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A Pelhamite 貝崙客
關於部落格
紀錄生活,想法,及其他種種
貝崙位於帝國首都北郊,離中城15哩
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Love Story

Recently, I received the letter reprinted below. Dear Mr Derman, You are always writing about the difficulty of being a good quant, but it’s not that hard. Read please my story and don’t be so serious! I have come to New York with a PhD from ********. Quickly, I answered an internet ad by a chasseur de tête who sent me to a foreign bank. Two interviews and I aced them all. A week later, I’m on the desk. “Dude, you are getting a Dell!” I say to myself. With my scientific PhD, I find option theory easy as π. I have studied heat conduction and quantum mechanics so I quickly comprehend the options: α is intercept, β slope, Γ curvature,∆ tangent, σ temperature, θ sensitivity, µ drift. If I know derivatives, I know Derivatives. Soon I am an expert at Black-Scholes and Beyond. Yield curves are strings. Feynman to me? Kaç to you! Everything’s an option. I am one dynamic hedger, man. On the prop desk my boss is Alden, an MBA, and I’m his quantitative guy. He calls me a geek; he knows no math but he sure knows business; he can use the same word as noun, adjective, exclamation and gerund in single sentence when he’s angry. Alden’s risque assistant is Lidia, a truly exotic option, a total knock-out with a non-normal distribution which makes the option salesman whistle and mutter softly about barrier penetration. I have rational expectations for Lidia but I feel she don’t respect me. She like old movies but has no taste for mathematics and its beauty. To her I am far out-of-the-money. Now the bank wants to do structured products. I have Excel, I buy VBA, I get models from optionmodels.com and now I’m in business. We’re doing long-term puts and calls, down-and-outs, converts, one-touches, spread options, CDS, vol swaptions, whatever, and I’m getting all the prices. I find model for anything. Easy as Dell. Once a week we run my spreadsheet to mark the book. Big P&L fast. Then late dinner with Alden at Bouley or Jean-Georges. But always Lidia’s on my mind. When I watch her wandering across the floor, I cannot but think of excess kurtosis. I try to cliquet with her for coffee but she DK my trade. I sense there is little chance of a transformation between her p-measure and my q-measure. One day someone offer Alden a big position in spread option barrier reversal American no-touch interest rate euro swaptions, denominated in Turkish lira. According to my model, these Sobranies are pretty cheap. Lots of α, high κ, big Sharpe. Alden take $100 million face for the desk and his boss bought some for his own PA too. Next day the broker offered us much more at the same price – great deal! Each day’s close I tell Alden how my model says to rehedge the Eurodollar futures and the lira, and then we execute. Except I am always thinking sadly about Lidia, dreaming of her capital assets. Will I ever know her efficient frontier? Next week comes by the head of model risk, ENS graduate Dr Jean-Martin Geille, an expert in Malliavin calculus. And Vlad, chief risk modeller. “Your VAR is way up, mon ami,” said J-M to Alden, very loud. “What model ‘ave you used for the Sobranies?” My model is one-factor Monte Carlo with control variate, $125 from the web. Vlad’s is three-factor Crank-Nicolson PDE with fat tails and LU decomposition, he tells me, written in Java on his Linux laptop. His say we have a lot less α than mine. “You pay too much µ for too little κ!” say Vlad. “What’s it all about, α?” Lidia sings in her deep voice. She cannot understand the situation is serious. But J-M does. “I am arrestin’ you for ze future mis-markin’ of complex instruments,” he yells, waving his hands as he jumps in front of Alden. He joke, but Alden doesn’t laugh. He knows J-M would do anything to make risk department look good. We are ε away from big trouble. That night the risk committee uses Vlad’s model. Their report shows big drop in our marks. “No-one knows what this is really worth,” moans Alden. “We’d better unwind and cut our losses. No Zermatt this Xmas ...” Bonus day is only a month away. So much volatility is difficult to concentrate... At the close I execute the end-of-day Eurodollar hedge and leave lira rebalancing for next morning. When I get to work Alden is popping. “Did you hedge last night?” he yell. “Eurodollars yes, lira no!” I say. “Great!” shout Alden. “Trouble in the Middle East – 7 percentage point drop in the Turkish lira overnight. The Sobranies knocked in. How’d you guess?” “I been learning extreme value theory,” I tell Alden. “Good call, guy!” he say as he squeeze my shoulder. The Sobranies triple and we close out. I make 20 units for the desk. Lidia looks at me with new respect. On bonus day I invite her to dinner at Jean-Georges. “How did you do it?” she smile at me over the Petrus ‘85. I can see our implied correlation is approaching unity and I am ready to early exercise. “Behavioural finance,” I tell Lidia as I take her hand. “The market is like a shy woman who suddenly find she’s beautiful: slow to passion but fiery when aroused...” Soon perhaps I start my own market-neutral hedge fund, offshore. Meanwhile, I hope my story encourage your readers. Yours, D***** B***** Emanuel Derman is a professor at Columbia University and a former head of the quantitative strategies group at Goldman Sachs. This is one in a series of quarterly columns. Email: emanuel@ederman.com
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