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2answers
34 views

Incorrect characterization of spot rate?

Is the t in the red boxed $R(t,T)$ supposed to be the same as the S in the green boxed $R(S,T)$?
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2answers
54 views

Factor immunization for bond portfolio

I'm trying to figure out some kind of immunization using a factor model I developed for interest rates. Here is the basic problem. Let's say that we have a bond portfolio containing $N$ bonds with ...
2
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1answer
33 views

Positive VaR when calculation on Total Return Indexes?

I recently saw a VaR calculation, and I was wondering whether that calculation made sense. Here the details: 1. Construction of a total return bond portfolio index. By total return I mean that the ...
2
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1answer
517 views

Bond Portfolio Immunization - Duration Matching

**Question is at the bottom** Suppose you have a portfolio of bonds A, B, and C with the following characteristics: (the "Frequency" column is the # of coupon pmts per year and also the # of ...
1
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1answer
20 views

Differential equation involving bond price and forward rate

Given forward rate f(t,T) and bond price P(t,T) where $f(t,T) = - \frac{\partial}{\partial T} \ln P(t,T)$, $P(T,T) = 1 = P(t,t)$, T>0 and $t \in [0,T]$ Does it follow that $P(t,T) = ...
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1answer
14 views

convention in borrowing money in a multiperiod model

I have a question concerning the idea of consumption in multi period. The following is given $$C_1=W_0-xS_1+B$$ $$C_2=xS_2-BR$$ where $W_0$ is initial wealth $x$ is the weight on an asset with ...
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0answers
116 views

Integral-differential equation for forward rates

I am struggling in this question: Let $P(t,T)$ denote the price of a zero-coupon bond (with marturity at time $T$) at time $t \in [0,T]$. As usual, at time $t$ for maturity $T$, the forward rate is ...
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0answers
47 views

I want to Derive $P(t)=P(t,T_{n})+\sum_{i=1}^{n}[P(t,T_{i-1})-P(t,T_{i})]$

Derive the pricing formula $$P(t)=P(t,T_{n})+\sum_{i=1}^{n}[P(t,T_{i-1})-P(t,T_{i})]$$directly, by constructing a self-financing portfolio which replicates the cash flow of the floating rate bond. ...
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0answers
153 views

RQuantLib: any difference between FixedRateBond() and FixedRateBondPriceByYield() with flat term structure?

Please, consider the following functions from RQuantLib package: FixedRateBond() ...
2
votes
0answers
107 views

How to price zero coupon bonds with the Monte Carlo method?

Im trying to calculate monthly ZCB bond prices with a fixed maturity T, over a period of months via Monte Carlo methods. Here is my attempt: For the first month, the price is $P_{t_0}(0,T) = ...
2
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0answers
137 views

How to determine risk-free rate of Ecuador?

I have a question in determining the risk-free rate of Ecuador. For developed countries like United States and Great Britain, the risk-free rate can be obtained in financial database such as Reuter or ...
2
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0answers
154 views

What is the highest frequency greek for options on futures on bonds?

I'm considering exchange traded options of futures on bonds. Options on bond futures are usually American, thus the Black model is out of question. Which is the most imporatant Greek with respect to ...
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0answers
19 views

Please recommend a book regarding Monte Carlo simulation in OAS

I couldn't find a book that explains in details how to use Monte Carlo Simulation to generate a number of interest rate scenarios. And then based on the interest rate scenarios, how to calculate the ...
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0answers
64 views

Differential of stochastic term

Question 1: How does one come up with the equation in the red box below? It looks like some kind product rule, but I'm not sure how to apply Ito's lemma here. Bjork doesn't seem to explain it ...
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0answers
9 views

Annuity Duration Based on Closed Derivative is half of Effective Duration?

I am analyzing an annuity with a stub. I calculate the effective duration as (P(-10bps) - P(+10bps))/(2*Principal * (.001)) I then take the derivative of the standard annuity formula discounted by ...
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0answers
74 views

Provide a bond pricing differential equation and invoke Feynman-Kac

Grateful for any assistance. Consider the process: $dZ=r(t)Z\,dt$ , where $r(t)$ is stochastic and $Z=Z(r,t;T)$ is a zero coupon bond. Provide a bond pricing differential equation and invoke ...
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0answers
80 views

Bond pricing with HJM simulation

I'm using Glasserman 3.16 and 3.17 algorithm to price bonds. The algorithms evaluates the forward rates and the discount factor $B(0,t_j)$. My question is: How can I price bonds in a future time? I ...
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0answers
11 views

Amortizing Bond QuantLibXL

I would ask if anybody knows how to do get the NPV of an amortizing bond with QuantLibXL in the most automated way. I found some solutions but are very close to a manual calc, say, pass the vector of ...
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0answers
13 views

Are the converses of these propositions on forward rates and bond prices true?

The class notes: Are propositions 1 and 3 converses of each other? If not, are their converses true? Why or why not? It seems like the converses should be true by the following: ?
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0answers
27 views

How to prove following order?

Consider a consol bond, i.e. a bond which will forever pay one unit of cash at $t = 1, 2, . . ..$ Suppose that the market yield $ y$ is constant for all maturities. (a) Compute the price, at $t = 0$, ...
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0answers
47 views

Duration calculation for perpetuity with continuous compounding

Let's say we have a continuously compounded perpetuity. Does macaulay duration = modified duration? I've read from wikipedia for Bond Duration that macaulay duration = modified duration for ...