Quant Interview Questions 1

1. What is the price of a call as sigma -> infinity?

Ans:
It approaches S. The lognormal distribution is negatively skewed. As sigma -> infinity, although the probability of obtaining a very large S increases, a large portion of the probability mass is pushed towards the origin, making the option more likely to be out of the money (http://en.wikipedia.org/wiki/Log-normal_distribution).

2. Consider a product with maturity T=1, S_0=100, r=0. The product has a "one-hit" payoff, namely it pays \$1 when the underlying hits 120 for the first time, at which point the product terminates. What is the price of such product and how do you hedge it?

Ans:
It is worth 1*100/120 = \$0.8333. The replicating portfolio is simply to buy 0.008333 unit of stock at the inception and sell it off to collect 0.008333*120 = \$1 when the underlying hits 120 for the first time.

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Interview Thoughts

1. HR can throw quant questions too
2. Enthusiasm
3. Read resume
4. Read resume
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Quant Interview Questions 2

1. sigma_A = 0.2, sigma_B = 0.3 and correlation = 0.5. Find the portfolio that has the lowest portfolio sigma.
Ans: 6/7 of A and 1/7 of B

2. Each cereal box contains a piece of toy. There are 4 kinds in total. What is the expected number of boxes you have to buy in order to get the entire collection?
Ans: 8.33333

3. What is the expected number of toss in order to get 3 consecutive H from a fair coin?
Ans: 1 H takes 2 tosses; 2 H's takes 6 tosses; 3 H's takes 14 tosses; n H's takes 2^(n+1)-2 tosses. See Zhou, under Markov chain, for details.

4. There are n people in the room, everyone has shaken hand with everyone else. If there are totally 66 handshakes, what is n?
Ans: 12

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