Lecture 16

Lecture 16 - When finance people talk about "The...

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When finance people talk about "The Greeks" they don't mean the lunchcounter on Amsterdam Ave! "The Greeks" in this context refer to the changes in the price of an option when some of the parameters are changed. So what? Consider an example about employee stock options, which can teach you something that your employer doesn't want you to know! Suppose you were granted a stock option long ago, exercising when the stock is $35 but now the company stock is $70. Should you cash in the option now? Your colleagues tell you to wait, the company is about to release some new products, things are going really good, that the latest investment report had a target of $80 per share. If you cash out now, you get $35; if you wait you could get $45 or who knows how much more!?!! This is a realistic depiction: many tech companies have huge "overhangs" of stock options granted to employees long ago, that their employees are just waiting to cash in. But wait is this really smart? What is the stock option worth today? Well, if you cashed it in you would get $35. There is not really any probability to worry about the probability that the stock could fall that far is, by any conventional measure (assuming volatility and returns are not too crazy), almost zero. So in the Black-Scholes formula, the d 1 and d 2 terms are .9999 or more and the option is worth its intrinsic value. So if you exercised the option, you could put $35 of your own money together with the option and buy one share of the company's stock. So how would your portfolio (of one share of stock) compare against one of your co-workers, who has an option with an exercise price of $35 just like you had? Well, if the company's stock goes up by $1 then her option is worth $1 more; just like your stock share is worth $1 more. If the company's stock goes up $10 then her option is worth $10 more, just like yours is. It doesn't matter whether you cash out or not, your wealth is the same. (Apart from things like tax considerations, of course I'm not giving any practical real-world advice since I'm not your accountant!) When the stock price gets so high above the exercise price, the call price approaches its intrinsic value (we did this several chapters before). Another way of putting it, the change in the call price, , is approximately the same as the change in the stock price that underlies the option, . Or we could write that, for very high S, the ratio, , is approaching one. This ratio, , is called . We used back in Chapter 11 to construct trees (and warned you that would be back, like a cheesy horror movie villain who keeps rising from the dead to attack again!).
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Is Delta always equal to 1? No, that wouldn't be very interesting! Delta shows the relative weights of an option versus one share of the underlier, that would have to be held, in order to make two portfolios give the same return (or in order to make a single portfolio riskless). Most
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This note was uploaded on 04/04/2012 for the course FIN 420 taught by Professor Poniachek during the Spring '12 term at Rutgers.

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Lecture 16 - When finance people talk about "The...

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