# Tag Info

I'm not sure I follow your question completely but I will try my best to explain how Bond Futures relate to their underlying contracts. First of all the 5 Year, 10 Year, 30 Year, and Ultrabond Futures that trade on the CME all have a par value of the $100,000. So let's say you hold short a 10 year future that expired with the price of 126.00. The ... 1 A simple example might help. You need to transform your coupon bonds in equivalent zeros. Imagine that you have 5 coupon bonds and you are at the end of 2011: Coupon, Maturity, Price = 5.25% 2012 101.69 Coupon, Maturity, Price = 4.5% 2013 101.52 Coupon, Maturity, Price = 5.5% 2014 104.49 Coupon, Maturity, Price = 5% 2015 103.35 From the first one you can ... 2 Zero coupon rates are outputs, not inputs. As mentioned in the other post, given the parameters (say the initial guesses), you can easily compute the theoretical prices of each bond, which can then be converted into their theoretical yields (standard price to yield conversion). You should minimize the residuals between these theoretical yields and the market ... 1 You really don't even need to put them into matrices, which I feel is confusing you more than helping... For each bond, you have a list of cash flows ($c_i$'s). For each cash flow, you can compute the corresponding discount factor ($d(t_i)$'s). Sum up the discounted cash flows gets you the theoretical price:$P = \sum_i c_i d(t_i)$. Repeat this for every ... 1 It is simply the difference between "today" and the cash flow date in years. A 30-years bond paying semi-annual coupons has 60 cash flows, and each cash flow has its own "TTM". 3 Jojo, once again the paper is about Nelson-Siegel and not Nelson-Siegel svensson (the former allows for one hump whereas the latter for two humps). Jojo, in practice people often start by fixing$\lambda$then estimate the model by OLS and check the squared errors of the model. Then change$\lambda$and repeat the procedure. This is highly efficient, and ... 1 Say at time$t$, the cash flows of some bond$b$can be described by the two vectors$\textbf{c}$and$\textbf{t}$, containing information about the value of the nominal cash flows and cash flow times in years, respectively. Similarly, if we have a range of bonds$B = \{ b_1, ..., b_n\}$that trade on a market, the matrices$\textbf{C}$and$\textbf{T}$... 0 if I read it correctly the paper you mention is about Nelson-Siegel and not Nelson-Siegel Svensson. The easier way to cross check it is to simply start by fixing theta and estimate the remaining parameters by OLS. If that works, then the optimization algorithm should work similarly. Below I attach a simple matlab code that does it and that you can adapt for ... 2 The Feynman-Kac theorem can be used in both directions. That is, If we know that$r_tfollows the Ito process as described by the following stochastic differential equation \begin{align} d{{r}_{t}}=\mu ({{r}_{t}},t)dt+\sigma ... 2 Bond Prices Assume that the short rater_tfollows the Ito process as described by the following stochastic differential equation \begin{align} d{{r}_{t}}=\mu ({{r}_{t}},t)dt+\sigma ({{r}_{t}},t)d{{W}_{t}^{P}} \end{align} we assume the bond price to be dependent onr_tonly, independent of default risk, liquidity and other factors. If we write the bond ... 2 In another solution, the answer is based on replication approach. Here, we provide some other approaches for the valuation of the LIBOR rate, \begin{align} L(T_{i-1}; T_{i-1}, T_i) = \frac{1}{\Delta T_i}\left(\frac{1}{P(T_{i-1}, T_i)}-1\right), \end{align} set aT_{i-1}$and paid at$T_i$, where$\Delta T_i =T_i-T_{i-1}$. Let$E$be the expectation ... 1 Edit for Gordon. First, fix point in time$T_0,...,T_n$whereas$T_1,...,T_n$are the coupon dates and$T_0$is interpreted as the emission date of the bond. At time$T_i$,$i = 1,...,n$the owner of the bond receives$c_i$.At time$T_n\$ the owner receives the face value K.We now go on to compute the price of this bond, and it is obvious that the coupon bond ...