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6

Day-count conventions. You can't live with them, you can't live without them. The reason the prices differ is that the pricing engine can't calculate correctly the time over which the first coupon is discounted, and thus it gets slightly different discount factors to apply to the coupon amounts. Please sit down, it'll take some explaining. Ultimately, both ...


6

This is called on the run/off the run arbitrage, a type of convergence trade. The basic idea is that as the liquidity premium disappears for the on-the-run issue, the price will fall and converge to the price of previous issues. Here are a couple papers - http://people.stern.nyu.edu/lpederse/courses/LAP/papers/SearchBargaining/VayanosWeill.pdf ...


6

I'm familiar with the library, but not with the way it is exported to R. Anyway: gearings are optional multipliers of the LIBOR fixing (some bonds might pay, for instance, 0.8 times the LIBOR) and spreads are the added spreads. In your case, the gearing is 1 and the spread is 0.0140 (that is, 140 bps; rates and spread must be expressed in decimal form). ...


5

As John already mentioned the formula for calculating yield to maturity is independent of any risk-related numbers. Its just the connection between coupons, time and price. In theory, default-risk can be seen as already incorporated in the yield. The yield spread between the bond and a comparable investment without default risk is a measure for the default ...


5

The general idea is to bootstrap the discount factors in the correct order, based on the data you have given. I'm going to make some assumptions that your bonds are paying annual coupons. The longest maturity is 2.5 years, meaning you need discount factors for 6M, 1.5Y and 2.5Y. The 6M deposit has a rate of 5%, this tells you that you should use the 5% rate ...


4

Note that $\frac{F(0,s,T)}{F(0,t,T)} = \frac{T-t}{T-s}\frac{B(0,s)-B(0,T)}{B(0,t)-B(0,T)}$ and $\frac{F(s,s,T)}{F(s,t,T)} = \frac{T-t}{T-s}\frac{B(s,s)-B(s,T)}{B(s,t)-B(s,T)}$. Multiplying the numerator and denominator of the last expression with $B(0,s)$ and noting that $B(0,s)B(s,u)=B(0,u)$ (investing one Dollar for $s$ years and then for another $u-s$ ...


3

The intuition behind Macaulay Duration is the average time it takes to get all the cash flows from a bond. Think of it as computing the centre of gravity for a see-saw. You can find the image depicting the same here: This should immediately tell you that Macaulay Duration for Zero coupon bond is the maturity of the bond. In continuous discounting ...


3

I would answer your question with no. First: what do you need the risk free rate for? If you want to price equity derivatives then probably a short money market rate would better fit this purpose. Second: the maturity. Look at yield curves. The short end is usually at a very different level than the 10 year rate. So two times no. A small "no" for ...


3

Dirty bond price refers to the price of a bond that reflects the interest that has accrued since the issuance of the bond or last coupon payment. It has nothing to do with how you discount cash flows but just whether accrued interest is priced in or not. Thus, dirty and clean bond prices apply to all bonds that pay intermittent cash flows.


3

Despite seeing one of the answers as having been chosen as the desired one, I like to offer a different perspective: Whether the yield to maturity can be derived from a bond's price in a rather identical fashion, regardless of the inherent risks is, imho, not the point of the OP, given I understood the question correctly. The yield of a bond with risk ...


2

The way you are trying to solve these equations makes assumptions about the rates less than 10 years and therefore the shape of the yield curve. \$90 is the value of 8% coupons plus a 10-year zero-coupon bond. \$80 is the value of the 4% coupons plus a 10-year zero-coupon bond. 8% coupons are worth twice 4% coupons over the same period, regardless of the ...


2

The value it is giving you is incorrect. This is known because every option-adjusted spread calculation in existence is incorrect. I am joking here, but only a little bit. They really are all terrible. In any case, there do exist different types of OAS calculations, so you have to know which stochastic model this external utility claims to be using. ...


2

The conversion factor associated with each bond the futures' delivery basket is constructed such that the invoice prices of the bonds are identical under the assumption that the yield curve is flat at the level of the futures' notional coupon. Therefore, the bond with the highest duration will be the CTD when yields are above the notional coupon and the bond ...


2

First, I am not sure which exact statement was made. Also, you cannot just say "without CF" because you are essentially creating an artificial market with messed-up utility. In summary the cheapest-to-deliver bond is: The bond that results in the smallest loss or greatest profit for the futures seller. Futures sellers have to buy the bonds they are going ...


2

This is wrong: effectiveDate / Valuation_date = 10 May 2014 Good that you included the ISIN, which states that the effective date (as contrasted with the issue date) was a few days after 03 May 2013.


2

Let's approximate the time to maturity to be 3 years and 10 months. Assume that coupon is paid on March 6 each year. Let face value $F=100$ and coupon $c=0.07375F$. Let the discount factor be $d(0,T)=e^{−r T}$ where $r=0.06535$. The price of the bond is $$ce^{−10/12 \bullet r}+ce^{−22/12 \bullet r}+ce^{−34/12 \bullet r}+(F+c)e^{−46/12 \bullet r}=103.24 \; ...


2

Your overall approach is correct. However to my knowledge it is formally more appealing to work with a parameterized and smoothed yield curve. Basically one assumes that the yield curve can be described by a smooth function $r(t,\alpha, \beta,\gamma)$ (mostly of three parameters) Given a set of market data $Y(t,T_1)\dots Y(t, T_n)$ one looks for ...


2

Bond Price Dynamics I do not know the source of the bond dynamics you show above but seeing how we are dealing with an affine model there is a very elegant way to derive those. Due to the model being affine the bond price is given by $$P(t,T)=A(t,T)e^{-r(t)B(t,T)}$$ you can find the exact formulas for $A(t,T)$ and $B(t,T)$ in this document (or just read ...


2

Normally, you do indeed add a credit spread $s$ to the risk-free spreads to price the bond. That is, if the coupons are $c_i$ at times $t_i$ and the notional is $Y$ then you price it as $$ R\!B(t) =Y \exp{\left( -\int_t^T s(x)+r(x) dx \right) } +\sum_{i \ni t_i>t}^{N_c} c_i \exp{\left( -\int_t^{t_i} s(x)+r(x) dx \right) } $$ Normally you have too ...


1

You represent your bond as a vector of 4 equivalently weighted parameter and try to find the optimal representation for the 1-norm. Parameters are not equivalent, more than that they have non linear ties, it is not okay to represent a bond with a set of common parameters. If you have a family of bond with the same Coupon, Issue Date, Volume and different ...


1

As Richard pointed out you will need the implied volatility (iV) for the option on the stock, the iV of an option with the zero bond as underlying and the iV of an option on the stock and zero bond combined (most likely an OTC derivative). You can then easily derive the implied correlation : impliedCorrel = (pow(iV[stock],2) + pow(iV[zBond],2) - ...


1

as in the question about average/implied correlation to do this in a straight way (in a perfect world where all this were given) you would need: immplied vol for the stock, implied vol for the bond and implied vol for an option on a portfolio/basket that contains both assets. If you get a quote for the latter then this sounds possible. I have never seen an ...


1

If you do not know anything about the dynamics of you short-rate $r_t$, then there is no way to express the price of the zero coupon bond better than what your already have: $ P(t,T) = \mathbb{E}^Q\left[\left. \exp{\left(-\int_t^T r_s\, ds\right) } \right| \mathcal{F}_t \right] $ You can use a model given in this page where you should be able to find close ...


1

For the sake of completeness: Taking pbr142's comment into account and working in the setting you described. Set $f(C,y)=Ce^{-y} + 2Ce^{-2y} + 3Ce^{-3*y} + 300e^{-3y}$. Write $B(C,y)$ instead of $B$. Applying the quotient rule to $\frac{\partial D(C,y)}{\partial C}$ with $D(C,y)=\frac{f(C,y)}{B(C,y)}$. This leads to the following expression ...


1

Like Aksakal already mentioned in his comment it might depend on the duration formula you use. (see e.g. the wikipedia page or here) It can also depend on the type of instrument as mentioned by Richard. This topic has also been already discussed on the Wilmott Forum (their proposed solution is a reverse floater) Theoretically bonds with embedded options ...


1

Assume we have $r(t)$ continuously compounded spot rate for maturity $t$. The price of the 2-year bond with semi-annual coupon $C$ is known to be $P$. We already have $r(0.5)$ and $r(1)$. We need $r(2)$ and $r(1.5) = f(r(1), r(2))$. Then $$ P = C [e^{-0.5 \times r(0.5)} + e^{-r(1)}+e^{-1.5 \times r(1.5)}] + (1+C)e^{-2 \times r(2)} $$ Using linear ...


1

Simply speaking, return means relative amount of extra money earned after investing of some amount of money: Return = $\frac{Received}{Invested}-1$. If you invested \$100 and received \$100, this means you have zero return (\$100/\$100-1). If you invested \$100 and received \$110, your return in 10% (\$110/\$100-1 = 1.1-1 = 0.1 = 10%). Next step is ...


1

(a) is false Consider a zero coupon bond. Yield to maturity clearly exceeds the coupon rate, but $$ Y_\text{current} = 0 = \text{Coupon} $$ while the question asks about a strict inequality.


1

The discount rate that you use to compute the price of the bond is a parameter that you use during the computation of both types of valuations (clean or dirty); it is the rate you use to discount the cash flows. The only difference between clean and dirty price is that the clean price removes the accrued interest since the last coupon. Hence, the discount ...


1

Just to clarify, the periodic coupon is $C_{\min} + \max(0, \text{perf}_i -1) $ or is it actually $\max(C_{\min}, C_{\min}\cdot(1+\text{perf})) $? I don't think the multiplicative version makes sense. In either case, it's a bond plus a forward striking option. The simple solution is to price it using Black Scholes with forward volatility $\sigma(t_i,t_j)$. ...



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