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In section 2.5 he describes an example of arbitrage-free pricing (attached below). I have a pretty solid understanding of how we arrived at $K' = K\frac{1+d}{1+r}$, but I got a little lost when he mentioned the alternative rate $L$.

Section 2.5

If $L$ is greater than $K$ do we buy or sell yen, and what does he mean by hedging the forward contracts using bonds? I'm very new to quantitative finance and I don't quite understand the steps a firm would take to generate a profit by exploiting this opportunity.

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As a general rule in arbitrage you buy the good which is attractively priced and sell the good which is expensively priced. If someone offers you L=200 Yen for one dollar a year from now and you calculate K'=100 yen per dollar then you buy the yen forward and hedge by selling the synthetic equivalent. And this is what Joshi says: "Of course... buy/sell ... bigger /less".

What may be confusing you is that L and K are expressed in Yen per Dollar which is the opposite how how goods such as widgets are usually priced (Dollars per widget). 200 yen per dollar is a "cheap yen" compared to 100 yen per dollar ("expensive yen"). So you buy the cheap and sell the expensive.

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  • $\begingroup$ Could you elaborate on what the synthetic equivalent is and how it hedges the forward contract? $\endgroup$ – DickyBrown Jun 6 at 22:56

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