Interview Test # 1:Job Interview of an Equity Options Trader
Team Latte March 8, 2007
This is a rough transcript of the job interview of Adam Pawlowski, who was interviewed for the position of an equity options trader in a European bank in Tokyo. This was a middle level position requiring around 3 to 5 years experience in options trading. Adam had a degree in liberal arts and a very fancy Ivy League MBA degree. He had around 2 years experience in trading index options and single stock options with a bulge bracket bank in Tokyo.
This was narrated to us by the interviewer himself. The candidate's answers, as presented here, are all highly abridged because most of the time the narrator did not go into the details of his answers.
Interviewer's Question :
The chief market strategist of this bank announces in the strategy meeting that the Nikkei has an 80% chance of going up and 20% chance of it going down. If the Nikkei goes up you make $10 and if it goes down you make $1,000. Would you rather go long on the Nikkei (via futures or futures options) or short the Nikkei?
Candidate's Answer :
Of course, I'll go long on the Nikkei, which idiot will not. It is better to make $10 rather than losing $1,000 and the chances of making that ten dollars is way too high.
Our Comment :
This is a wrong answer, but one that perhaps many of us will say. In such situation the person will not even think beyond the 8020 probabilities. What matters to a trader is his expected payoff  and he should always try to maximize that  and not the pure probabilities of an up move and a down move.
Interviewer's Question :
I see... ...(a long silence)....ok let's say that there is only a 1% chance of the market going down and a 99% chance of it going up. If the market goes down then it goes down by 1,000 points and if it goes up then it goes up by 10 points. Is this a fair game?
Candidate's Answer :
I am not sure, but it does not look like a fair game. The probabilities are way too skewed and the payoff is very uneven.
Our Comment :
This is a fair game. The probability of an up move times the up move is equal to the probability of a down move times the down move. In a fair game the sum of the expected payoffs is zero, which is the case here.
Interviewer's Question :
Actually, it is a fair game. Can you think of a situation in real life where such probabilities might actually come into play? Well, maybe not in equities but how about a currency band, or a government intervention levels in FX markets? Around such barriers do you think this kind of probabilities will hold?
Candidate's Answer :
I don't have any experience in currency trading, but I guess one could possibly face such extreme eventualities if there is some sort of pegging.
Our Comment :
Currency bands, such as the one that exited in Europe in the early nineties  the ERM  and the pegging of Thai Baht and Malaysian Ringgit in the late nineties, do indeed display such probabilities around them. Near a barrier there is a very low chance of the barrier being crossed owing to government intervention but the upside is unlimited as there is no barrier there. Of course, in the case of ERM, there existed both upper and lower bands.
Interviewer's Question :
When you have a situation like this  according to your own words, " probabilities are way too skewed and the payoff being uneven "  would you expect the volatility of the asset to drop near such a level or increase. Give reasons for your answer.
Candidate's Answer :
I think volatilities will become quite low. Because the asset has every chance of going up rather than down, and up moves in the market is accompanied by low volatility I think the volatility certainly drop.
Our Comment :
This is actually a highly complex question . Theoretically speaking, the volatility should drop substantially to accommodate for the fair game. The volatility should dampen around the currency band  any market barrier  and the asset will start to paste around the band. But in practice, most of the times the volatility will increase sharply near the band as the asset will try to pierce through the band on the one hand (speculators try to break the band, etc.) and jump around the band on the other (central banks, regulators trying to intervene furiously to push it away from the band ) . This analysis is not an easy one; both mathematically and empirically, it is a difficult subject to analyze .
Interviewer's Question :
If you were to analyze the correlation between two assets , would you look at the correlation between their returns or correlation between their volatilities?
Candidate's Answer :
Well, I have so far looked at the correlation between the returns of the two assets. I am not sure how we can measure the correlation between volatilities, I mean, which volatilities to use  implied or historical. Returns and volatilities are two different processes.
Our Comment :
Once again this is not a straightforward question to answer and the explanation isn't all that simple. Many practitioners (some risk managers) and option traders spend less time analyzing the correlation between the respective asset returns and more time on analyzing the correlation between the asset volatilities . This line of reasoning draws support from the observation that rates of return of assets are correlated with changes in volatility, rather than volatility itself and this is believed to be one of the reasons why asset correlations are not stable, especially during heteroskedastic time periods. This has implications for risk managers; for example, during the market crash of 1987 both stocks and bonds were uncorrelated to each other in terms of their return but both these assets were extremely volatile and extremely risky to hold. This is an upcoming but a very interesting area of research.
Interviewer's Question :
Ok, how about correlation between asset price movement and the volatility? Will that give us an indication of the risk and perhaps help us in making trading decisions?
Candidate's Answer :
Asset price movements and volatility of the asset are related because when the asset goes up the volatility goes down  empirically speaking  and vice verse. So, we can say that the asset and the volatility are inversely correlated.
Our Comment :
If you estimate a return series, such that then the correlation between and will give us the indication of skew of the asset. Skew is the correlation between the asset return and the asset volatility. Positive and negative skew tell us about the tail risk in the distribution and can help in making trading decisions, i.e. either to go long skew or short the skew.
Interviewer's Question :
Your sales guy wants to sell a knock out conditional trigger swap linked to an equity index to a customer. You are familiar with conditional trigger swaps, I hope? ( seeing the blank look on the candidate's face...) Ok, what is a conditional trigger swap?
Candidate's Answer :
I don't know exactly, but it seems like an interest rate product linked to some kind of a trigger. Is that right?
Our Comment :
A conditional trigger swap is a hybrid product between equity and interest rate. Say, you have a swap whereby the dealer pays a stream of LIBOR and receives a fixed coupon every reset date, where that coupon is given by the level of an equity index, say, Nikkei225 on the reset days. Conventionally only the first fixed coupon is fixed and rest are all conditional on the level of the equity index.
Interviewer's Question :
( after explaining it to the candidate...) So, your sales wants to sell this 2 year knock out conditional trigger swap linked to say, Nikkei, to a client and asks you to price this swap. The bank will receive a stream of LIBOR and plus a margin and pay a fixed coupon to the client based on the current level of the Nikkei, which is 14,500. If the Nikkei finishes above this level on any reset day, after the first six monthly reset the bank pays 6%, if it finishes below this level then the bank pays 4.5% coupon. Moreover, if the Nikkei every hits 13,000 during the life of the swap the fixed coupons are knocked out. You have never traded this product before. How would you price this swap? Give me a back of the envelop pricing method?
Candidate's Answer :
This is easy. I'll price the vanilla IR swap and add in the value of the binary options for the conditional payment to it plus value a knock out option. The total is the price. For the binaries and the knock out I'll use closed formulas and price the IR swap using standard cash flow discounting using forward LIBORs.
Our Comment :
That is truly easier said than done. This is a hybrid multiasset exotic product and we are not aware of any well defined closed form technique to price this product. We would therefore price this product using a Monte Carlo engine, and we need to use a stochastic interest rate model as well. The stochastic process for LIBOR could be the Libor market model or a Vasichek's model and that of equity could be the standard stochastic differential path with zero or risk free drift. The key is the correlation between the interest rate and the equity. This is where the greatest sensitivity will be and the correlation parameter needs to be tested. But remember the interviewer is just asking a back of the envelope method and this is as good as it gets on an Excel spreadsheet.
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