Calculate a volatility smile, Financial Accounting

I am taking  finance class. Our books is John C. Hull 2nd edition Risk Management and Financial Institutions.  Our HW  are from this book. I have four questions I need help with.

1)  What difference does it make to the Var calculated in Example if the exponentially weighted moving average model is used to assign weights to scenarios as described ?


Suppose that, in the example in, five stressed scenarios are considered. They lead to losses($000s) of 235, 300, 450, 750, and 850. The subjective probabilities assigned to the scenarios are 0.5%, 0.2%, 0.2%, .05% and.05% respectively. The total probability of the stressed scenarios is, therefore, 1%, This means that the probability assigned to the scenarios generated by historical simulation if 99%, Assuming the equal weighting is used, each historical simulation scenario is assigned a probability of .99/500 =.00198. The probabilities assigned to scenarios are accumulated from the worst scenario to the best. The Var level when the confidence level is 99% is the first loss for which the cumulative probability is greater than.01. in the our example this is $300,000

The historical Simulation approach

 On September 25,2008 a portfolio worth $10 million consisting of investments in four stock indices: DJIA, FTSE 100, CAC 40 and NIKKEI 225. The value of the investment in each index o September 25, 2008 is shown in Table 12.1.  An excel spreadsheet containing 501  days of historical data on the closing prices of the four indices and a complete set of Var.


Investment portfolio used for VaR Calculations.

Index                                       Portfolio Value ($000s)

DJIA                                          $4,000

FTSE 100                                  $3,000

CAC 40                                     $1,000

Nikkei 225                                  $2,000

Total                                          $10,000


Scenarios generated for September 26, 2008

Scenario Number   DJIA       FTSE100   CAC 40    Nikkei 224   Portfolio Value (000s) Loss ( $000s)

1                          10,977.08  5,187.46     4,236.71  12,252.62    10,021.502                   -21.502

2                          10,925.97   5,234.87    4,275.48   12,155.54     10,023.327                  -23.327

3                           11,070.01  5,164.10     4,186.01   11,986.84    9,985,478                    14.522                             

499                       10,831.43  5,057.36   4,117.75   12,030.80         9828.450                   171.550

500                        11,222.53  5,300.42  4,342.14     11,899.00       10,141.826               -141.826

2) Discuss whether hedge funds are good or bad for the liquidity of markets.

3) Suppose that a financial institution uses an imprecise model for pricing and hedging a particular  type of structured product. Discuss how, if at all, it is likely to realize its mistake.

4) A Future prices is currently at $40. The risk-free interest rate is 5%. Some news is expected tomorrow that will cause the volatility over the next three months to be either 10% or 30%. There is a 60% chance of the first outcome and a 40% chance of the second outcome. Use the derivaGem Software to calculate a volatility smile for three-month options.

Posted Date: 2/21/2013 4:44:23 AM | Location : United States

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