Answer below questions.
1. Download and study some options of SPY by looking at the relationships between implied volatility, interest rate (maybe looking at two cases: 0.02 and 0.03), time to maturity and strike prices. Can you relate implied volatility to VIX? (Warning: sometimes, the data have abnormalities – I cannot foresee what, depends on what you download, you need to think about how to deal with these independently if possible).
2. Study the quantitative aspects of hedging, using options and/or complimentary assets (eg. Oil and airline) to see if such strategies make sense. Must use asset prices from real world in illustration. The results must be performance comparison, in figures or graphs, using the at least one statistical tools taught in the module, not general statements.
3. Study the definition of the following risk functions and how they are computed using MATLAB with concrete examples: VaR, Expected Tail loss, Omega and Drawdown
4. Design a retail business whose profit depends on a number of factors which can fluctuate randomly according some rules and run a MonteCarlo simulation on it and plot the profit distribution histogram, and fit the histogram using different probability distributions as you see fit.
Explain how you made your assumptions and consequences on the outcome.
5. Carry out independent research on the coherence definition for risk functions, use concrete example to illustrate why coherence and incoherence are needed in different circumstances. Take a couple of risk functions to verify, using numerical examples, if they are coherent or incoherent.
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