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percent price change ≈ −modified duration × yield change Example Consider a bond whose modified duration is 11.54 with a yield of 10%. If the yield increases instantaneously from 10% to 10.1%, the approximate percentage price change will be: −11.54 × 0.001 = −0.01154 = −1.154%. Source https://www.csie.ntu.edu.tw/~lyuu/finance1/2008/20080227.pdf


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At risk of sounding pedantic, I don't think cheat sheets are the way to learn things. May I suggest reading the following book for a relatively quick but quite robust introduction to linear IR derivatives and the current market practice: http://www.tradinginterestrates.com/ Not sure if your goal is quantitative analysis or trading/portfolio management. If ...


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The answer to your question clearly fills entire book shelves, not just books. I can try to give you a brief overview and answer regarding short rate, the simplest interest rates to be modelled. Typically, you model the short rates $(r_t)$ from which you obtain zero-coupon bond (ZCB) prices. Then, you can price zero-coupon bond options (ZCBO) which allow ...


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Sorry I am bit late to the party. Just saw your post while trying to write my own black model. I am going to the mistake is a typo in dplus d_plus = ((math.log(F_0 / y) + 0.5 * vol * vol * expiry)/ vol / math.sqrt(expiry)) Should be: d_plus = ((math.log(F_0 / y) + 0.5 * vol * vol * expiry)/( vol * math.sqrt(expiry))) Warm Regards, Varun


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Let the first coupon be fixed at c, and consider the duration of the bond immediately thereafter. At this point $L_(0,6)$ can move. Now in your notation you should find that $$P=N(1+c/2)/(1+L_(0,6)/2)$$. Now if you calculate $(1/P)dP/dL$ you get $1/2* (1/(1+L/2))$ which is 1/2, discounted for 6 months, where $L=L_(0,6)$.


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Under the Rendleman-Bartter model, a closed-form formula exists for the zero-coupon bond price. However, it is very complex involving Bessel functions and complex numbers... Deriving the formula is actually the purpose of a paper by Uri Dothan called "On the term structure of interest rates" that you can find here: https://www.sciencedirect.com/science/...


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The first method assumes that the value of a floating leg at libor flat is 100. This contains an inbuilt assumption that the discount rate is Libor flat, which is an assumption that used to be made. Nowadays , we discount cash flows at Fed Funds (or Eonia in Europe), so the second method is better: first replace the floating rates by their forward rates, ...


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To put it in simplest terms, take the current effective overnight fed funds rate. Lets Say today its 2.38, and lets say the market is projecting that at next months FOMC meeting in 30 days the fed is going to cut rates .25 bp and then leave rates unchanged there after. That leaves the projected fed funds rate over the next 90 days to be roughly 30 days ...


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You know the bond price formula takes this form: $P \left( t, T \right)= A \left( t, T \right) e^{ -r_{t} B \left(t, T \right) }$ Now apply Ito's lemma, so you will get after some manipulation: $\frac{dP}{P}= \left(\frac{1}{A} \frac {\partial A}{\partial t} -r \frac {\partial B}{\partial t} - \kappa \theta B + \kappa r B+ \frac{1}{2} B^2 {\sigma}^2\right)...


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When interest rates go up, there are two effects that explain the positive link with the increase in the price of a call option (according to Hull). There is the quote: " As interest rates in the economy increase, the expected return required by investors from the stock tends to increase. In addition, the present value of any future cash flow received by the ...


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Please read the Interest Rates Instruments and Market Conventions paper from OpenGamma (https://developers.opengamma.com/quantitative-research/Interest-Rate-Instruments-and-Market-Conventions.pdf). The conventions are implied but it is also worth checking with the counter party/vendor when in doubt.


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Please recheck, from what i can understand this question is trying to test pricing for currency options on currency forwards.Spot price is $0.6868$. If underlying is a currency forward, the underlying price $S0$ would be the forward price calculated using the interest rate parity. $$ S0 = 0.6868*\exp((0.028 - 0.0145)*0.5) $$ ATM options means strike price is ...


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