상세정보

Option Pricing in a Nutshell 
The super-replication paradigm
Stochastic representation of solutions of linear PDEs

Monte Carlo 
The Monte Carlo method 
Euler discretization error 
Romberg extrapolation

Some Excursions in Option Pricing 
Complete market models
Beyond replication and super-replication

Nonlinear PDEs: A Bit of Theory 
Nonlinear second order parabolic PDEs: some generalities
Why is a pricing equation a parabolic PDE? 
Finite difference schemes
Stochastic control and the Hamilton-Jacobi-Bellman PDE
Viscosity solutions

Examples of Nonlinear Problems in Finance 
American options 
The uncertain volatility model
Transaction costs: Leland’s model 
Illiquid markets 
Super-replication under delta and gamma constraints
The uncertain mortality model for reinsurance deals 
Credit valuation adjustment 
The passport option

Early Exercise Problems 
Super-replication of American options 
American options and semilinear PDEs 
The dual method for American options 
On the ownership of the exercise right 
On the finiteness of exercise dates 
On the accounting of multiple coupons 
Finite difference methods for American options 
Monte Carlo methods for American options
Case study: pricing and hedging of a multi-asset convertible bond
Introduction to chooser options 
Regression methods for chooser options 
The dual algorithm for chooser options 
Numerical examples of pricing of chooser options

Backward Stochastic Differential Equations 
First order BSDEs
Reflected first order BSDEs
Second order BSDEs

The Uncertain Lapse and Mortality Model 
Reinsurance deals 
The deterministic lapse and mortality model 
The uncertain lapse and mortality model 
Path-dependent payoffs 
Pricing the option on the up-and-out barrier 
An example of PDE implementation 
Monte Carlo pricing 
Monte Carlo pricing of the option on the up-and-out barrier 
Link with first order BSDEs 
Numerical results using PDE
Numerical results using Monte Carlo

The Uncertain Volatility Model 
Introduction 
The model 
The parametric approach
Solving the UVM with BSDEs 
Numerical experiments

McKean Nonlinear Stochastic Differential Equations 
Definition 
The particle method in a nutshell 
Propagation of chaos and convergence of the particle method

Calibration of Local Stochastic Volatility Models to Market Smiles 
Introduction 
The calibration condition 
Existence of the calibrated local stochastic volatility model 
The PDE method 
The Markovian projection method 
The particle method
Adding stochastic interest rates
The particle method: numerical tests

Calibration of Local Correlation Models to Market Smiles 
Introduction 
The FX triangle smile calibration problem 
A new representation of admissible correlations 
The particle method for local correlation 
Some examples of pairs of functions (a, b) 
Some links between local correlations
Joint extrapolation of local volatilities 
Price impact of correlation
The equity index smile calibration problem 
Numerical experiments on the FX triangle problem
Generalization to stochastic volatility, stochastic interest rates, and stochastic dividend yield
Path-dependent volatility

Marked Branching Diffusions 
Nonlinear Monte Carlo algorithms for some semilinear PDEs 
Branching diffusions 
Marked branching diffusions 
Application: Credit valuation adjustment algorithm
System of semilinear PDEs 
Nonlinear PDEs

References 
Index

Exercises appear at the end of each chapter.

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