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ABN AMRO. Price of Risk. Ton Vorst Global Head of Quantitative Risk Analytics October 7, 2005. Quantitative Risk Analytics. Staff: 56(roughly 50% Ph-D’s) Most in Amsterdam (roughly 25% foreign). Some in London and New York

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Price of risk

ABN AMRO

Price of Risk

Ton Vorst

Global Head of Quantitative Risk Analytics

October 7, 2005


Quantitative risk analytics
Quantitative Risk Analytics

  • Staff: 56(roughly 50% Ph-D’s)

  • Most in Amsterdam (roughly 25% foreign). Some in London and New York

  • Activities: Validation of Trading Models, Credit Portfolio and Counterparty Risk Models, Quantitative consultancy

  • After a while people move to other positions within ABN AMRO


Other positions within abn amro
Other Positions within ABN AMRO

  • Development teams for trading models

  • Asset Management and Asset Allocation

  • Department of Economics

  • Developers of rating models


Abn amro career
ABN AMRO Career

Career Development Programs.

  • Introduction Course (+/- 6 weeks)

  • Industry conferences / courses


Financial instruments
Financial instruments

Product Analysis within QRA

Equity (stock: KPN, Shell, IBM,…; indices: AEX, DJ, Nikkei)

  • Currency (Foreign Exchange, FX)

  • Interest rates (Bonds, LIBOR)

  • Commodities

  • Derivatives: Futures, Options


Abn amro wereldwijd koopkracht garantie note 2005 2015
ABN AMRO Wereldwijd KoopkrachtGarantie Note 2005-2015

EUR 100,000,000 Capital Protected Securities

Linked to the Performance of an Inflation Index and Basket of Indices, due 2015

  • 125% of your investment

  • Equal purchasing power of your investment

  • 75% of market rise + your investment back

Best of


Abn amro wereldwijd koopkracht garantie note 2005 20151
ABN AMRO Wereldwijd KoopkrachtGarantie Note 2005-2015

  • The purchasing power of your investment

HICP - Harmonised Index of Consumer

Prices excluding Tobacco

20%


Abn amro wereldwijd koopkracht garantie note 2005 20152
ABN AMRO Wereldwijd KoopkrachtGarantie Note 2005-2015

  • 75% of Market Rise

Basket value


Option
Option

Option

payoff

Gain/loss

Option

100%

Stock

Stock

value

Stock

value

100

100

-100%

Three types of financial instruments:

  • Bank account (virtually risk-less)

  • Share (moderate risk)

  • Option (very risky)


Risk neutral valuation one step binomial model
Risk neutral valuationOne step binomial model

S(1)=110

V(1)= 5

S(0)=100

V(0)= ?

S(1)=90

V(1)= 0

  • We create a portfolio:

    • A number of shares, Δ

    • Sell one option with strike 105 and unknown value V(0)

    • The value of the portfolio P(t) = Δ·S(t) – V(t)

  • Find Δ such that value of portfolio, P(1), is independent of the stock value

    • Stock goes UP: P(1) = Δ·110 – 5

    • Stock goes DOWN: P(1) = Δ·90 – 0

    • UP = DOWN follows Δ·110 – 5 = Δ·90 and Δ = 0.25

    • P(1) = 22.5

  • Risk-less portfolio must earn the risk-free interest rate, say 5% per year

    • Portfolio value today is P(0) = 22.5/e0.05×1 = 21.4

    • Option value today V(0) = 0.25·100 – 21.4 = 3.6


Risk neutral valuation risk neutral world
Risk neutral valuationRisk neutral world

  • Risk neutral valuation can be generalized:

    • We can assume that all assets grow with the risk-free interest rate, if we can hedge all risks

    • Mathematically, this corresponds to using a “risk free measure”

  • Put it in a mathematical form

where r is the risk free interest rate.

The risk free interest rate is used to calculate a future value and to discount them.


Mathematical methods
Mathematical methods

  • Trees (binomial, trinomial)

S(1)=121

V(1)=16

  • Monte Carlo

S(1/2)=110

V(1/2)= 9.8

S(1)=99

V(1)= 0

S(0)=100

V(0)= 6.0

S(1/2)=90

V(1/2)= 0

  • Partial differential equations

S(1)=81

V(1)= 0

  • Analytical solutions (Black-Sholes equation, for example)


References
References

  • Probability theory

  • Stochastic calculus

  • Measure theory

  • C++, MATLAB,…

  • John Hull, Options, Futures, and Other Derivatives

  • http://www.wilmott.com (Forums)


Abn amro quantitative risk analytics
ABN AMROQuantitative Risk Analytics

Group Market Risk Management

Quantitative Risk Analytics

Ton Vorst

Market Risk Modelling

& Product Analysis

Credit Risk Modelling &

Product Analysis

Quantitative Consultancy & Operations Research


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