Chapter

Appendix 4. Stress Testing of “In-the-Money” Options under the Five Scenarios Shown in the Reserves Data Template*

Author(s):
International Monetary Fund. Statistics Dept.
Published Date:
October 2013
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A4.1 All options should, if necessary, first be converted into puts and calls in foreign currency. For this conversion, the strike price is used. For example, the central bank has written a call option whereby the purchaser of the option has the right to buy LC100 million at a strike price of LC90 = $1.001 (in this example, the dollar is a foreign currency to the central bank that wrote the call option). As it is written, this is a local currency call option. In converting it into a foreign currency option, the right to buy LC100 million at a price of LC90 = $1.00 is equivalent to the right to sell $1.11 million (100 million/90) at the same strike price of LC90 = $1.00. In terms of the Template, this will be treated as a put option that the central authorities have written with a notional value of $1.11 million. Similarly, if the central bank has purchased a local currency put option with a notional value of LC200 million and a strike price of LC110 = $1.00, this will be treated as a purchased foreign currency call option with a notional value of $1.818 million (200 million/110).

A4.2 To aggregate the notional values, the options need to be expressed in a common currency. For purposes of this Template, that common currency is recommended to be the one in which the Template data are reported. For example, if the reporting currency is the U.S. dollar, to convert the notional values to U.S. dollar, the current market exchange rates are used, not the strike prices. Suppose, for example, that the central authorities wrote a call option to buy JY1.0 million with a strike price of JY1.4 = LC1.00. Assuming the exchange rate of JY 125 = $1.00, this would translate into an $8,000 call option (JY1,000,000 × 1/125). The strike price should not be used when converting from one foreign currency to another.

A4.3 To sum up, in computing the notional value of the options, neither the current nor the future local currency market exchange rate is used. When options written in terms of a given amount of local currency received or delivered in exchange for foreign currency are converted into foreign currency options, the strike prices are used. When options are written in terms of a foreign currency other than the foreign currency used in reporting the Template data, the market rate between the reporting currency and the foreign currency of the contract should be used to convert the notional value of the options to the reporting currency.2

A4.4 After all options have been converted to puts and calls in the reporting currency (say, U.S. dollars) and maturities have been determined, filling in the Template requires entering the relevant data.

A4.5 In the Pro Memoria section of the Template, five simple scenarios for the local currency exchange rate are used to gauge the potential impact of the options on foreign exchange resources. This appendix illustrates the foreign currency flows under the five scenarios.

A4.6 The first scenario assumes the local currency exchange rate remains unchanged relative to all foreign currencies. The second scenario assumes an immediate 5 percent depreciation of the local currency relative to all foreign currencies and no further change in exchange rates thereafter. The third scenario posits an immediate 5 percent appreciation of the local currency against all foreign currencies and no further change in exchange rates. The fourth and fifth scenarios examine 10 percent depreciation and appreciation, respectively.

A4.7 As noted in Chapter 4 of this document, a foreign currency call option gives its holder the right to buy foreign currency at a given local currency strike price. If the strike price is below the market price, the call option holder can exercise his option and receive (buy) foreign currency at the below-market strike price. Thus, a call option will be exercised, and is “in the money,” when the market price is above the strike price. A foreign currency put option gives its holder the right to sell foreign currency at a given local currency strike price. If the strike price is above the market price, the put option holder can exercise his option and sell foreign currency at the above-market strike price. Thus, a put option will be exercised, and is “in the money,” when the market price is below the strike price.

A4.8 If the central bank buys a call option and then exercises it, this results in an inflow of foreign currency. Similarly, if the central bank writes (sells) a put option and it is exercised, this also results in an inflow of foreign currency. As such, for purposes of this Template, bought calls and written puts are considered long foreign currency positions because their exercise results in an inflow of foreign currency. On the other hand, if the central bank writes (sells) a call option, and if it buys a put option, and they are exercised, this results in outflows of foreign currency. As such, for purposes of this Template, written calls and bought puts are considered short foreign currency positions.

A4.9 In the tables that follow, the convention of expressing the exchange rate as local currency (LC) per unit of foreign currency (viz., LC/$) is applied. That is, appreciation of the local currency is associated with a decline in LC/$; and vice versa, for a depreciation of the local currency. In Table A4.1, these are shown as +5% (depreciation); –5% (appreciation); +10% (depreciation), and –10% (appreciation), respectively, under pro memoria items (2), (3), (4), and (5). Table A4.1 shows the notional value of the options that are in the money at current exchange rates and under the four additional scenarios of currency depreciation and appreciation.

Table A4.1Results of An Illustration of In-the-Money Options and Related Stress-Testing Under Specific Assumptions of Exchange Rate Changes (Nominal Value)
Maturity breakdown (residual maturity, where applicable)
TotalUp to 1 MonthMore than 1 month and up to 3 monthsMore than 3 months and up to 1 year
5. Aggregate short and long positions of options in foreign currencies vis-à-vis the domestic currency
(a) Short position−2850−1000−1250−600
(i) Bought puts−1050−300−350−400
(ii) Written calls−1800−700−900−200
(b) Long positions25001000700800
(i) Bought calls1800800400600
(ii) Written puts700200300200
PRO MEMORIA: In-the-money options
(1) At current exchange rates
(a) Short position−350−300−500
(b) Long position800200300300
(2) +5 % (depreciation of 5%)
(a) Short position−1200−700−400−100
(b) Long position1300400400500
(3) −5 % (appreciation of 5%)
(a) Short position−650−100−350−200
(b) Long position900300300300
(4) + 10 % (depreciation of 10%)
(a) Short position−1800−700−900−200
(b) Long position1800800300700
(5) −10 % (appreciation of 10%)
(a) Short position−1050−300−350−400
(b) Long position700200300200
(6) Other (specify)
(a) Short position
(b) Long position

A4.10 In the tables, the sign (+) is used to indicate inflows of foreign currency; and the (–) sign, outflows of foreign currency.

A4.11 In Table A4.1 the results shown for pro memoria items (1)(a) short position (viz., –300, –50, 0) and (1)(b) long position (viz., +200, +300, +300) at current exchange rates correspond to short and long positions under exchange rates of LC/$ = 100, as depicted by figures that are in italics in supporting Tables A4.2A4.4.

Table A4.2Foreign Currency Flows Resulting from Options Positions with Possible Exercise Date Less Than One Month Hence
Options positionsExchange rates (LC/$)
Strike price (LC/$)Position size ($-million)9095100102.5105107.5110112.5
Currency flows ($-million)
Short Position1000−300−100−300−300−700−700−700−700
Total bought puts300−300−100000000
Bought put93200−2000000000
Bought put97100−100−100000000
Total written calls70000−300−300−700−700−700−700
Written call9830000−300−300−300−300−300−300
Written call1044000000−400−400−400−400
Long Position1000200300200400400600800800
Total bought calls8000100100300300600800800
Bought call931000100100100100100100100
Bought call102200000200200200200200
Bought call10630000000300300300
Bought call109200000000200200
Total written puts200200200100100100000
Written put96100100100000000
Written put106100100100100100100000
Exchange rate change−10−502.557.51012.5
Table A4.3Foreign Currency Flows Resulting from Options Positions with Possible Exercise Date One to Three Month Hence
Options positionsExchange rates (LC/$)
Strike price (LC/$)Position size ($-million)9095100102.5105107.5110112.5
Currency flows ($-million)
Short position1250−350−350−50−400−400−900−900−900
Total bought puts350−350−350−5000000
Bought put96300−300−300000000
Bought put10250−50−50−5000000
Total written calls900000−400−400−900−900−900
Written call101400000−400−400−400−400−400
Written call10550000000−500−500−500
Long position700300300300300400300300400
Total bought calls40000100100200300300400
Bought call9710000100100100100100100
Bought call1031000000100100100100
Bought call10610000000100100100
Bought call1111000000000100
Total written puts300300300200200200000
Written put96100100100000000
Written put106200200200200200200000
Exchange rate change−10−502.557.51012.5
Table A4.4Foreign Currency Flows Resulting from Options Positions with Possible Exercise Date Three Months to One Year Hence
Options

positions
Exchange rates

(LC/$)
Strike price

(LC/$)
Position size

($-million)
9095100102.5105107.5110112.5
Currency flows ($-million)
Short Position600−400−2000−100−100−200−200−200
Total bought puts400−400−200000000
Bought put93200−2000000000
Bought put97200−200−200000000
Total written calls200000−100−100−200−200−200
Written call102100000−100−100−100−100−100
Written call10610000000−100−100−100
Long position800200300300300500500700600
Total bought calls6000100100200400400600600
Bought call931000100100100100100100100
Bought call102100000100100100100100
Bought call1042000000200200200200
Bought call109200000000200200
Total written puts2002002002001001001001000
Written put10110010010010000000
Written put1111001001001001001001001000
Exchange rate change−10−502.557.51012.5

A4.12 Results shown in Table A4.1 for pro memoria items (2)(a) (viz., –1200, –700, –400, –100) and (2)(b) (viz., +1300, +400, +400, +500) correspond to figures that are in bold in supporting Tables A4.2A4.4. The “total” in Table A represents the sum of each row.

A4.13Figures A4.1A4.5 present graphically the results shown in Tables A4.1A4.4 under long and short positions for the three periods under the one-year horizon.

Figure A4.1Foreign Currency Flows from Options Positions (up to 1 month)

Figure A4.2Foreign currency Flows from Options Positions (1 to 3 month)

Figure A4.3Foreign currency Flows from Options Positions (3 months to 1 year)

Figure A4.4Foreign currency Flows from Short Options Positions

Figure A4.5Foreign Currency Flows from Long Options Positions

This Appendix was provided by Charles Thomas of the U.S. Federal Reserve Board of Governors.

In the examples that follow, we denote the local currency as LC and assume the following for the current market exchange rates: LC100 = $1.00; JY125 = $1.00; $1.10 = EUR1.00. If market exchange rates are not readily available, the rates used should be indicated in the notes accompanying the data in the Template.

In other words, the dollar notional value of all options is independent of the local currency exchange rate.

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