Derivatives analyst Interview Questions

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Optiver
Derivatives Trader was asked...January 18, 2016

If A and B are playing tennis and the score is 30-30, what is the chance that A wins the game? Assume on any given point, A has a 0.7 chance of winning the point (and B 0.3)

4 Answers

The way I approached it was as follows: Starting from the initial state, one player has to win 2 points in a row to win. If that does not happen, we're back to the initial state. Therefore, P(A) = 0.49, P(B) = 0.09, P(repeating) = 1 - P(A) - P(B) = 0.42 I enjoy using the intuition that A is 49/9 more likely to win and then find the probabilities by dividing both by 0.42 (making 49 and 9 add up to 100 while preserving their proportions). Grats on the JS offer! Less

Shouldn't it be 0.7?

84.5 % (sum of 0.49x(0.42)^n)

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Group One Trading

Given two die, what is the probability that the sum when rolled would add up to six?

4 Answers

5/36

5/36 is right.... Combinations that add up to six: 1 and 5, 2 and 4, 3 and 3, 4 and 2, 5 and 1. So we have 5 successes. There are 36 individual outcomes because there are 6 sides on each die and 6*6 = 36 So we have 5/36. Less

1/6

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Optiver

3/?=?/48

4 Answers

12

Actually, +/- 12

Hey, could you please tell me more about the final round interview at their office? Less

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Group One Trading

100 pennies in a jar. 1 penny has 'heads' on both sides. You pick a penny out of the jar and give it to your friend (without looking at the penny). Your friend flips the penny in the air and gets 7 heads in a row. Which penny do you have? Why?

3 Answers

Chance of 1 Heads = .5 Chance of 7 heads in a row = (.5)^7 to do this in your head think of fractions... (1/2)^7 = (1/2*1/2=1/4, * 1/2=1/8, * 1/2 = 1/16....if you do it seven times you get 1/128. so you have a better chance to pick out the penny with two heads (1/100) than to get 7 heads in a row (1/128) Less

99 times out of 100 you take the normal penny. prob that normal penny give 7 heads in a row is 1/128. so, prob that he has special penny is 1/100 / (1/100 + 0.99*1/128) = 56.2% Less

~56.4% that you have the 2-headed penny.

Mansukh Securities & Finance

Q: What is 2.5% of 64000? Q: What is 3604-2487? (Something like that) Q: If I had 30 rupees and the price of 1 chocolate is Re. 1 and for every 3 wrappers of chocolate I get one more chocolate, how many chocolates would I have in total?

3 Answers

40 choclates in total.

43 chocolates

30 chocolates for Rs. 30 then, 30/3 =10 Chocolates for 30 wrappers. Now, 10/3=3 Chocolates for that 10 Chocolate's wrapper (1 Remainder) now 3 Chocolate's wrapper+1 remainder=4/3=1 Chocolate (1 Remainder). 1w+1w=2 so there you won't get any chocolate after this. So total chocolates 30+10+3+1=44 Chocolates. Less

Goldman Sachs

Can you tell me the formula for sample variance? Is this formula biased, and if so, prove it!

2 Answers

sigma = mean^2 of the sample - (mean of the sample)^2 Yes, it is biased, look up the proof on wikipedia. Less

S^2 is an unbiased estimator of sigma^2

Eni Spa

If the current market is in contango and you are short are you losing money or making money?

2 Answers

You’re making a profit. Selling at a higher price than what you bought

The simple answer is that if you are short on a contango curve then you are losing money, for the curve is sloped positively. Less

Mansukh Securities & Finance

Not related to market bc

2 Answers

I explain each and everything with examples

How was the aptitude test? And what do they ask?

Commerzbank

Are you better than the previous candidate?

2 Answers

Yes

No, you aren't.

NAB - National Australia Bank

what is your best achievement

2 Answers

I told them I achieved a first place award for the accuracy of my team in a business icon competition which has been accomplished during digitising the paper documents project on June 2011 Less

I told them I get into second place in business icon competition Overall it's very long interview and quite details Less

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