chapter 24 advanced topics in international finance

Chapter 24

Advanced Topics in International Finance

Copyright © 2004 Pearson Addison-Wesley. All rights reserved. 24-2

The Currency Hedge Ratio

• The hedge ratio, frequently termed beta (β), is the percentage of an individual exposure’s nominal amount covered by a financial instrument such as a forward contract of currency option.

• Beta is then defined as follows:

β = value of currency hedge

value of currency exposure



• The value of an individual currency position can be expressed as a portfolio of two assets:

– A spot asset (the exposure)

– A hedge asset (a forward, future, or option)

• The hedge is constructed so that whatever spot value is lost as a result of adverse exchange rate movements (Δ spot) is replaced by an equal but opposite change in the value of the hedge asset, the futures position (Δ futures):

Δ position value = Δ spot – Δ futures ≈ 0



• The optimal currency hedge can be found by minimizing the terminal (end-of-period) variance of the two asset portfolio.

• The hedge asset amount as a percentage of the exposure is altered to minimize the terminal portfolio variance.



• Sometimes there are no available futures or forward markets for currencies.

• In these cases the risk manager may substitute a proxy for the underlying currency in a proxy-hedge or a cross-hedge.

• The cross-hedger would likely go through a simple two-step process to determine the optimal cross-hedge:– First, find the currency futures most highly correlated with the

actual currency of exposure

– Second, find the optimal hedge ratio using the covariance between the proxy futures and the actual currency as in the previous model



• A slightly more sophisticated currency hedging strategy than the traditional one demonstrated in Chapter 6 is called delta hedging.

• The objective of delta hedging is to construct a position – the combined exposure of the hedging instrument – whose market values (not terminal values) will change in opposite directions with changes in the spot exchange rate; it is the value of the position at all times which is being managed, not the value of the position only at termination.



• Returning to the basis position valuation principle introduced at the beginning of this chapter: if the hedge is constructed so that the changes in the spot position and hedge position are equal and opposite in currency value at all times in the life-span of the exposure, it is termed delta-neutral.

Δ position value = Δ spot – Δ futures


Financial Engineering and Risk Management

• Financial engineering has come to mean very different things to different people.

• We use it here to describe the use of basic financial building blocks (spot positions, forwards, options) to construct positions that provide the user with desired risk and return characteristics.

• The number of combinations and deviations is indeed infinite.



• The following problem is utilized for the remainder of the chapter:– A US-based firm, Dayton Manufacturing, possesses

a long £1,000,000 exposure – an account receivable – to be settled in 90 days

– The firm believes that the exchange rate will move in its favor over the 90-day period (the British pound will appreciate versus the US dollar)

– Despite having this directional view or currency expectation, the firm wishes downside protection for the event that the pound were to depreciate instead



• Clearly, Dayton could sell the receivable forward at the forward rate, yielding $1,470,000.

• In addition, Dayton could construct a synthetic forward in which the company would buy a put and sell a call (at the forward rate), again yielding $1,470,000.

• A firm would undertake this relatively complex position if it altered the strike prices from the forward-ATM (at the money) and was able to make a slight premium (net) on the purchase and sale of the options.

24-11

Exhibit 24.3 Construction of a Synthetic Forward for a Long FX Position

US dollar value ofA/R (millions)

1.401.40

End-of-period spot rate (US$/£)

1.42

1.44

1.46

1.48

1.50

1.52

1.54

1.56

1.42 1.44 1.46 1.50 1.52 1.541.48 1.56

Forward

Uncovered

Buy a put:$1.47 strike

Sell a call: $1.47 strike

$1.47 strike

Instruments Strike Rates Premium Notional Principal

Buy a putSell a call

$1.4700/£ $1.4700/£

$0.0318/£ $0.0318/£

£ 1,000,000 £ 1,000,000


Second-Generation Currency Risk Management Products

• Second-generation risk-management products are constructed from the two basic derivatives used throughout this book; the forward and the option.

• We will subdivide them into two groups:

– The zero-premium option products (which focus on pricing in and around the forward rate)

– The exotic option products (which focus on alternative pricing targets)



• The primary “problem” with the use of options for risk management in the eyes of many firms is the up-front premium payment.

• Although the premium payment is only a portion of the total payoff profile of the hedge, many firms view the expenditure of substantial funds for the purchase of a financial derivative as prohibitively expensive.



• Zero-premium option products are designed to require no out-of-pocket premium payment at the initiation of the hedge.

• This set of products includes what are most frequently labeled the range forward and the participating forward.

• Both of these products:– Are priced on the basis of the forward rate

– Are constructed to provide a zero-premium payment up front

– Allow the hedger to take advantage of expectations of the direction of exchange rate movements



• The basic range forward is constructed by:– Buying a put option with a strike rate below the forward rate, for the

full amount of long currency exposure (100% coverage)

– Selling a call option with a strike rate above the forward rate, for the full amount of the long currency exposure (100% coverage)

• The hedger chooses one side of the “range” or spread, normally the downside (put strike rate), which then dictates the strike rate at which the call option will be sold.

• The call option strike rate must be chosen at an equal distance from the forward rate as the put option strike price from the forward rate.

24-16

Exhibit 24.4 The Range Forward: Hedging a £1,000,000 Long Position


1.401.40


1.42

1.44

1.46

1.48

1.50

1.52

1.54

1.56

1.42 1.44 1.46 1.50 1.52 1.541.48 1.56

Forward

Uncovered

Buy a put:$1.45 strike

Sell a call: $1.49 strike



$1.4500/£ $1.4900/£

$0.0226/£ $0.0231/£

£ 1,000,000 £ 1,000,000

$1.45 strike $1.49 strike



• The participating forward, is an option combination that allows the hedger to take a position that will share in potential upside movements in the exchange rate, while providing option-based downside protection, all at a zero-net premium.

• The participating forward is constructed in two steps:

– Buy a put with a strike price below the forward rate for the full amount of the long exposure (100%) coverage

– Sell a call option with a strike price that is the same as the put, for a portion of the total exposure (less than 100% coverage)

24-18

Exhibit 24.5 The Participating Forward: Hedging a £1,000,000 Long Position


1.401.40


1.42

1.44

1.46

1.48

1.50

1.52

1.54

1.56

1.42 1.44 1.46 1.50 1.52 1.541.48 1.56

Forward

Uncovered



$1.4500/£ $1.4500/£

$0.0226/£ $0.0425/£

£ 1,000,000 £ 531,765

$1.45 strike

Participating Forward


Exotic Options

• This second set of instruments offers alternative pricing, timing, or exercise provisions of the product.

• All of these in some way have altered the valuation principles of the basis option-pricing model; hence the term exotic.

• These products are therefore products only, and not easily reproducible (though generally possible) by the corporate risk manager.


Exotic Options

• The knock-out option, differs markedly from previous products covered.

• The knock-out option is designed to behave like any option, offering downside protection, but to offer only a limited upside range before crossing a previously specified barrier or knock-out level, at which it automatically expires.

• The automatic expiration of the option would occur only after the exchange rate has moved in the expected direction of the hedger (a favorable movement).

• In return for giving up the full maturity period coverage, the premium of the option – being a shorter-term option – is smaller.


Exhibit 24.6 The Knock-Out Option: Hedging a £1,000,000 Long Position


1.401.40


1.42

1.44

1.46

1.48

1.50

1.52

1.54

1.56

1.42 1.44 1.46 1.50 1.52 1.541.48 1.56

Forward

Uncovered


Buy a put $1.4700/£ Barrier: $1.49/£

$0.0103/£ £ 1,000,000

$1.49 Barrier

Put option

$1.47 Strike

Knock-outoption


Exotic Options

• In addition, there are more recent second-generation (possibly third generation) currency derivatives:– Average rate option (ARO)

– Average strike option (ASO)

– Compound option

– Chooser option

chapter 24 advanced topics in international finance

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