Quantitative Analysis
Parallel Processing
Numerical Analysis
C++ Multithreading
Python for Excel
Python Utilities
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I. Basic math.
II. Pricing and Hedging.
1. Basics of derivative pricing I.
2. Change of numeraire.
3. Basics of derivative pricing II.
A. Option pricing formula for an economy with stochastic riskless rate.
B. T-forward measure.
4. Market model.
5. Currency Exchange.
6. Credit risk.
7. Incomplete markets.
III. Explicit techniques.
IV. Data Analysis.
V. Implementation tools.
VI. Basic Math II.
VII. Implementation tools II.
VIII. Bibliography
Notation. Index. Contents.

T-forward measure.

he measure associated with the numeraire MATH is called the " $T-$ forward measure". It is particularly useful when evaluating a price of a derivative. Indeed, the regular risk neutral measure corresponds to the defined above, see ( MMA numeraire ), numeraire $\beta_{t}$ , $\beta_{0}=1$ and MATH MATH Hence, the transformation to the T-forward measure moves the discounting outside of the expectation term.

Suppose an asset $S_{t}$ and the riskless bond MATH are given by the equations MATH MATH with respect to the risk neutral measure. Here $dW_{t}^{\ast}$ and $dZ_{t}^{\ast}$ are correlated increments of the standard Brownian motions, MATH We perform transformation of the SDEs to the T-forward measure. The old numeraire is MATH : MATH and the new numeraire is MATH . Hence, according to the formula ( Change of drift recipe ), the drift of $S_{t}$ in the MATH -measure is MATH Therefore MATH where the $dW_{t}^{T}$ is increment of the standard Brownian motion with respect to the $T$ -forward probability.

Notation. Index. Contents.

Copyright 2007