Appendix IV: Stress-Testing of “In-the-Money” Options Under the Five Scenarios Shown in the Data Template1

Anne Y. Kester

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Appendix IV: Stress-Testing of “In-the-Money” Options Under the Five Scenarios Shown in the Data Template¹

Author: Ms. Anne Y. Kester

Language:: English

Keywords:: M&G; long position; option contract; market value; put; options position; market price; foreign currency option; foreign currency flow; reporting currency; Currencies; Options; Exchange rates; Depreciation; foreign exchange resource

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Abstract

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 = $1.00.2 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 LC 90 = $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 put option with a notional value of LC200 million and a strike price of LC110 = $1.00, this will be treated as a purchased call option with a notional value of $1.818 million (200 million/110).

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 = $1.00.² 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 LC 90 = $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 put option with a notional value of LC200 million and a strike price of LC110 = $1.00, this will be treated as a purchased call option with a notional value of $1.818 million (200 million/110).

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 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 sell JY1.0 million with a strike price of JY1.4 = LC1.00. Assuming the exchange rate of JY 1.25 = $1.00, this would translate into an $8,000 call option (JY 1,000,000 × 1/125). The strike price should not be used when converting from one foreign currency to another.

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 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 written to the reporting currency.³

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.

In the PRO MEMORIA section of the template, five simple scenarios for the local currency exchange rate are used for stress testing of “in-the-money” options to gauge the impact of the options on foreign exchange resources. This appendix illustrates the foreign currency flows under the five scenarios.

The first scenario assumes the local currency exchange rate remains unchanged relative to all foreign currencies. The second scenario assumes a 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.

As noted in Chapter 4 of this document, generally, a put option is “in the money” if the market price is below the strike price. A call option is “in the money” if the market price is above the strike price. Where long positions are held, calls are exercised if market price is above strike price; and puts are exercised when market price is below strike price. When these options are exercised, they will add to foreign currency resources.

In this example, the convention of expressing 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 A, these are shown as +5% (depreciation); –5% (appreciation); +10% (depreciation), and –10% (appreciation), respectively, under pro memoria items (2), (3), (4), and (5). Table A 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.

In the example, the sign (+) is used to indicate inflow of foreign currency; and the (-) sign, outflows of foreign currency.

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 B, C, and D.

Results shown in Table A 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 B, C, and D.

The “total” in Table A represents the sum of each row.

Figures 1–5 present graphically the results shown in Table A under long and short positions for the three periods under the one-year horizon.

Table A.

Results of An Illustration of In-the-Money Options and Related Stress-Testing Under Specific Assumptions of Exchange Rate Changes (Nominal Value)

Table A.

Results 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)
			Total	Up to 1 month	More than 1 month and up to 3 months	More than 3 months and up to 1 year
4. Aggregate short and long positions of options in foreign currencies vis-à-vis the domestic currency
	(a) Short positions		-2,850	-1,000	-1,250	-600
		(i) Bought puts	-1,050	-300	-350	-400
		(ii) Written calls	-1,800	-700	-900	-200
	(b) Long positions		+2,500	+1,000	+700	+800
		(i) Bought calls	+1,800	+800	+400	+600
		(ii) Written puts	+700	+200	+300	+200
PRO MEMORIA: In-the-money options
(1) At current exchange rates
	(a) Short position		-350	-300	-50	0
	(b) Long position		+800	+200	+300	+300
(2) + 5 % (depreciation of 5%)
	(a) Short position		-1,200	-700	-400	-100
	(b) Long position		+1,300	+400	+400	+500
(3) –5 % (appreciation of 5%)
	(a) Short position		-650	-100	-350	-200
	(b) Long position		+900	+300	+300	+300
(4) +10% (depreciation of 10%)
	(a) Short positron		-1,800	-700	-900	-200
	(b) Long position		+1,800	+800	+300	+700
(5) –10%(appreciation of 10%)
	(a) Short position		-1,050	-300	-350	-400
	(b) Long position		+700	+200	+300	+200
(6) other(specify)

Table A.

Results 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)
			Total	Up to 1 month	More than 1 month and up to 3 months	More than 3 months and up to 1 year
4. Aggregate short and long positions of options in foreign currencies vis-à-vis the domestic currency
	(a) Short positions		-2,850	-1,000	-1,250	-600
		(i) Bought puts	-1,050	-300	-350	-400
		(ii) Written calls	-1,800	-700	-900	-200
	(b) Long positions		+2,500	+1,000	+700	+800
		(i) Bought calls	+1,800	+800	+400	+600
		(ii) Written puts	+700	+200	+300	+200
PRO MEMORIA: In-the-money options
(1) At current exchange rates
	(a) Short position		-350	-300	-50	0
	(b) Long position		+800	+200	+300	+300
(2) + 5 % (depreciation of 5%)
	(a) Short position		-1,200	-700	-400	-100
	(b) Long position		+1,300	+400	+400	+500
(3) –5 % (appreciation of 5%)
	(a) Short position		-650	-100	-350	-200
	(b) Long position		+900	+300	+300	+300
(4) +10% (depreciation of 10%)
	(a) Short positron		-1,800	-700	-900	-200
	(b) Long position		+1,800	+800	+300	+700
(5) –10%(appreciation of 10%)
	(a) Short position		-1,050	-300	-350	-400
	(b) Long position		+700	+200	+300	+200
(6) other(specify)

Table B.

Foreign Currency Flows Resulting from Options Position with Possible Exercise Date Less Than One Month Hence

Table B.

Foreign Currency Flows Resulting from Options Position with Possible Exercise Date Less Than One Month Hence

		Options Positions		Exchange Rates (LC/$)
		Strike Price	Position Size	90	95	100	102.5	105	107.5	110	112.5
		(LC/$)	($-million)	Currency Flows ($-million)
Short position			1000	-300	-100	-300	-300	-700	-700	-700	-700
Total bought puts			300	-300	-100	0	0	0	0	0	0
	Bought put	93	200	-200	0	0	0	0	0	0	0
	Bought put	97	100	-100	-100	0	0	0	0	0	0
Total written calls			700	0	0	-300	-300	-700	-700	-700	-700
	Written call	98	300	0	0	-300	-300	-300	-300	-300	-300
	Written call	104	400	0	0	0	0	-400	-400	-400	-400
Long position			1000	200	300	200	400	400	600	800	800
Total bought calls			800	0	100	100	300	300	600	800	800
	Bought call	93	100	0	100	100	100	100	100	100	100
	Bought call	102	200	0	0	0	200	200	200	200	200
	Bought call	106	300	0	0	0	0	0	300	300	300
	Bought call	109	200	0	0	0	0	0	0	200	200
Total written puts			200	200	200	100	100	100	0	0	0
	Written put	96	100	100	100	0	0	0	0	0	0
	Written put	106	100	100	100	100	100	100	0	0	0
				-10	-5	0	2.5	5	7.5	10	12.5

Table B.

Foreign Currency Flows Resulting from Options Position with Possible Exercise Date Less Than One Month Hence

		Options Positions		Exchange Rates (LC/$)
		Strike Price	Position Size	90	95	100	102.5	105	107.5	110	112.5
		(LC/$)	($-million)	Currency Flows ($-million)
Short position			1000	-300	-100	-300	-300	-700	-700	-700	-700
Total bought puts			300	-300	-100	0	0	0	0	0	0
	Bought put	93	200	-200	0	0	0	0	0	0	0
	Bought put	97	100	-100	-100	0	0	0	0	0	0
Total written calls			700	0	0	-300	-300	-700	-700	-700	-700
	Written call	98	300	0	0	-300	-300	-300	-300	-300	-300
	Written call	104	400	0	0	0	0	-400	-400	-400	-400
Long position			1000	200	300	200	400	400	600	800	800
Total bought calls			800	0	100	100	300	300	600	800	800
	Bought call	93	100	0	100	100	100	100	100	100	100
	Bought call	102	200	0	0	0	200	200	200	200	200
	Bought call	106	300	0	0	0	0	0	300	300	300
	Bought call	109	200	0	0	0	0	0	0	200	200
Total written puts			200	200	200	100	100	100	0	0	0
	Written put	96	100	100	100	0	0	0	0	0	0
	Written put	106	100	100	100	100	100	100	0	0	0
				-10	-5	0	2.5	5	7.5	10	12.5

Table C.

Foreign Currency Flows Resulting from Options Position with Possible Exercise Date One to Three Months Hence

Table C.

Foreign Currency Flows Resulting from Options Position with Possible Exercise Date One to Three Months Hence

		Options Positions		Exchange Rates (LC/$)
		Strike Price	Position Size	90	95	100	102.5	105	107.5	110	112.5
		(LC/$)	($-million)	Currency Flows ($-million)
Short position			1250	-350	-350	*-50*	-400	-400	-900	-900	-900
Total bought puts			350	-350	-350	-50	0	0	0	0	0
	Bought put	96	300	-300	-300	0	0	0	0	0	0
	Bought put	102	50	-50	-50	-50	0	0	0	0	0
Total written calls			900	0	0	0	-400	-400	-900	-900	-900
	Written call	101	400	0	0	0	-400	-400	-400	-400	-400
	Written call	105	500	0	0	0	0	0	-500	-500	-500
Long position			700	300	300	300	300	400	300	300	400
Total bought calls			400	0	0	100	100	200	300	300	400
	Bought call	97	100	0	0	100	100	100	100	100	100
	Bought call	103	100	0	0	0	0	100	100	100	100
	Bought call	106	100	0	0	0	0	0	100	100	100
	Bought call	111	100	0	0	0	0	0	0	0	100
Total written puts			300	300	300	200	200	200	0	0	0
	Written put	96	100	100	100	0	0	0	0	0	0
	Written put	106	200	200	200	200	200	200	0	0	0
				-10	-5	0	2.5	5	7.5	10	12.5

Table C.

Foreign Currency Flows Resulting from Options Position with Possible Exercise Date One to Three Months Hence

		Options Positions		Exchange Rates (LC/$)
		Strike Price	Position Size	90	95	100	102.5	105	107.5	110	112.5
		(LC/$)	($-million)	Currency Flows ($-million)
Short position			1250	-350	-350	*-50*	-400	-400	-900	-900	-900
Total bought puts			350	-350	-350	-50	0	0	0	0	0
	Bought put	96	300	-300	-300	0	0	0	0	0	0
	Bought put	102	50	-50	-50	-50	0	0	0	0	0
Total written calls			900	0	0	0	-400	-400	-900	-900	-900
	Written call	101	400	0	0	0	-400	-400	-400	-400	-400
	Written call	105	500	0	0	0	0	0	-500	-500	-500
Long position			700	300	300	300	300	400	300	300	400
Total bought calls			400	0	0	100	100	200	300	300	400
	Bought call	97	100	0	0	100	100	100	100	100	100
	Bought call	103	100	0	0	0	0	100	100	100	100
	Bought call	106	100	0	0	0	0	0	100	100	100
	Bought call	111	100	0	0	0	0	0	0	0	100
Total written puts			300	300	300	200	200	200	0	0	0
	Written put	96	100	100	100	0	0	0	0	0	0
	Written put	106	200	200	200	200	200	200	0	0	0
				-10	-5	0	2.5	5	7.5	10	12.5

Table D.

Foreign Currency Flows Resulting from Options Position with Possible Exercise Date Three Months to One Year Hence

Table D.

Foreign Currency Flows Resulting from Options Position with Possible Exercise Date Three Months to One Year Hence

		Options Positions		Exchange Rates (LC/$)
		Strike Price	Position Size	90	95	100	102.5	105	107.5	110	112.5
		(LC/$)	($-million)	Currency Flows ($-million)
Short position			600	-400	-200	0	-100	-100	-200	-200	-200
Total bought puts			400	-400	-200	0	0	0	0	0	0
	Bought put	93	200	-200	0	0	0	0	0	0	0
	Bought put	97	200	-200	-200	0	0	0	0	0	0
Total written calls			200	0	0	0	-100	-100	-200	-200	-200
	Written call	102	100	0	0	0	-100	-100	-100	-100	-100
	Written call	106	100	0	0	0	0	0	-100	-100	-100
Long position			800	200	300	300	300	500	500	700	600
Total bought calls			600	0	100	100	200	400	400	600	600
	Bought call	93	100	0	100	100	100	100	100	100	100
	Bought call	102	100	0	0	0	100	100	100	100	100
	Bought call	104	200	0	0	0	0	200	200	200	200
	Bought call	109	200	0	0	0	0	0	0	200	200
Total written puts			200	200	200	200	100	100	100	100	0
	Written put	101	100	100	100	100	0	0	0	0	0
	Written put	111	100	100	100	100	100	100	100	100	0
				-10,00	-5,00	0.00	2.50	5.00	7.50	10.00	12.50

Table D.

Foreign Currency Flows Resulting from Options Position with Possible Exercise Date Three Months to One Year Hence

		Options Positions		Exchange Rates (LC/$)
		Strike Price	Position Size	90	95	100	102.5	105	107.5	110	112.5
		(LC/$)	($-million)	Currency Flows ($-million)
Short position			600	-400	-200	0	-100	-100	-200	-200	-200
Total bought puts			400	-400	-200	0	0	0	0	0	0
	Bought put	93	200	-200	0	0	0	0	0	0	0
	Bought put	97	200	-200	-200	0	0	0	0	0	0
Total written calls			200	0	0	0	-100	-100	-200	-200	-200
	Written call	102	100	0	0	0	-100	-100	-100	-100	-100
	Written call	106	100	0	0	0	0	0	-100	-100	-100
Long position			800	200	300	300	300	500	500	700	600
Total bought calls			600	0	100	100	200	400	400	600	600
	Bought call	93	100	0	100	100	100	100	100	100	100
	Bought call	102	100	0	0	0	100	100	100	100	100
	Bought call	104	200	0	0	0	0	200	200	200	200
	Bought call	109	200	0	0	0	0	0	0	200	200
Total written puts			200	200	200	200	100	100	100	100	0
	Written put	101	100	100	100	100	0	0	0	0	0
	Written put	111	100	100	100	100	100	100	100	100	0
				-10,00	-5,00	0.00	2.50	5.00	7.50	10.00	12.50