'
The Virtual Board
Winter 2001 Questions
Q: Prof. Veronesi:
I don't understand your Harr.xls spreadsheet.
One period zero
t=0 t=1 t=2 t=3
How is it that a one period zero has 4 periods for prices? It seems like that would be a four period zero. Or is this a 1 year maturity and each node is .25 years?
A No: The question asks to find the evololution of the one-period zeros, given the evolution of interest rates. So, given the tree for interest rate, what is the price of one-period zero AT TIME t=3, t=2, t=1 and t=0? Figuring out the evolution of these prices is important to then solve the question about the option (given that the payoff at maturity is the difference between the price of a one-period zero and the strike).See also the teaching notes 4 (Addedum, example on page A24)
My E-mail of
Hi all,
A few points:
(1) The reading for the assignment for next time is Jorion Ch 7.1-7.2, Jorion Ch. 9.3 -9.4 (the page numbers in the current assignment is incorrect. By the way, the whole chapter 9 is interesting).
(2) No need to read the LTCM reading for the assignment (we will do it later on)
(3) There has been a change in terminology in Jorion's book: He now calls "Component VaR" what we called "Incremental VaR" in class. The term "Incremental VaR" is reserved for the change in VaR that one would obtain by increasing the portfolio by a given position "a". You can check the differences in Chapter 7.1 and 7.2 mentioned above.
Q: The course packet has TN #3 and the Jorion VaR readings assigned for this Wednesday while the "Assignment for Class #3" handout excludes these readings. Are these two readings to be done for class three or only the two listed in the handout?
A: Only the ones in the assignment should be read. However, the class of this week will also go over my TN3 and Jorion VaR. If you want to get the most out of the lecture, you can read the material beforehand.
Q: Also, I think there is a typo in TN#3 bottom of page 53. In your variance equation, shouldn't it be 2x5.64x7.629x the stand devs and corr? You don't have the "2". Please verify if the "2" should be in there as it may be important for the homework.
A: YES! Thank you for catching the typo
Spring 1999 Questions
On the course 1999
Date:
Dear professor Veronesi, I have a question about hedging strategy.
In the last class, you mentioned in "stack hedge strategy" of Metallgesellschaft,
- Company will Long Short Term Futures (2months)
- Close the open position
- Repeat the above
I'm confused because I may have fundamental misunderstanding in the hedging strategy. Metallgesellschaft had long term oil delivery contract, so I thought it should have entered "short hedging strategy" as described in page 31 of JOHN C. HULL text book.
A: As we said in class, if you have a long term *delivery* contract of oil, it is as if you have a SHORT long-term forward position (you have to deliver oil at a fixed delivery price). Hence, you need LONG positions in futures to hedge this short position. Remember always when you lose money: in the original delivery contract you lose money if you have to sell oil for a price ABOVE the delivery price, hence you lose when the price goes up. You need to take positions that give you money when the price goes up, and this is a LONG position.
To: pietro.veronesi@gsbpop.uchicago.edu
Subject: homework 1
Dear Professor Veronesi,
In problem 2 of part 1, should the 5th line read "December 1993" instead of "December 1994" - i.e. the stacked hedge is June to Dec 1993, and then Dec 1993 to June 1994.
A: YES. Thank you.
Date:
Subject: Possible corrections?
Professor,
I think I found some errors in the packet:
1. Page 28, 4 lines from the bottom, shouldn't the second C1,u be C1,d?
2. Page 44, 5 lines from the bottom, should the (T-t) be a subscript.
3. Page 55, 5th bullet point from top, should April 00 be March 00?
A: YES TO ALL. Thank you
Old Questions
Q: I haven't taken Bus 337. May I take this course?
A: No, unless you convince me that you have a backgroung
in derivative security pricing at the level of B337.
Q: Since I'm graduating this quarter I need provisional grade for 438. Dean
of Students is saying I have to confirm whether or not I can get it and if so
what the condition is.
A: You can get a provisional grade. Hand in memos, homeworks
and participate, you will get the passing grade.
Q: ON HOMEWORK 2: 1. Question 2 asks us to use Black-Scholes
to value the Gold Trust, but the case does not seem to give enough information
about the payoff. Specifically, it says that investors get 3% of output when
spot price is $399 or below, and 10% if spot price is
above $1,000, but what if the spot price is between $399 and $1000?
2. I'm having trouble in putting this question into the Black-Scholes options framework. Can you give me some pointers on
what I would use, say, for the strike price? This problem seems very unlike
anything we covered in 337.
A: Follow the instructions in the exercise. For each oz of gold produced, you are getting a particular percentage of that oz, depending on the price of gold at that time. If S is very high, you get 10% of production. If it is very low, you get 3% of production. In the middle, you may assume it goes up linearly. So? What is the dollar payoff at maturity? How can you express this using an option valuation method? Be creative. Another Hint: Maybe you want an approximate solution!
Q: In TN#2, variances and correlations are computed using DIFFERENCES in
variables. Yet the hedging analysis yields formulas that involve variances and
correlations of FINAL values of the variables. So, why use DIFFERENCES? Is
there an underlying assumption about the stochastic process that the variables
follow? For example, have you asumed that the
increments are i.i.d.? In this case, the variance of
the terminal value should equal the sume of the
variances of the increments (not the increments themselves). Please explain.
A: The formula for the hedge ratio on page 10 of TN #2 uses *predicted* covariances and variances, i.e. they are conditional on time
t information. The point now is to see how we can estimate them. Using levels -
cov(G,F)
- is generally not good, because the series may be non-stationary. With
financial variables it is better to estimate these
quantities using variables in first differences or (even better) using log
returns. In any case, the hedge ratio is H = - Cov(F_T,G_T)/Var(F_T) = - Cov(F_T-F_t, G_T-G_t)/Var(F_T-F_t) = - Cov(delta F_T, delta
G_T)/Var(delta F_T) where I can do the above because
the prices F_t and G_t are
known at the time of devising the hedge. First difference series have much
better properties: in particular, it is possible to justify the assumption
about OLS estimation if you regress (delta G_T) over (delta F_T). This has been
discussed in the review session (or it will next week).
Q: Do you plan on distributing solutions to the homeworks?
A: If a question of the homework is "case specific", in the sense
that numbers etc. are taken from the case, then I will discuss the solution in
class (during the case analysis) but I will not hand out solutions to
the exercise. If instead the exercise is unrelated to the case material, then I
will hand out a solution.
Last updated