There are 2 pills A from bottle A and 2 pills B from bottle B. You have to take 1 pill A and 1 pill B every day, for two days, to survive. After taking 1 pill A from bottle A, you accidentally retrieved 2 pills B from bottle B. Now you have 3 indistinguishable pills in your hand (you do know that 1 out of the 3 is A and the rest are B). What's your survival strategy?
Ans:
Cut all 3 indistinguishable pills in halves (6 half-pills in total) and separate them into two piles. Make sure that each pile only contains a half from each individual pill. Now, each pile would necessarily contain 0.5 pill A and 1 pill B. Take the remaining pill A (still in bottle A) and split that in halves. We have created two "daily-doses" (the two piles) of the right composition for survival, although we still do not know which pill is which type.
Remark:
This can be trivially extended to n pills, n>2.
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Thursday, May 26, 2011
Tuesday, May 3, 2011
Instantaneous vs. Terminal volatility/correlation
Instantaneous vol. and correlation refer to the sigma and rho within the SDE's.
Terminal vol. and correlation require integrations. For an explanation on how instantaneous and terminal correlation differ, see Brigo pp.234-237.
Question to think about: are variance swap and correlation swap trading on instantaneous or terminal vol./correlation?
Terminal vol. and correlation require integrations. For an explanation on how instantaneous and terminal correlation differ, see Brigo pp.234-237.
Question to think about: are variance swap and correlation swap trading on instantaneous or terminal vol./correlation?
Trading Interview Questions
Brainteaser 1
There are N dice, each having x faces. What is the number of combination that give at least one 1 or x?
Ans: (x - 2)^N
Brainteaser 2
What is the longest diagonal within a k-dimensional hypercube?
Ans: sqrt(k)
Finance 1
You purchase a 5yr pure discount bond at 5% yield. One month later you sell it at 4% yield. What is the IRR of this investment?
Ans: ~60%
Finance 2
You enter into a pair trade consisting of CDS_A of 5yr tenor and 100bps, and CDS_B of 5yr tenor and 300bps. Suppose the spread narrows down to 100bps (from 200 bps) after 1 year and you are to unwind it. Describe the strategy and estimate the profit of this trade.
Ans: Sell protection with CDS_B and buy protection with CDS_A. Profit = 600bps (why?)
Finance 3
Part I
You, an American investor, are holding a 10yr convertible bond that is convertible over the first 5 years. Explain what risks you are exposed to and how they can be hedged away.
Ans:
a) Price risk (wrt the underlying equity). Can be hedged by shorting vanilla call.
b) IR risk. Can be hedged by shorting one (or more) zero coupon bonds, or entering into a fixed EUR for floating EUR swap.
c) FX risk. Can be hedged by entering into a floating EUR for floating USD swap.
NOTE: or we can enter into a fixed EUR for floating USD swap to hedge both IR and FX risks.
d) Credit risk. Can be hedged using CDS.
Part II
Suppose this is the only bond issued by the company. How do you calculate/estimate the price of a non-convertible 5yr bond issued by the same company?
Ans:
1. Strip away the embedded option to find the price of non-convertible 10yr
2. Find the spread of non-convertible 10yr over treasury curve/LIBOR swap curve
3. Here we have to make some sort of assumption regarding the term structure of the spread: constant, or usually slowing increasing
4. Using the spread term structure, find the spread of non-convertible 5yr over treasury curve/LIBOR swap curve
5. Using the spread of non-convertible 5yr over treasury curve/LIBOR swap curve, find the yield and hence the bond price
See here for more interview questions/brainteasers
There are N dice, each having x faces. What is the number of combination that give at least one 1 or x?
Ans: (x - 2)^N
Brainteaser 2
What is the longest diagonal within a k-dimensional hypercube?
Ans: sqrt(k)
Finance 1
You purchase a 5yr pure discount bond at 5% yield. One month later you sell it at 4% yield. What is the IRR of this investment?
Ans: ~60%
Finance 2
You enter into a pair trade consisting of CDS_A of 5yr tenor and 100bps, and CDS_B of 5yr tenor and 300bps. Suppose the spread narrows down to 100bps (from 200 bps) after 1 year and you are to unwind it. Describe the strategy and estimate the profit of this trade.
Ans: Sell protection with CDS_B and buy protection with CDS_A. Profit = 600bps (why?)
Finance 3
Part I
You, an American investor, are holding a 10yr convertible bond that is convertible over the first 5 years. Explain what risks you are exposed to and how they can be hedged away.
Ans:
a) Price risk (wrt the underlying equity). Can be hedged by shorting vanilla call.
b) IR risk. Can be hedged by shorting one (or more) zero coupon bonds, or entering into a fixed EUR for floating EUR swap.
c) FX risk. Can be hedged by entering into a floating EUR for floating USD swap.
NOTE: or we can enter into a fixed EUR for floating USD swap to hedge both IR and FX risks.
d) Credit risk. Can be hedged using CDS.
Part II
Suppose this is the only bond issued by the company. How do you calculate/estimate the price of a non-convertible 5yr bond issued by the same company?
Ans:
1. Strip away the embedded option to find the price of non-convertible 10yr
2. Find the spread of non-convertible 10yr over treasury curve/LIBOR swap curve
3. Here we have to make some sort of assumption regarding the term structure of the spread: constant, or usually slowing increasing
4. Using the spread term structure, find the spread of non-convertible 5yr over treasury curve/LIBOR swap curve
5. Using the spread of non-convertible 5yr over treasury curve/LIBOR swap curve, find the yield and hence the bond price
See here for more interview questions/brainteasers
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