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Daneel Olivaw
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I'm trying to follow the replication argument in the first page of the following paper

http://www.math.columbia.edu/~fts/Collateralized%20trade%20pricing%20made%20simple%20v1a.pdf

One can however instead replicate directly with the holder of the zero coupon bond: Consider the collateralized zero coupon bond is valued as $V(t)$. As holder of the bond requires $V(t)$ as cash collateral, the issuer receives nothing net. Note the collateral grows at the rate of $c(t)$. Therefore, putting $e^{-c(T)}$ as collateral, one sees that at time $T$, holder of the bond will find the collateral account containing exist one unit of currency $i$ which is exactly the payoff of the bond.

I'm afraid I don't understand many things. The purchaser gives $V(t)$ to the issuer, and the issuer gives $V(t)$ to the purchaser as collateral. So neither the issuer nor purchaser receives anything net at the start of the contract. Finally, the collateral is paid from the holder of the bond from the issuer, so I don't see how the holder would stand to gain from the collateral rates - shouldn't it be the issuer instead?

Overall, where isif the risk-free rate was not the collateral interest rate, how could we create arbitrage in this argument? Could someone explain in more detail what is going on?

I'm trying to follow the replication argument in the first page of the following paper

http://www.math.columbia.edu/~fts/Collateralized%20trade%20pricing%20made%20simple%20v1a.pdf

One can however instead replicate directly with the holder of the zero coupon bond: Consider the collateralized zero coupon bond is valued as $V(t)$. As holder of the bond requires $V(t)$ as cash collateral, the issuer receives nothing net. Note the collateral grows at the rate of $c(t)$. Therefore, putting $e^{-c(T)}$ as collateral, one sees that at time $T$, holder of the bond will find the collateral account containing exist one unit of currency $i$ which is exactly the payoff of the bond.

I'm afraid I don't understand many things. The purchaser gives $V(t)$ to the issuer, and the issuer gives $V(t)$ to the purchaser as collateral. So neither the issuer nor purchaser receives anything net at the start of the contract. Finally, the collateral is paid from the holder of the bond from the issuer, so I don't see how the holder would stand to gain from the collateral rates - shouldn't it be the issuer instead?

Overall, where is the arbitrage in this argument? Could someone explain in more detail what is going on?

I'm trying to follow the replication argument in the first page of the following paper

http://www.math.columbia.edu/~fts/Collateralized%20trade%20pricing%20made%20simple%20v1a.pdf

One can however instead replicate directly with the holder of the zero coupon bond: Consider the collateralized zero coupon bond is valued as $V(t)$. As holder of the bond requires $V(t)$ as cash collateral, the issuer receives nothing net. Note the collateral grows at the rate of $c(t)$. Therefore, putting $e^{-c(T)}$ as collateral, one sees that at time $T$, holder of the bond will find the collateral account containing exist one unit of currency $i$ which is exactly the payoff of the bond.

I'm afraid I don't understand many things. The purchaser gives $V(t)$ to the issuer, and the issuer gives $V(t)$ to the purchaser as collateral. So neither the issuer nor purchaser receives anything net at the start of the contract. Finally, the collateral is paid from the holder of the bond from the issuer, so I don't see how the holder would stand to gain from the collateral rates - shouldn't it be the issuer instead?

Overall, if the risk-free rate was not the collateral interest rate, how could we create arbitrage? Could someone explain in more detail what is going on?

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Collateral replication argument

I'm trying to follow the replication argument in the first page of the following paper

http://www.math.columbia.edu/~fts/Collateralized%20trade%20pricing%20made%20simple%20v1a.pdf

One can however instead replicate directly with the holder of the zero coupon bond: Consider the collateralized zero coupon bond is valued as $V(t)$. As holder of the bond requires $V(t)$ as cash collateral, the issuer receives nothing net. Note the collateral grows at the rate of $c(t)$. Therefore, putting $e^{-c(T)}$ as collateral, one sees that at time $T$, holder of the bond will find the collateral account containing exist one unit of currency $i$ which is exactly the payoff of the bond.

I'm afraid I don't understand many things. The purchaser gives $V(t)$ to the issuer, and the issuer gives $V(t)$ to the purchaser as collateral. So neither the issuer nor purchaser receives anything net at the start of the contract. Finally, the collateral is paid from the holder of the bond from the issuer, so I don't see how the holder would stand to gain from the collateral rates - shouldn't it be the issuer instead?

Overall, where is the arbitrage in this argument? Could someone explain in more detail what is going on?