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The current estimate of daily volatility is 1.5%. The closing price of an asset yesterday was $30. The closing price of the asset today is $30.50. Using the EWMA model, with λ = 0.94, calculate the updated estimate of volatility .
Suppose an existing short option position is delta neutral and has a gamma of － 6000. Here, gamma is negative because we have sold options. Assume there exists a traded option with a delta of 0.6 and gamma of 1.25. Create a gamma neutral position.
A delta neutral position has a gamma of － 3200. There is an option trading with a delta of 0.5 and gamma of 1.5. How can we generate a gamma neutral position for the existing portfolio while maintaining a delta neutral hedge?
Once we have all the relevant market price/rate scenarios, the next step is to calculate the portfolio value for each scenario.
For an options portfolio, depending on the size of the portfolio, it may be more efficient to use the delta approximation rather than a full option pricing model (such as Black-Scholes) for ease of calculation.
Δoption = Δ(ΔS)
Thus the change in the value of an option is the product of the delta of the option and the change in the price of the underlying.
The Basel Committee prescribes an increase in capital requirements if, based on a sample of 250 observations (a one-year observation period), the VAR model underpredicts the number of exceptions (losses exceeding the 99% confidence level).
For such purposes, three 'zones' have been distinguished by the Committee.
Single-factor stress testing (sensitivity testing) involves applying a shift in a specific risk factor to a portfolio in order to assess the sensitivity of the portfolio to changes in that risk factor.
Multiple-factor stress testing (scenario analysis) involves applying simultaneous moves in multiple risk factors to a portfolio to reflect a risk scenario or event that looks plausible in the near future.