Market Risk Modelling

Market Risk Modelling By A.V. Vedpuriswar July 31, 2009

Basics of volatility ,[object Object],[object Object],[object Object],[object Object]

Estimating Volatility ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Estimating Volatility ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Solution ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Introduction ,[object Object],[object Object],[object Object]

Delta ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Gamma ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Theta ,[object Object],[object Object],[object Object],[object Object]

Vega ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Solution ,[object Object],[object Object]

[object Object],[object Object],[object Object]

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Illustration

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Solution ,[object Object],[object Object],[object Object],[object Object],[object Object]

Solution Weekly VAR ＝ (12,500) (√5) ＝ 27,951 Monthly VAR ＝ ( 12,500) (√20) ＝ 55,902 Semi annual VAR ＝ (12,500) (√125) ＝ 139,754 Annual VAR ＝ (12,500) (√250) ＝ 197,642

Solution ,[object Object],[object Object],[object Object],[object Object],Ref : Options, futures and other derivatives, By John Hull

Solution ,[object Object],[object Object],[object Object]

Solution ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

What is Monte Carlo VAR? ,[object Object],[object Object],[object Object]

Step 1: Generate Scenarios ,[object Object],[object Object],[object Object],[object Object],[object Object]

Opportunity Cost of Capital ,[object Object],[object Object]

Stochastic Element ,[object Object],[object Object],[object Object],[object Object]

Probability Distribution ,[object Object],[object Object],[object Object],[object Object]

Step 2: Calculate the Value of the Portfolio ,[object Object],[object Object],[object Object],[object Object]

Other approximations ,[object Object],[object Object],[object Object],[object Object],[object Object]

Step 3: Reorder the Results ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Formula used typically in Monte Carlo for stock price modelling

Advantages of Monte Carlo ,[object Object],[object Object],[object Object],[object Object],[object Object]

Problems with Monte Carlo ,[object Object],[object Object],[object Object],[object Object],[object Object]

[object Object],[object Object],[object Object],[object Object],[object Object]

Few assumptions ,[object Object],[object Object],[object Object],[object Object],[object Object]

Steps ,[object Object],[object Object],[object Object],[object Object]

Problem What is VAR (90%) ? % Returns Frequency Cumulative Frequency - 16 1 1 - 14 1 2 - 10 1 3 - 7 2 5 - 5 1 6 - 4 3 9 - 3 1 10 - 1 2 12 0 3 15 1 1 16 2 2 18 4 1 19 6 1 20 7 1 21 8 1 22 9 1 23 11 1 24 12 1 26 14 2 27 18 1 28 21 1 29 23 1 30

[object Object],[object Object],[object Object],Solution

Advantages ,[object Object],[object Object],[object Object]

Disadvantages ,[object Object],[object Object],[object Object],[object Object]

Comparison of different VAR modeling techniques

Simulation vs Variance Covariance ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Basel Committee Standards ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Introduction ,[object Object],[object Object],[object Object],[object Object]

Two approaches to Stress testing ,[object Object],[object Object]

Conducting Stress Tests ,[object Object],[object Object],[object Object],[object Object],[object Object]

Extreme Value Theory ,[object Object],[object Object],[object Object]

EVT Parameters ,[object Object],[object Object],[object Object],[object Object]

Market Risk Modelling

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Market Risk Modelling