Currency Forward Arbitrage and Hedging with Bonds

Summary

The document explains how to compare a quoted currency forward rate with a no-arbitrage rate derived from borrowing and lending rates. When the quoted rate differs, the arbitrageur buys the currency through the cheaper route and sells it through the more expensive route. The example emphasizes that the quote is yen per dollar, so a higher number means yen are cheaper relative to dollars in the forward market.

The hedge uses bonds to construct the synthetic forward position that offsets the quoted contract’s exposure. The answer gives a directional example: if the market offers more yen per dollar than the calculated rate, buy yen forward and sell the synthetic equivalent. It is a conceptual explanation rather than a complete trade specification; it does not detail contract sizes, funding, transaction costs, credit risk, or settlement mechanics.

Key ideas

• Compare the quoted forward exchange rate with the rate implied by interest rates to identify a possible arbitrage.
• Buy the currency through the cheaper forward route and sell it through the more expensive route.
• Interpret the quote convention carefully because yen per dollar reverses the usual intuition about which currency is cheap.
• Bond positions can create a synthetic forward that hedges the exposure of a quoted forward contract.

Tags

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


# 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.

## Answer by nbbo2 (score 1)

https://quant.stackexchange.com/a/54686

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.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.