EMBAF

1
Financial Engineering

• Zvi Wiener
• mswiener_at_mscc.huji.ac.il
• 02-588-3049

2
Multi-Asset Options

• Following
• Paul Wilmott, Introduces Quantitative Finance
• Chapter 11

3
Multidimensional Lognormal Random Walk
4
Correlation Matrix

• Note that ?ii 1 and ?ji ?ij.
• Positive definite for any vector y we have
• yT ? y ? 0.

5
Measuring Correlation

• Cov(X,Y) E( (E(X)-X) (E(Y)-Y) )
• Let Ra(t), Rb(t) be returns on assets a and b on
  day t. Then

Problems time delay in observations,
missing data, time delay in response
(CPI), correlation does not mean dependence
(copula).
6
Correlation

• Can be a bad measure of dependence!
• Consider X N(0, 1) and X2.
• Are they dependent?
• What is the correlation?
• Cointegartion two time series are cointegrated
  if their linear combination has constant mean and
  standard deviation.
• Bonds of emerging markets

7
Options on Many Underlyings

• Exchanging one asset for another
• Max(QaSa-QbSb, 0 )
• Note that
• Max(x, y) y Max(x-y, 0)
• Min(x, y) x Max(x-y, 0)
• Similarity reduction Application of Numeraire

8
Options on Many Underlyings

• Analytical solution
• Reasonable approximation
• Numerical Approach
• trees
• Monte Carlo (bad for American style)
• finite difference

9
Home Assignment

• Read chapter 11 in Wilmott.
• Follow Excel files coming with the book.
• Read and analyze (do not price) the structured
  notes of LEUMI and HAPOALIM submit to Oz before
  the end of February.