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Questions based on week 11 topics due in week 12

T11Q1This question refers to the volatility smile; a) What is the option smile?

b) Why does it arise from fat-tailed stock return distributions?

c) A skewed implied volatility smile occurs more often than a symmetric smile in

equity markets. Explain?

d) Suppose that S&P 500 options display a smile with an upward skew on the left.

If your view that the market has overestimated crash risk(large negative

return) and the smile has a skew that is much steeper than it should be, what options trading strategy could you adopt to profit from this?

T11Q2This question refers to the various aspects of Value at Risk (VaR). a) What are the three different approaches to computing VaR? b) State some advantages and disadvantages of each method.

c) How is Value-at-Risk (VaR) different as a measure of risk than the variance of

return?

d) Explain the difference between VaR and Expected Shortfall

T11Q3Consider a position consisting of a $100,000 investment in asset A and a $100,000 investment in asset B. Assume that the daily volatilities of both assets are 1% and that the coefficient of correlation between their returns in 0.3. What is the 5-day 99% VAR for the portfolio?

T11Q4 (BKM Ch5 – Q18) Consider these long-term investment data:

? The price of a 10-year $100 par zero coupon inflation-indexed bond is

$84.49

? A real-estate property is expected to yield 2% per quarter (nominal) with

a SD of the (effective) quarterly rate of 10%. a) Compute the annual rate on the real bond

b) Compute the continuously compounded annual risk premium on the

real-estate investment.

c) Use the appropriate forula and Excel Solver to find the SD of the

continuously compounded annual excess return on the real-estate investment.

d) What is the probability of loss or shortfall after 10 years?

Questions based on week 12 topics (no submission required)

T12Q1You are a desk quant and asked to price a two-year annual payment credit default swap (CDS). The market convention is to determine and quote the CDS spread ??.

The risk-free interest rate is for two-years ??=10%. Suppose the conditional probability of default each year ?? is also constant.

Please find the relationship expresses the two-year fair value CDS spread ?? in terms of time to maturity, recovery rate and notional value of the contract. (Assume that all default payments are made at the end of the period, and all premium payments are made at the beginning of each period. Also assume that recovery is ??=40% of notional value is 100.)

T12Q2The Merton (1974) model may be used to value bonds with default risk in a company. Explain how debt is viewed as an option in this framework.

T12Q3Explain the 2 ways a Credit Default Swap can be settled

T11Q4“Thepositionofabuyerofacreditdefaultswapissimilartothepositionofsomeonewhoislongarisk-freebondandshortacorporatebond.”Explainthisstatement.