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Law of one Price

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Chapter 1 Full or dirty price= clean or quoted+price of the bond plus accrued interest. Settlement day is one business day after trading day

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大C是老,小c是新bond比方被replicate的现金流

law of one price (LOOP), absent confounding factors (e.g., liquidity, financing, taxes, credit risk), identical sets of cash flows should sell for the same price

An arbitrage trade implies buying (selling) the cheap (rich) bond and shorting or selling (buying) a replicating portfolio

Coupon strips-C-STRIPS; principal strips P-STRIPS. Discount factor for that date is STRIP price/100

Then F0 + F9 = 100 and 4 x F9 = 1.875. Solving, F0 = 58.33 and F9 = 41.67. Therefore, the price of the 3¾s should be 58.33 x 76.068% + 41.67 x 144.719% which is 104.675

a REPO dealer (A) would sell securities to a counterparty (B) and simultaneously agrees to (A) sells the repo the dealer “lends” the security and borrows cash Clearly then repos serve to finance long positions. Reverse repos serve to finance short positions

[pic 3] [pic 4][pic 5]If the investor uses a repo, buying first the security and then repoing it, he can get funds cheaper because there will be collateral behind the loan A money market fund typically uses repo for investing only

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Chapter2 SWAP The basic structure is the “plain vanilla swap” where a counterparty pay a fixed interest rate in exchange of receiving a floating both calculated on the same “notional”

Spot rate is the rate on a spot loan: only 2 exchanges of cash (borrow(+) and repay principal and interest (-))     𝑟 𝑡 = semi-annually compounded t-year spot rate

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A forward loan is an agreement made today to lend money at some future date at an agreed upon rate called a forward rate 

Par rate: [pic 11] In fact, swap rates are par rates at the inception of the swap. As time passes and rates change, bonds and swaps cease to trade at par

Price increases whenever c>f over period of maturity   decreases whenever c

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if 𝑟 𝑡 is increasing with maturity, forward curve lies above the spot curveIf the term structure of spot rates is flat, forward rates is also flat, spot rate equals the forward.

spot rate is a complex average of all the forward rates

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