Interview #13:Job Interview of a Financial Derivatives Trader
May 24, 2011
These questions are fundamental in nature and without understanding the concepts behind them, the so called "mathematical ground realities" (as one option trader recently termed it) of options trading, it would be impossible for anyone to understand financial derivatives, let alone trade them. All these questions were asked in a real life job interviews.
The answer to these questions will be released shortly.
You are an options trader. A client comes to you and asks for quote for a call option on this building (where we are currently sitting). Even though you can price the call option using a conventional Black-Scholes model, or any other model, you’d be very reluctant to sell it to the client. Why?
You are trading an asset which is capped at 100 (like say, a Eurodollar futures which is capped at 100 and cannot go above that value, as a value of 100 implies an interest rate of zero). What would be the value of a 100 strike put?
In a Black-Scholes formula, you see two terms, and . Which of these terms is a probability measure?
You have studied a lot of probability theory in your Engineering school. What sets an option trader apart from a probability theorist (mathematician) as far as his belief in probability distribution is concerned?
You know what "equilibrium" means in physics or engineering. We all hear the term "equilibrium" every now and then in finance literature as well and in fact, Black-Scholes option pricing model is based on the notion of "equilibrium". That's why it's called an equilibrium model. Every experienced option trader (and in fact, every experienced derivatives professional) knows that "equilibrium" does not exist in real life. What do you mean by "equilibrium"?
A trader is trading a European style binary option (digital) and hedging it with a call spread. He finds that the call spread always has a higher price and even if he narrows the strike spacing (spread) the price remains a bit high (though it begins to come close to the binary). Why is this so, given the fact that for a reasonably small spread (strike spacing) a call spread accurately replicates a binary option?
What is the most intuitive way of looking at a barrier option (in terms of a vanilla option)?
You are trading Dollar-Yen (USD/JPY) options and the drift (domestic risk free rate minus the foreign risk free rate) of Dollar-Yen is 5% and the volatility is 10%. If you were now to price a Yen-Dollar (JPY/USD) option what would happen to your drift and volatility?
You are trading USD/HKD options. USD/HKD trades in a currency band between, say, 7.7300 and 7.7800. A hedge fund client comes to you to buy a put on HKD (call on USD) at a strike price of 8.1000 for a large notional amount. What would you do? Would you sell him the option?
You must have read about Ito's Lemma in your MBA and every mathematical finance text devotes many chapters on Ito's Lemma and stochastic calculus. The math is too complex for me. Yet it seems that without Ito's lemma there would be not Black-Scholes option pricing model and you and I might be working on a factory shop floor instead of a trading floor. Can you explain Ito's Lemma - or what it tries to do - in simple English?
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