# Hedging With Zero Coupon Bonds from The Concepts and Practice of Mathematical Finance by Mark Joshi

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 $$L$$.

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.

## 1 Answer

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.

• Could you elaborate on what the synthetic equivalent is and how it hedges the forward contract? Jun 6, 2020 at 22:56