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-   -   Errata for Derivatives Markets (M/FE Textbook) (http://www.actuarialoutpost.com/actuarial_discussion_forum/showthread.php?t=100390)

 Captain Nemo 01-14-2007 11:38 AM

Errata for Derivatives Markets (M/FE Textbook)

I thought it might be useful to provide links to the errata, and to create a thread where any of us can post mistakes we've found in either the first or second edition that are not listed on the errata page.

http://www.kellogg.northwestern.edu/...m/typos1e.html

This is a sort of "master link" to all editions of the book. The link in the introduction to the textbook takes you here.

I have contacted the author about something I noticed in chapter 12 that I think needs addressing and I will post again here when I receive a response.

 Captain Nemo 01-14-2007 08:02 PM

Excerpted:

I noticed something on page 380 that I think is incorrect but is not listed on the errata page.

When you discuss applying the Black-Scholes formula to stocks with discrete dividends, I note that while you input the forward value into the Black-Scholes formula, you don't adjust the volatility to reflect the difference between the stock price and the forward price, as you do in section 11.5, page 365. In Example 12.3, I checked the result, and indeed agree with your result if the volatility in the example is supposed to refer to the relative volatility of the forward, but I would get a different (higher) answer if I were to assume this was the stock volatility and adjust sigma in B-S as well.

Response:

I agree with you that the discussion here (esp at the top of p. 381) should have included a discussion like that on p. 365. I've posted an erratum.

 Captain Nemo 02-11-2007 03:58 PM

I e-mailed the author about these questions awhile back and haven't gotten an answer... Anyone else want to offer an opinion?

(1) Regarding equation 12.12 on page 394 - while this is true for a call option, I believe that it would be false for a put option because the sign of the volatility must be positive, correct?

(2) Regarding the application to the use of compound options to determine the value of an American call option (pp 455-456), I believe that the discussion regarding "modified volatility" applies here as well?

(3) Using compound option parity and regular put-call parity, it seems that one can derive a more intuitive expression for the value of an American call option as a European call option plus a put-on-put compound option with the same parameters as the call-on-put, correct?

(4) At the bottom of page 657, you say that the correlation between dZ and dZ' is rho*dt. Should that instead be the covariance?

 Abraham Weishaus 02-11-2007 08:26 PM

(1) Not sure why not -- negative omega appears both in the numerator and denominator, canceling the negative sign.

(4) Since dZ and dZ' are standard normal, their variances are 1, so it makes no difference.

 Captain Nemo 02-12-2007 07:58 PM

Quote:
 Originally Posted by Captain Nemo (Post 1959224) I e-mailed the author about these questions awhile back and haven't gotten an answer... Anyone else want to offer an opinion? (1) Regarding equation 12.12 on page 394 - while this is true for a call option, I believe that it would be false for a put option because the sign of the volatility must be positive, correct? (2) Regarding the application to the use of compound options to determine the value of an American call option (pp 455-456), I believe that the discussion regarding "modified volatility" applies here as well? (3) Using compound option parity and regular put-call parity, it seems that one can derive a more intuitive expression for the value of an American call option as a European call option plus a put-on-put compound option with the same parameters as the call-on-put, correct? (4) At the bottom of page 657, you say that the correlation between dZ and dZ' is rho*dt. Should that instead be the covariance?
As usual, my timing was impeccable... he responded today.

Quote:
 1. You're right. I think the way to resolve this is that in the denominator, the volatility should be times the absolute value of the volatility, as in 12.9. So for a put, the risk premium is negative, and 12.12 holds with an absolute value in the denominator (which flips the sign if omega is negative). 2. Correct. 3. There are always multiple ways to express these and you're probably right that there is a more intuitive way to do so. 4. On your other message, yes rho*dt is the covariance, not the correlation.

 Marid Audran 01-04-2009 04:50 PM

Exercises 10.4, 10.6, 10.8: Conflicting information?

These exercises provide values for $\sigma, u, d$. Isn't the sole purpose of $\sigma$ in this section to calculate u and d if they are not given? And doesn't the given value of $\sigma$ conflict with the given values of u and d in these exercises?

Thanks in advance. And apologies in advance if I'm missing something, in which case I'll delete this subthread.

 Joe F 01-13-2010 04:43 PM

Quote:
 Originally Posted by Marid Audran (Post 3375813) These exercises provide values for $\sigma, u, d$. Isn't the sole purpose of $\sigma$ in this section to calculate u and d if they are not given? And doesn't the given value of $\sigma$ conflict with the given values of u and d in these exercises? Thanks in advance. And apologies in advance if I'm missing something, in which case I'll delete this subthread.
You're right. The values for $\sigma$ are ignored in the solutions to the questions. The textbook's errata should probably be updated to say that the references to $\sigma$ need to be deleted from the questions. For now, you can just ignore them as extraneous.

 Actuarialsuck 01-14-2010 04:25 PM

Quote:
 Originally Posted by Joe F (Post 4148561) You're right. The values for $\sigma$ are ignored in the solutions to the questions. The textbook's errata should probably be updated to say that the references to $\sigma$ need to be deleted from the questions. For now, you can just ignore them as extraneous.
Why is this errata? If you are given u and d, you should always use those. Suppose you want to use $\sigma$. How do you know which model you should use to define u and d? Does

$u \, = \, e^{(r-\delta)h + \sigma \sqrt{h}}$

or does $u \, = \, e^{\sigma \sqrt{h}}$ (CRR tree)

or does $u \, = \, e^{(r - \delta - \frac{1}{2} \sigma^{2})h \, + \sigma \sqrt{h}$ (Lognormal tree or Jarrow-Rudd binomial model)?

 Joe F 01-14-2010 05:20 PM

Quote:
 Originally Posted by Actuarialsuck (Post 4151593) Why is this errata? If you are given u and d, you should always use those. Suppose you want to use $\sigma$. How do you know which model you should use to define u and d? Does $u \, = \, e^{(r-\delta)h + \sigma \sqrt{h}}$ or does $u \, = \, e^{\sigma \sqrt{h}}$ (CRR tree) or does $u \, = \, e^{(r - \delta - \frac{1}{2} \sigma^{2})h \, + \sigma \sqrt{h}$ (Lognormal tree or Jarrow-Rudd binomial model)?
Yes, I agree that if you are are given u and d, then you should always just use them.

The u and d in the questions do not correspond with the standard binomial model, the CRR model, or the J-R model. The CRR model and the J-R model aren't covered until Chapter 11 anyway, so we wouldn't expect them to appear in questions at the end of Chapter 10.

For Problems 10.4, 10.6, and 10.8, the textbook uses what we could call the "arbitrary" method, meaning that someone just made up values for u and d. The arbitrary method is valid (and frequently appears on the exam!), but there isn't any $\sigma$ used as an input to it, so including $\sigma$ in the problems seems misleading to me.

 Actuarialsuck 01-14-2010 05:48 PM

I wouldn't say it's arbitrary. I listed three models, there are likely others and the author might even be able to provide support for them. I think what he's testing here is your ability to know to use u and when those are given. You call it misleading, I call it knowing what to use when :)

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