Scholes Model

#### 5.1 Call, Put In/Out

##### 5.1.1 Analytic
• Kunitomo-Ikeda Formula Pricing formula expressed as the sum of an infinite series 

##### 5.1.2 Approximation
• Geman-Yor Method Laplace transform method 
• Labart-Lelong Method Laplace transform method for Parisian option 

##### 5.1.3 Trees
• Ritchken Trinomial Algorithm Choosing the strech parameter λ of the Kamrad-Ritchken method such that the barrier is hit exactly 

##### 5.1.4 Finite-Difference
• Gauss Method Finite-difference algorithm with interpolation scheme
• Finite Element Method Finite Element Method 

##### 5.1.5 Montecarlo
• Baldi-Caramellino-Iovino Method Large deviations technique 

### 6 Double Barrier American Options In/Out in the Black-Scholes Model

#### 6.1 Call, Put In/Out

##### 6.1.1 Trees
• Ritchken Trinomial Algorithm Choosing the strech parameter λ of the Kamrad-Ritchken method such that the barrier is hit exactly 

##### 6.1.2 Finite-Difference
• Psor Method Psor Finite-difference algorithm with interpolation scheme 
• Cryer’s Algorithm Pivoting method to solve directly linear complementarity problem algorithm with interpolation scheme 
• Finite Element Method Finite Element Method 

### 7 Lookback European Options in the Black-Scholes Model

#### 7.1 Call, Put Fixed-Floating

##### 7.1.1 Analytic
• Goldman-Sosin-Gatto and Conze-Viswanathan Formula Black-Scholes type formula ,

##### 7.1.2 Trees
• Babbs Method Change of numeraire technique ,

##### 7.1.3 Finite-Difference
• Explicit Finite Difference algorithm

##### 7.1.4 Montecarlo
• Anderson-Brotherton-Ratcliffe Method Bias Elimination for efficient simulation procedure 

### 8 Lookback American Options

#### 8.1 Call, Put Fixed-Floating

##### 8.1.1 Trees
• Babbs Method Change of numeraire technique ,

##### 8.1.2 Finite-Difference
• Explicit Finite Difference algorithm

### 9 European Asian Options in the Black-Scholes Model

#### 9.1 Call, Put Fixed-Floating

##### 9.1.1 Approximation
• Geman-Yor Method Laplace transform method 

##### 9.1.2 Trees
• Forward Shooting Grid Method Barraquand-Pudet or Hull-White enhanced method ,
• Singular Points Method

##### 9.1.3 Finite-Difference
• Rogers-Shi Method Reduction to a one-dimensional PDE 
• Dubois-Lelievre Method New finite difference scheme 
• Hameur Breton Ecuyer Method Finite Element Method 

##### 9.1.4 Montecarlo
• Kemma-Vorst Method Control variate variance reduction method to compute the price of fixed-strike average-rate options with the approximation of the integral using the law of the brownian bridge ,
• Glasserman-Heidelberger-Shahabuddin Method Gaussian Importance sampling and stratification computational issue ,,
• Variance Reduction and Robbind-Monro algorithm 
• Exact retrospective Monte Carlo computation of arithmetic average Asian options 

##### 9.1.5 Approximation
• Rogers-Shi Method Rogers-Shi upper and lower bounds
• Thompson Method Upper and lower bounds 
• Levy Formula Lognormal approximation with first two moments.
• Turnbull-Wakeman Formula Edgeworth expansion around a lognormal using first four moments.
• Milevski-Posner Formula Reciprocal gamma distribution using first two moments. 
• Fusai-Tagliani Approximation Edgeworth expansion around a normal and maximum entropy approximation using first four logarithmic moments.
• Zhang Approximation Analytical approximation formula with error correction obtained by numerical solution of PDE.
• Laplace-Fourier Algorithm Laplace and Fourier Transform Alogorithm.
• Lord Method Upper and lower bounds 

### 10 American Asian Options in the Black-Scholes Model

#### 10.1 Call, Put Fixed-Floating

##### 10.1.1 Trees
• Forward Shooting Grid Method Barraquand-Pudet or Hull-White enhanced method ,
• Singular Points Method

##### 10.1.2 Finite-Difference
• Hameur Breton Ecuyer Method Finite Element Method

### 11 Europeen nD Standard Options in the Black-Scholes Model

#### 11.1 CallMax, PutMin, BestOf, Exchange

##### 11.1.1 Analytic
• Stulz and Johnson Formula Black-Scholes type formula  ,
• Generalizing the Black-Scholes formula to multivariate contingent claims 

##### 11.1.2 Tree
• Boyle-Evnine-Gibbs 4-branches Algorithm General lattice method to price contingent claims on k assets 
• Kamrad-Ritchken 5-branches Algorithm 5-branches tree with a stretch parameter λ 
• Euler 4-branches Algorithm Stock price paramenters and probabilities obtained from the discretization of the Wiener motion processes 
• Product Tree 4-branches Algorithm The tree is the product of two one-dimensional trees

##### 11.1.3 Finite-Difference
• Alterning Direction Implicite Algorithm(ADI) At each time step, one can integrate “in each direction” , 
• Explicit Method Direct explicit scheme 
• Implicit Method Implicit scheme solved with iterative stationary(SOR) and not stationary methods(GMRES and BiCgStab).,, 
• Multigrid Method The elliptic problem is solved by a FMG multigrid algorithm 
• Howard Method Implicit scheme solved with iterative Howard Method

##### 11.1.4 Montecarlo
• Monte Carlo Standard
• Quasi Montecarlo Low discrepancy sequences(Faure, SquareRoot, Halton,
Sobol, Niedereitter, Owen’s Randomization Technique) , , , , 
• Variance Reduction Various reduction variance methods(Antithetic Methdod, Stratified Sampling, Control Variate,Moment Matching, Importance Function, Newton) ,, 

### 12 American nD Standard Options in the Black-Scholes Model

#### 12.1 CallMax, PutMin, BestOf, Exchange

##### 12.1.1 Tree
• Boyle-Evnine-Gibbs 4-branches Algorithm General lattice method to price contingent claims on k assets 
• Kamrad-Ritchken 5-branches Algorithm 5-branches tree with a stretch parameter λ 
• Euler 4-branches Algorithm Stock price paramenters and probabilities obtained from the discretization of the Wiener motion processes 
• Product Tree 4-branches Algorithm The tree is the product of two one-dimensional trees

##### 12.1.2 Finite-Difference
• Splitting Adi Method One combines an Adi method with splitting technique ,
• Splitting Explicit Method Splitting method and an explicit scheme 
• Splitting Implicit Method Implicit scheme solved with iterative stationary(SOR) and not stationary methods(GMRES and BiCgStab).,, 
• FMGH Multigrid Method The linear complementarity problem is solved by a FMGH multigrid algorithm
• Howard Method Implicit scheme solved with iterative Howard Method

##### 12.1.3 Montecarlo
• Barraquand-Martineau Algorithm Stratification method. 
• Broadie-Glassermann Algorithm Approximation of dynamical programming using a stochastic mesh method. 
• Tsitsiklis-VanRoy Algorithm Approximation of dynamical programming using regression method.,
• Longstaff-Schwartz Algorithm Estimation of optimal stopping time using regression method. Variance Reduction.,
• Pages-Bally Algorithm Approximation of dynamical programming using quantization method. 
• Broadie-Glassermann Algorithm Simulation algorithm for estimating the prices of American option with exercise opprtunities in a finite set of times. 
• Lions Regnier Algorithm Method based on Malliavin Calculus. 
• Barty Roy Strugarek Algorithm Stochastic algorithm. 
• Ehrlichman Henderson Algorithm Adaptive control variates for pricing multi-dimensional American options.
• Andersen-Broadie Algorithm Primal-Dual Simulation Algorithm for Pricing Multidimensional American Options. 
• Broadie-Cao Algorithm Improved lower and upper bound algorithm for pricing American options by simulation. 
• Pricing and Hedging American-Style Options: A Simple Simulation-Based Approach
• Pricing Convertible Bonds with Call Protection,
• Nonparametric Variance Reduction Methods on Malliavin Calculus.

##### 12.1.4 Sparse Grid
• The effect of coordinate transformations for sparse grid pricing of basket options 

### 13 Standard European Options in the Merton Model

#### 13.1 Call, Put, CallSpread, Digit

##### 13.1.1 Analytic
• Merton Formula Pricing formula expressed as the sum of an infinite series. 

##### 13.1.2 Approximation
• Carr-Madan Approximation Fourier Transform Algorithm 
• Static Hedging of Standard Options 

##### 13.1.3 Finite-Difference
• Explicit Method Direct explicit scheme 
• Imp-Exp Method Splitting in Implicit and Explicit algorithm 

##### 13.1.4 Montecarlo
• Monte Carlo Standard
• Malliavin Monte Carlo in Pure Jump Model
• Malliavin Monte Carlo in Merton Model

### 14 Standard American Options in the Merton Model

#### 14.1 Call, Put, CallSpread, Digit

##### 14.1.1 Finite-Difference
• Splitting Explicit Method The obstacle problem is splitted in two steps. Explicit finite-difference algorithm 
• Splitting ADI-FFT Method The obstacle problem is splitted in two steps. ADI-FFT finite-difference algorithm ,

### 15 Standard European Options in the Dupire-Local Volatility Model

#### 15.1 Call, Put, CallSpread, Digit

##### 15.1.1 Finite-Difference
• Implicit Method Implicit scheme 
• Adaptative Finite Element Method Adaptative time step and space varies to improve precision. 
• Numerical algorithms for backward differential equations in local volatility models and BS n-dimensional model 

##### 15.1.2 Montecarlo
• Monte Carlo with variance reduction

##### 15.1.3 Approximation
• Analytical formulas for local volatility model with stochastic rates.

### 16 Standard European Options in the Hull-White,Stein,Scott Model

#### 16.1 Call, Put, CallSpread, Digit

##### 16.1.1 Montecarlo
• Variance Reduction and Robbind-Monro algorithm , 
• A generalization of the Hull and White formula with applications to option pricing approximation 
• Multi-level Monte Carlo path simulation
• A Stochastic Volatility Alternative to SABR
• Empirical martingale simulation of asset prices
• Multi-level Monte Carlo path simulation
• High order discretization schemes for stochastic volatility models.

### 17 Standard European Options in the Heston Model

#### 17.1 Call, Put, CallSpread, Digit

##### 17.1.1 Montecarlo
• Heston Closed-Form Solution ,
• Variance Reduction and Robbind-Monro algorithm
• Finite Difference method.
• Functional quantization algorithms for Asian options.
• Ninomiya-Victoir Scheme approximation of SDE for Asian options
• Kusouka-Ninomiya-Ninomiya Scheme approximation of SDE for Asian options
• A second-order discretization scheme for the CIR process: application to the Heston model
• Efficient Simulation of the Heston Stochastic Volatility Model
• An almost exact simulation method for the Heston model 
• Fast strong approximation Monte-Carlo schemes for stochastic volatility models 
• Exact Simulation of Option Greeks under Stochastic Volatility and Jump Diffusion Modelchjos11
• A Comparison of Biased Simulation Schemes for Stochastic Volatility Models
• Efficient, Almost Exact Simulation of the Heston Stochastic Volatility Model
• A Simple and Exact Simulation Approach to Heston Model
• A.Alfonsi A.Ahdida High order discretization of Wishart process.
• Polynomial Processes and their applications to mathematical Finance
• Time dependent Heston model
• On The Heston Model with Stochastic Interest Rates
• A Novel Option Pricing Method based on Fourier-Cosine Series Expansions
• Pricing early-exercise and discrete barrier options by Fourier-cosine series expansions
• A Fourier-based valuation method for Bermudan and barrier options under Heston’s model
• Pricing options under stochastic volatility : a power series approach
• Gamma expansion of the Heston stochastic volatility model
• Fast and Accurate Long Stepping Simulation of the Heston Stochastic Volatility Model
• Wiener-Hopf methods for Heston model
• Robust Approximations for Pricing Asian Options and Volatility Swaps Under Stochastic Volatility.
• Small-time asymptotics for implied volatility under the Heston model
• Robust approximations for pricing Asian options and volatility swaps under stochastic volatility
• A Mean-Reverting SDE on Correlation Matrices

##### 17.1.2 Finite Difference
• Sparse wavelet approach 
• Finite Difference Schemes
• Finite Element Schemes

##### 17.1.3 Tree
• A Tree-based Method to price American Options in the Heston Model

### 18 Standard European Options in the Bergomi Model

• Option pricing for a lognormal stochastic volatility model.

### 19 Standard European Options in the Foque Papanicolau Sircar Model

• Monte Carlo methods with variance reduction.

### 20 Standard European Options in the Multi-Factor Foque Papanicolau Sircar Model

• Finite Difference method.

### 21 Standard European Options and Barrier Options in Exponential Lévy models

Fourier transform , and Finite difference methods ,,Wiener-Hopf, Closed Formulas for pricing American, Barrier options and Lookback options in Kou model ,, Pricing Fast pricing of American and barrier options under Levy processes, Tree methods

• Merton’s model (X has Gaussian jumps)
• Lévy processes with Brownian component (Kou).
• Tempered stable process, variance gamma.
• Normal inverse Gaussian.
• Monte Carlo for pricing Exotics options in jump models .
• Backward Convolution Algorithm for Discretely Sampled Asian Options .
• Computing exponential moments of the discrete maximum of a Levy process and lookback options 
• Estimating Greeks in Simulating Levy-Driven Models
• Finite intensity Levy process with non-parametric (calibrated) Lévy measure.
• Fourier space time-stepping for option pricing with Levy models
• Saddlepoint methods for option pricing
• Saddlepoint Approximations for Affine Jump-Diffusion Models

### 22 Path Dependent Options in Exponential Lévy models

• Barrier options and Lookback options in Kou model. ,, Pricing
• Discretely Monitored Asian Options under Levy Processes. 
• Pricing Discretely Monitored Asian Options by Maturity Randomization. 
• Wiener-Hopf techniques for Lookback options in Levy models. O. Kudryavtsev

### 23 Standard European Options in Stochastic volatility models with jumps

• Bates model.
• Barndorff-Nielsen and Shephard OU-SV model.
• Exponential Lévy models with stochastic time change, given by an integrated stochastic volatility process.

### 24 Pricing European options in affine jump-diffusion

• Non-Gaussian Ornstein–Uhlenbeck-based models and some of their uses in financial economics
• Stochastic volatility for Lévy processes.
• Transform Analysis and Asset Pricing for Affine Jump-Diffusions 

### 25 Calibration in the Dupire Model

• Numerical solution of an inverse problem.,,
• Mercurio-Brigo Lognormal-mixture dynammics and calibration to market 
• Weighted Monte-Carlo Approach 
• Inference of a consistent implied volatility under a minimum of entropy criterion 
• Tree calibration algorithm ,
• Empirical semi-groups and calibration

### 26 Calibration in Stochastic Volatility and Jump Model

• Calibration in a Heston-Merton Model
• Algorithm of Andersen Andreasen ,.
• Non-parametric exponential Lévy models
• A.Achdou D.Pommier T.Arnarson : Calibration of American options in Levy models.

### 27 Pricing Interest Rate Derivatives

#### 27.1 Zero-Coupon Bond,Coupon Bearing,European, American Option on ZCB,Cap/Floor,Swaptions, Bermudan Swaptions

##### 27.1.1 Vasicek,Hull-White,Hul-White 2D
• Closed Formula and Implicit Finite Difference Methods 
• Hull-White Trinomial Tree,
##### 27.1.2 Cir,Cir++
• Closed Formula
• Explicit and Implicit Finite Difference Methods
• Trinomial Tree,
• Teichmann-Bayer:Cubature on Wiener space in infinite dimension. Finite difference methods for SPDEs and HJM-equations
##### 27.1.3 Black-Karasinski
• Trinomial Tree,
##### 27.1.4 Squared-Gaussian
• Schmidt Lattice
• Closed Formula 
##### 27.1.5 Li,Ritchken,Sankarasubramanian
• Li,Ritchken,Sankarasubramanian Lattice Methods 
• Carr-Yang American Monte Carlo Methods
##### 27.1.7 LMM Models
• Black Formula
• Approximation of Swaptions 
• Monte Carlo Methods ,,
• Tang Lange Bushy tree methods
• Pedersen Monte Carlo Methods
• Andersen Monte Carlo Methods[?]
• Jump Diffusion Libor Market Model
• LMM-CEV :Closed Formula, Monte Carlo
• The Levy LIBOR model
• Extended Libor market models with stochastic volatility
• Iterative Construction of Optimal Bermudan stopping time 
• True upper bounds for Bermudean products via Non-Nested Monte Carlo. 
• Pricing and hedging callable Libor exotics in forward Libor models 
• A stochastic volatility forward Libor model with a term structure of volatility smiles 
• A new approach to LIBOR modeling 
• Iterating cancelable snowballs and related exotics in a many-factor Libor model ,
• Jump-adapted discretization schemes for Levy-driven SDEs 
• Efficient and accurate log-Lévy approximations to Lévy driven models 

##### 27.1.8 Hunt Kennedy Pellser Markov-functional interest rate models
• Monte Carlo 
• An n-Dimensional Markov-functional Interest Rate Model 

##### 27.1.9 Affine Models
• Collin-Dufresne Goldstein Algorithm 
• Finite Difference Algorithm for Affine 3D Gaussian Model 

##### 27.1.10 Multi-factor quadratic term structure models
• The eigenfunction expansion method in multi-factor quadratic term structure models

### 28 Calibration Interest Rate Derivatives

• Calibration in LMM Model 
• Calibration in LMM-Jump Model 
• Calibration in LMM-Stochastic Volatility model 

### 29 Pricing Inflation Derivatives

• Pricing Inflation-Indexed Derivatives in Jarrow-Yildirim model 
• Pricing Inflation-Indexed Options with Stochastic Volatility 

### 30 Pricing Credit Risk Derivatives

##### 30.0.11 Credit Default Swaps:Models Reduced form approaches on single name
• HW,CIR++
• HW Tree ,Monte Carlo methods ,
• CIR++ Monte Carlo Method, Derivatives pricing with the SSRD stochastic intensity model 

##### 30.0.12 CDO
• Hull-White 
• Basket Default Swaps, CDO’s and Factor Copulas
• Andersen-Sidenious 
• A comparative anailsys of CDO pricing models 
• Saddlepoint approximation method for pricing CDOs 
• Valuing Credit Derivatives Using an Implied Copula Approach 
• Approximation of Large Portfolio Losses by Stein’s Method and Zero Bias Transformation 
• A dynamic approach to the modelling of credit derivatives using Markov chains 
• Calibration of CDO Tranches with the dynamical Generalized-Poisson Loss model 
• Portfolio losses and the term structure of loss transition rates: a new methodology for the pricing of portfolio credit derivatives 
• A dynamic approach to the modelling of credit derivatives using Markov chains. 
• Default Contagion in Large Homogeneous Portfolios. 
• Advanced credit portfolio modeling and CDO pricing. 
• Dynamic hedging of synthetic CDO-tranches with spread-and contagion risk. 
• Monte Carlo Computation of Small Loss Probabilities. 
• Pricing Credit from the top down with affine point processes 
• A.Alfonsi J.Lelong: A Closed-form extension to Black-Cox formula.
• Recovering portfolio default intensities implied by cdo quotes 
• Interacting particle systems for the computation of rare credit portfolio losses

### 31 Pricing Energy Derivatives

##### 31.0.13 Swing Options
• Pricing of Swing options (,)
• Finite difference methods for pricing of Swing options in Lévy-driven models
• Variance optimal hedging for processes with independent increments and applications 

### 32 Pricing Volatility Product

##### 32.0.14 Variance/Volatility Swap,Options on Realized Variance/Volatility
• Numerical methods and volatility models for valuing cliquet options
• Pricing Variance Swap,Options on Realized Variance in Tempered Stable model ,
• Pricing Variance Swap,Options on Realized Variance in Heston, Double Heston, Bates Model model
• Pricing Variance Swap : Consistent Variance Curve Models 
• Pricing Variance Swap : Pricing options on realized variance in the Heston model with jumps in returns and volatility.
• Forward variance dynamics : Bergomi’s model revisited.

### 33 Pricing Insurance Derivatives

• A bivariate model for evaluating fair premiums of equity-linked policies with maturity guarantee and surrender option.

### 34 Risk

• Computing VaR and AVar in Infinitely Divisible Distributions.

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