1. Maths
What is i^i? Give your answer to 2 decimal places for both the real and the imaginary parts.
2. Black-Scholes
Assume Black-Scholes and no dividend. P and C are, respectively, European vanilla put and call that are otherwise identical. What is the strike price that would make
i) their price; and
ii) their delta
the same?
3. Fixed income
The current yield curve is upward sloping. You speculate that it will get steeper and want to take advantage of it by long-shorting zero coupon bonds with different maturities (5 yrs and 10 yrs).
i) What is the duration-neutral strategy?
ii) What is the impact to your duration-neutral portfolio if there is a small parallel shift in the yield curve? A large (>>1bps) upward shift? A large (>>1bp) downward shift?
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