9、面试进行中：投行技术面试 揭开顶级投 ...
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然而Johnny并没有问这个问题，他接着说道：“So what do you learn in the school? Which class do you like best?（那么你在学校里学到了什么？你最喜欢哪节课）”
晓兮暗暗松了一口气，说道：“I am a finance major student. I took a lot of classes in finance and economics， like accounting， corporate finance， options and fixed income securities， macro and micro economics， monetary economics.（我是一名金融专业的学生。我上了很多金融和经济学课程，比如会计、公司金融、期权和固定收益证券、宏观和微观经济学、货币经济学）”
还没等晓兮说完，Johnny好像发现了什么：“Oh， you and the girl coming before you are from the same major， and you two share the same English name.（哦，你和你前面来的那个女孩是同一专业的，你们两个有着相同的英文名字）”
晓兮答道：“Yeah， we study the same major.（是的，我们学的是同一个专业）”
Johnny继续问道：“Do you take most of the classes together?（你们一起上大部分课吗）”
晓兮道：“Yeah， we took most of the classes together.（是的，我们一起上了大部分课）”
Johnny接着说道：“Well， to be fair for the other Alice， I will ask you the same set of questions. Both of you had the options class last semester. Let’s start with options. Do you still remember Black-Scholes formula?（好吧，为了对另一个爱丽丝公平，我会问你同样的问题。你们俩上学期都上过选修课。让我们从选项开始。你还记得 Black-Scholes公式吗）”
晓兮觉得自己不经意将就踩到了Johnny挖的坑里。他这是要那两个Alice直接对比了。晓兮早上刚刚复习了一遍布莱克-舒尔斯模型，她心中暗暗高兴自己蒙对了题，答道：“Yeah。”
“Can you tell me the parameters in the Black-Scholes formula?（你能告诉我 Black-Scholes公式中的参数吗）” Johnny问道。
这个怎么可能忘记，晓兮答道：“There are five parameters， stock price， strike price， risk-free rate， volatility and time to maturity.（有五个参数，股票价格、行使价、无风险利率、波动率和到期时间）”
Johnny把一张A4白纸和一支铅笔递给晓兮，继续问道：“Can you please write down the formula?（你能把公式写下来吗）”
晓兮很快就在纸上把这个公式写了出来，Johnny看了一眼说道：“Let us say that a client comes to us and want to buy a European call option on shanghai composite index at 3000 expired in 3 months from today. Let’s work out the pricing. what is the Shanghai Composite Index level today?（比方说，一位客户来找我们，并希望购买从今天起 3个月后到期的上海综合指数行使价在 3000点的欧式看涨期权。我们一起来算一下价格。今天上证指数是多少）”
沪市从去年下半年开始猛涨，班上有好几个同学都从家里拿了钱，开始炒股，晓兮虽然没有钱去投资股票，但是她也密切关注股市，她马上回答道：“Around 2700.（大概2700）”
Johnny继续问道：“What is the risk free interest rate?（无风险利率多少）”
晓兮前几天刚读过关于上海银行业同业拆放利率从一月四号开始运行的新闻，这个她很有自信，她说道：“3M shibor is about 2.8%. we can use that.（3M shibor约为2.8%。我们可以使用它）”
Johnny紧接着问道：“Can you explain what is shibor?（你能解释一下什么是shibor吗）”
“Shibor is Shanghai interbank offering rate. It is the average of the interest rates that each bank needs to pay if they want to borrow from another bank.（Shibor为上海银行间同业拆借利率。它是每家银行要从另一家银行借款需要支付的利率的平均值）”
Johnny继续问道：“Why do you think the government spends all the efforts? Why do we need Shibor?（您认为政府为什么要弄出这么一个东西呢？为什么我们需要Shibor）”
这个也在新闻报道里面有，晓兮记得很清楚:“ Because a lot of fixed income products need a reference rate for pricing. For example， in US， most of the fixed income products， such as interest rate options， mortgage securities， are indexed to LIBOR.（因为很多固定收益产品需要一个参考利率来定价。例如，在美国，大多数固定收益产品，如利率期权、抵押贷款证券，都与 LIBOR挂钩）”
Johnny继续问道：“Now we only need volatility. If we compare the volatility of Shanghai composite and SP500， which one is higher and why is that?（现在我们只需要波动率。如果我们比较上证综指和标普500的波动率，哪个更高，为什么？）”
晓兮想了一想，答道：“SP500 should have a lower volatility. If we compare the market cap， the stocks in SP500 have a larger market cap than those in Shanghai. Large cap stocks have less volatility. Also， US stock market has been there for many years. They have better system， so less risk.（标普500应该具有较低的波动性。如果比较市值的话，标普500的股票市值比沪市的要大。大盘股的波动性较小。此外，美国股市已经存在多年。他们有更好的系统，所以风险更小）”
Johnny完全不让晓兮有喘息的机会继续问道：“Let us assume that the volatility is 20%. Can you calculate the option prices now?(让我们假设波动率为 20%。你现在可以计算期权价格吗)”
晓兮正要下笔开始算，突然想到这个公式还有几个前提条件，她说道：“No， there are some assumptions for Black Scholes formula. One of them is that you can buy and sell any amount of shares，but you can only long stocks in China.(不，Black Scholes公式有一些假设。其中之一是你可以做多和做空任意数量的股票，但你只能做多中国的股票)”
Johnny继续绷着脸问问题：“It is good that you realize that before you start working. What are the other assumptions?（在开始工作之前就意识到这一点很好。其他假设是什么）”
晓兮答道：“There are five other assumptions. First， the risk free rate is constant. Second， the stock price follows geometric Brownian motions with constant drift and volatility.（还有其他五个假设。首先，无风险利率是恒定的。其次，股票价格遵循具有恒定漂移和波动性的几何布朗运动）”
还没等晓兮说完，Johnny就打断了她：“All right. You don’t need to say the rest. I understand you know them all. Now let us assume that it is okay to use the Black-Scholes formula. Can you calculate the option price now?（好的。你不需要说剩下的。我知道你知道所有的假设。现在让我们假设可以使用 Black-Scholes公式。你能计算出期权价格吗）”
晓兮马上开始在白纸上写，她开始计算d1，各个部分都很简单，除了那个自然对数，等于1这大家都知道，但是并不是常用的，晓兮一下子并不知道是多少。这时晓兮抬头看了Johnny一眼，发现Johnny也一直都在看着他。
Johnny面无表情，但是语气严厉：“You must have taken your calculus class. Don’t tell me you don’t know how to calculate that.（你一定上过微积分课。别告诉我你不知道怎么计算）”
晓兮脑海中出现的方法只有泰勒级数，于是她就开始套公式开始算。当她把d1算出来时，Johnny突然说道：“You can stop here. I have got an idea of you math skill. Let us move on to the next question. Can you explain to me what is delta?（你可以在这里停下来。我对你的数学能力已经了解啦。让我们继续下一个问题。你能给我解释一下什么是delta吗）”
这个晓兮当然知道：“Delta measures the sensitivity of the option price to the changes in the underlying stock prices. For example， if a call option’s delta is 0.4， it means if the underlying stock price increases by 1， the options prices will increase by 0.4.（Delta衡量期权价格对标的股票价格变化的敏感度。例如，如果看涨期权的 delta为 0.4，则意味着如果标的股票价格上涨 1元，则期权价格将上涨 0.4元。）”
Johnny还是一贯的紧追不舍：“why do I bother with delta? Why do I need it?（为什么我需要delta）”
晓兮答道：“If you have an option and want to hedge it， delta tells you how many shares of stock you need.（如果您有期权并想对其进行对冲，delta会告诉您需要多少股股票）”
Johnny继续问道：“Can you estimate the delta of the index option I specified just now?（你能估算一下我刚才说的指数期权的delta吗）”
晓兮答道：“Delta is N(d1). N(d1) is N(-0.933). We know that 1 standard deviation covers 68%. So N(-1) is about 1 minus 0.68 divided by 2. It is 0.16. Delta is 0.16.（Delta是0.16）”
Johnny并不认同这个答案，他说道：“That is N(-1)， not N(-0.933). Is it larger or smaller than 0.16?（你的是估算，实际值是大一点还是小一点）”
晓兮急忙修正答案：“Smaller than 0.16.（小一点）”
然后马上意识到说错了：“Sorry， larger than 0.16.（对不起，是大一点）”
Johnny继续问道：“Let’s say that I sold 100 such options at 25. Let’s assume that delta is 16 so I bought 16 shares of stocks to hedge the position. The next day the index drops by 30 points. Can you approximate the option price?（假设我以 25的价格卖出了 100份这样的期权。假设 delta是 16，所以我买了 16股股票来对冲头寸。第二天该指数下跌了 30点。你能估计一下期权价格吗）”
晓兮略微思索了一下，继续答道：“The change in the option price is related to delta， theta and gamma. The delta part is 0.16 times 30. It is minus 4.8. Theta is negative and gamma is positive， but they are very small so we can ignore them. So option price should be close to 20.2.（期权价格的变化与delta、theta和gamma有关。增量部分是 0.16乘以 30。它是负 4.8。 Theta是负的，gamma是正的，但是它们很小所以我们可以忽略它们。所以期权价格应该接近 20.2）”
Johnny继续问道：“Let’s assume that the option price is 20.5. Can you calculate the PnL for the day?（假设期权价格为 20.5。你能计算当天的收益吗）”
晓兮答道：“For the option part， the PnL is 25 minus 20.5 times 100. It is 45. For the stock part， it is 30 times 16 which is 480. So the total PnL is 435.（对于期权部分，PnL是 25减去 20.5乘以 100。它是 45。对于股票部分，它是 30乘以 16即 480。所以总 PnL是 435）”
Johnny说道：“Are you sure this is correct?（你确定吗）”
晓兮又在心里算了一下，还确定了一下符号的正负，她并没有算错啊。
Johnny不等她说话，有继续说道：“You forget something very important. How did you buy the shares?（你忘记了一件非常重要的事情。你是怎么买股票的）”
晓兮有些疑惑，没等她反应过来，Johnny紧接着说到：“You borrowed money to buy shares， right?（你贷款买的股票，对不）”
晓兮心中大喊糟糕，怎么这么重要的条件都给忘了。Johnny并没有给她时间懊悔，又说到：“How do you think the delta will change the next day?（你认为 delta第二天会如何变化）”
晓兮答道：“The call option delta drops with the stock price. Also， the option is out of the money， so its delta also drops with time to maturity. If we add these two effects， we will see a smaller delta.(看涨期权 delta随股价下降。此外，期权是虚值期权，因此它的 delta也会随着到期时间的推移而下降。如果我们将这两个效应相加，我们将看到更小的delta)”
Johnny继续问道：“Do you see any problem with the delta hedging strategy?(你认为 delta对冲策略有什么问题吗)”
晓兮想了想：“You bought the shares at high price and sell them at low price.(你买入股票的价格高，卖出的价格低)”
Johnny说道：“That’s right. How do you solve this problem?（那你怎么解决这个问题）”
晓兮想了想，她并不知道答案，但是也不好长时间不开口，她说道：“Hedging costs money.（对冲是要花钱的）”
Johnny打断了她的话，说道：“That’s right. How do you reduce the hedging cost?（是的，你怎么降低对冲成本）”
晓兮继续说道：“I think you can rebalance your portfolio less frequently.（我认为您可以减少重新平衡投资组合的频率）“
Johnny摊摊手：“Sorry， your boss wants to see a delta neutral book at the end of the day.（可是你的老板想在一天结束时看一个 Delta中□□易账户）”
晓兮继续说道：“You can hedge your option position with other options.（您可以用其他期权对冲您的期权头寸）”
Johnny说道：“You can think about this problem at home. Now let’s try other greeks. I want you to build a short vega long gamma portfolio. How are you going to do it?(你可以回去思考这个问题。现在让我们试试其他greek。我希望你建立一个空头 vega长 gamma投资组合。你打算怎么做)”
晓兮心中大喜，她在准备面试时曾经想过这个问题，她边说边在纸上画图：“Vega and Gamma has the same sign. So you cannot achieve this using just one option， you need to have two. Gamma and vega have the same shape. They are higher for at the money options and lower for in and out of money options. If we choose options at different strikes， net gamma and vega will.（Vega和 Gamma的符号相同。所以你不能只使用一个选项来实现这一点，你需要有两个。 Gamma和 Vega具有相同的形状。它们在平值期权中较高，在实值和虚值期权中较低。如果我们选择不同行使价的期权，gamma和vega将）”
晓兮故意停顿了一下，这也是李逸兰教她的。显示自己并不是事先准备过，而是临时用所学过的只是推出的结论，“ They will have the same sign. This is not correct.（它们有相同的符号，这是不对的）”
晓兮继续在纸上画着，她假装着突然有了个灵感，兴奋地说道：“Gamma and vega also change with time， in different direction. When we are getting close to maturity，（Gamma和 Vega也会随时间变化，方向不同。当期权快到期时）”晓兮故意停顿了一下，“gamma is increasing and vega is decreasing. So we can build a portfolio by buying a short dated call option and sell a long dated call option.（gamma在增加，而 vega在减少。因此，我们可以通过买入短期看涨期权并卖出长期看涨期权来构建投资组合）”
晓兮原来以为Johnny会觉得她回答的很好，没想到他还是面无表情的说道：“Look at your graph， do you really think that gamma increases across all strikes?（看看你的画的图，你真的认为gamma在所有行权价格中都会增加吗）”
晓兮低头一看，糟糕，刚才一激动画错了，她连忙更正到：“No， No. Gamma increases for at-the-money options and decreases for out-of-the-money and in-the-money options.（不不，gamma对于平值期权增加，对于虚值和实值期权减少）”
Johnny突然说道：“Tell me a joke about Black-Scholes.（给我讲个关于Black-Scholes公式的笑话）”
作者有话说
第9章 面试进行中：投行技术面试
