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First of all it is not clear what exactly you mean by right number, you definitely do not adjust forward swap rate. You probably mean adjusting euro dollar futures contract rates so that you can later use these values to fit the swap/forward libor curve. Reason for adjustment is simple. If you are short ED futures and rates go higher futures price drops ...

3

I have asked myself the very same question when I first read the book. As far as I can tell, the "scalability" condition is only imposed for technical reasons. It simplifies the subsequent proof of the Fundemental Theorem of Asset Pricing in constrained markets. There are several papers that have shown that the theorem is valid for conic constraints. ...

3

I dont think you can see convexity in such a plot, since each of these prices are not observed from a single bond deliverable, but from different coupon bond deliveries. If the delivery was always based on same coupon type bond and quite similar maturity ...

2

The upper bound for the 80 call is C(90) + 10, or 30. At least assuming no arbitrage. Let's start by assuming the risk-free rate is 0 (this isn't a problem, but the math is clearer without it), so we don't have to discount the price. Then, the call price is given by $C(K) = E_t[(S_T - K)^+]$, which gives: \begin{array} \$C(K - 10) &= E_t[max(S_T - (K - ...

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In our lecture, we were told to omit the proof because it was too difficult. Maybe it will help you though if you can read it here:

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Yes, an adjustment has to be made and the reason is that a forward curve now will evolve and not be the same as the future spot curve. For example, a one year forward today is not equal to your spot rate a year hence. So spot curve discount factors have to be adjusted or directly replaced through the forward DFs. Convexity adjustments are already supposed ...

1

Yes, because you're entering into an implicit currency swap. There was an article in "Risk" some time ago on this topic: http://www.risk.net/risk-magazine/technical-paper/1935412/choice-collateral-currency

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