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Quantitative Analysis
Parallel Processing
Numerical Analysis
C++ Multithreading
Python for Excel
Python Utilities
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I. Basic math.
II. Pricing and Hedging.
III. Explicit techniques.
1. Black-Scholes formula.
2. Change of variables for Kolmogorov equation.
3. Mean reverting equation.
4. Affine SDE.
A. Ricatti equation.
B. Evaluation of option price.
C. Laplace transform.
D. Example: CDFX model.
a. Definition of CDFX model.
b. The martingale normalization (CDFX).
c. Fourier transform (CDFX).
d. Calculation of Fourier transform (CDFX).
e. Calculation of Premium Leg of CDS.
f. Calculation of the protection leg of the CDS.
5. Heston equations.
6. Displaced Heston equations.
7. Stochastic volatility.
8. Markovian projection.
9. Hamilton-Jacobi Equations.
IV. Data Analysis.
V. Implementation tools.
VI. Basic Math II.
VII. Implementation tools II.
VIII. Bibliography
Notation. Index. Contents.

Definition of CDFX model.

e are modelling the quantities $X_{t}$ and $\lambda_{t}$ . The $X_{t}$ is dollar price of a foreign currency (exchange rate), see the section ( Currency exchange ). The $\lambda_{t}$ is intensity of sovereign default pertaining to the foreign currency. We use the following equations under the risk neutral measure. MATH where the $X,v,\lambda,z$ are stochastic processes, MATH are standard Brownian motions under the risk neutral measure, MATH are constant parameters, $q$ is the random jump magnitude and $\zeta$ is the martingale normalization constant.

The $r_{t}$ and $r_{t}^{f}$ are stochastic riskless rates of accrual on dollar and foreign MMAs. We will also use the notations MATH , MATH . These processes are determined by the term structure of bond prices MATH

The $q$ is modelled as a normal variable MATH .

The $N_{t}$ is a Poisson process, see the section ( Poisson process ).

The MATH are subsequently assumed to be 0.

Notation. Index. Contents.

Copyright 2007