
#161




Wow, Adapt doesn't think much of dg approximation:
Has anyone come across questions like this already? I'm guessing the zero difficulty score means either a) too few responses to assign a difficulty b) no one's missed it yet c) bug
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#162




Quote:

#163




The stochastic calculus/IRM questions only appear scary before you actually attempt them. Almost all of my real exam questions on these topics were Ito's Lemma, S^a, and general theory (trivially simple multiple choice) which were all relatively quick and straightforward material. The hardest questions I had were actually Black Scholes pricing questions due to the lengthy algebra. I don't see the pass mark doing anything crazy  I passed under the old syllabus with a 6 and likely would have failed under the new.

#164




I'm completely lost on something with BDT trees. Can anyone help?
Quote:
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In the tree being discussed each branch is one year in length. The general BDT material talks about the yield volatility of 1year bonds (σh) being a parameter necessary for constructing the tree. Any two verticallyadjacent nodes must have a ratio of e^2σh√h. It looks like this example is maybe saying that the same relationship exists here? Even though we're looking at bonds that are two periods in length? I'm missing something crucial I think. 
#165




Your definition of 'h' is incorrect. They are 2year bonds, but the time period from node to node is only 1 year (this is h; "the price of 2 year bonds at time 1). Thus Sqrt(h) = 1 and the adjacent vertical nodes only differ by a factor of e^(2*sigma).

#166




Interesting. Thank you.
The other problem I was having was just inferring how far I could take that relationship between nodes. So is the following correct? If I have a tree like the following with 1year nodes and p* = 0.50, I could determine the yield volatility of twoyear bonds sold at time 4 using just the 1year rates in the red squares? [0.5/A + 0.5/B]/W = [0.5/B + 0.5/C]/X * e^2σ√1 (then solve for σ) I would also get the same yield volatility of twoyear bonds sold at time 4 if I used only the blue squares? [0.5/D + 0.5/E]/Y = [0.5/E + 0.5/F]/Z * e^2σ√1 (then solve for σ) Or if I really wanted to, I could get the same yield volatility of twoyear bonds sold at time 4 with nonadjacent nodes? [0.5/A + 0.5/B]/W = [0.5/E + 0.5/F]/Z * e^8σ√1 (then solve for σ) And just to clarify, this is the same as the yield volatility of 6year bonds sold at time zero after 4 years? 
#167




I clearly only have a tenuous grasp of some of the rules of BDT trees.
In problem 22.14 of the ASM manual we're given a 3period BDT tree that has 3month branches. The yields shown in the tree are all annual yields. We're asked to find the "yield volatility for 6month zerocoupon bonds issued at the end of 3 months". I did this problem wrong, differently, on several attempts, but these are the lessons I've taken away from it. I was hoping someone could confirm them for me. 1. To construct anything using a BDT tree you need to start with yields which correspond to the length of the branches. So in this case we need to take the annual yields shown in the tree, and we need to convert them to quarterly yields. This, as opposed to taking the annual yields shown at 3 months, and splitting them into semiannual yields at three months. 2. When we're asked for yield volatilities we're necessarily talking about annualized yields. Once we compute the prices of 6month bonds at the up and down nodes at 3 months, the solution says that we need to annualize their 6month yields before backing out the yield volatility. I'm afraid I've worded these poorly, but the solution has us following these steps: 1. break the annual yields shown in the tree into 3month rates. 2. construct 6month bond prices at time 3months out of the 3month rates using the normal process. I.e., Pu = (0.5/ruu + 0.5/rud)/ru; Pd = (0.5/rud + 0.5/rdd)/rd. 3. Annualize the yields of these bond prices. yu = (1/Pu)^2 1; yd = (1/Pd)^2 1. 4. Extract the yield volatility as ln(yu/yd)/(2√0.25). And my takeaways were: 1) you have to work with yields that match the length of each period, and 2) the yield volatilities require us to annualize the yields of whatever we're looking at. Does that sound right? Last edited by The Disreputable Dog; 06032017 at 11:32 AM.. Reason: a words 
#168




Are you working problems at the end of sections from the Mahler manual? Any other problems?

#169




I've been doing all of the ASM problems, and supplementing with ADAPT quizzes if I wanted additional practice. The only Mahler questions I really sat down and worked were on option Greeks.

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