1 PACKAGE XTR_FX_FORMULAS AS
2 /* $Header: xtrfxfls.pls 120.2 2005/06/29 08:06:01 badiredd ship $ */
3
4 --
5 /*-----------------------------------------------------------------------
6 FX_GK_OPTION_PRICE_CV
7 Cover procedure to calculate the price of a currency option
8 using Garman-Kohlhagen formula, which is the extension of
9 Black-Scholes formula.
10
11 IMPORTANT: it is better to supply a Simple 30/360 (from GET_MD_FROM_SET)
12 interest rates for this procedure in order to avoid redundant conversions.
13
14 IMPORTANT: this procedure is only accurate up to six decimal places due
15 to CUMULATIVE_NORM_DISTRIBUTION procedure it calls.
16
17 GK_OPTION_CV_IN_REC_TYPE:
18 p_SPOT_DATE date
19 p_MATURITY_DATE date
20 p_RATE_DOM num
21 p_RATE_TYPE_DOM varchar2(1) DEFAULT 'S'
22 p_COMPOUND_FREQ_DOM num
23 p_DAY_COUNT_BASIS_DOM varchar2(15)
24 p_RF_RATE_FOR num
25 p_RATE_TYPE_FOR varchar2(1) DEFAULT 'S'
26 p_COMPOUND_FREQ_FOR num
27 p_DAY_COUNT_BASIS_FOR varchar2(15)
28 p_SPOT_RATE num
29 p_STRIKE_RATE num
30 p_VOLATILITY num
31
32 GK_OPTION_CV_OUT_REC_TYPE:
33 p_CALL_PRICE num
34 p_PUT_PRICE num
35 p_FX_FWD_RATE num
36 p_Nd1 num
37 p_Nd2 num
38 p_Nd1_a num
39 p_Nd2_a num
40
41 Formula:
42 1. Converts interest rates to fit the FX_GK_OPTION_PRICE assumptions.
43 2. Calls FX_GK_OPTION_PRICE.
44
45 Example to calculate p_SPOT_RATE:
46 Given: CAD = foreign, USD = domestic
47 1 USD = 1.5 CADThen: p_SPOT_RATE = 0.666667
48
49 p_SPOT_DATE = the spot date where the option value is evaluated
50 p_MATURITY_DATE = the maturity date where the option expires
51 p_RF_RATE_DOM = domestic risk free interest rate.
52 p_RATE_TYPE_DOM/FOR = the p_RF_RATE_DOM/FOR rate's type. 'S' for Simple
53 Rate. 'C' for Continuous Rate, and 'P' for Compounding Rate.
54 Default value = 'S' (Simple IR)
55 p_DAY_COUNT_BASIS_DOM/FOR = day count basis for p_RF_RATE_DOM/FOR.
56 p_RATE_FOR = foreign risk free interest rate.
57 p_SPOT_RATE = the current market exchange rate = the value of one unit
58 of the foreign currency measured in the domestic currency.
59 p_STRIKE_RATE = the strike price agreed in the option.
60 p_VOLATILITY = volatility
61 p_CALL_PRICE = theoretical fair value of the call.
62 p_PUT_PRICE = theoretical fair value of the put
63 p_FX_FWD_RATE = the forward rate of the exchange calculated from the
64 p_SPOT_RATE
65 p_Nd1/2 = cumulative distribution value given limit probability values
66 in Black's formula = N(x) (refer to Hull's Fourth Edition p.252)
67 p_Nd1/2_a = N'(x) in Black's formula (refer to Hull's Fourth Edition p.252)
68 p_COMPOUND_FREQ_DOM/FOR = frequencies of discretely compounded input/output
69 rate. This is only necessary if p_RATE_TYPE_DOM/FOR is 'P'.
70 -----------------------------------------------------------------------*/
71 TYPE GK_OPTION_CV_IN_REC_TYPE IS RECORD (p_SPOT_DATE date,
72 p_MATURITY_DATE date,
73 p_RATE_DOM NUMBER,
74 p_RATE_TYPE_DOM varchar2(1) DEFAULT 'S',
75 p_COMPOUND_FREQ_DOM NUMBER,
76 p_DAY_COUNT_BASIS_DOM varchar2(15),
77 p_RATE_FOR NUMBER,
78 p_RATE_TYPE_FOR varchar2(1) DEFAULT 'S',
79 p_COMPOUND_FREQ_FOR NUMBER,
80 p_DAY_COUNT_BASIS_FOR varchar2(15),
81 p_SPOT_RATE NUMBER,
82 p_STRIKE_RATE NUMBER,
83 p_VOLATILITY NUMBER);
84
85 TYPE GK_OPTION_CV_OUT_REC_TYPE IS RECORD (p_CALL_PRICE NUMBER,
86 p_PUT_PRICE NUMBER,
87 p_FX_FWD_RATE NUMBER,
88 p_Nd1 NUMBER,
89 p_Nd2 NUMBER,
90 p_Nd1_a NUMBER,
91 p_Nd2_a NUMBER);
92
93 PROCEDURE FX_GK_OPTION_PRICE_CV(p_in_rec IN GK_OPTION_CV_IN_REC_TYPE,
94 p_out_rec OUT NOCOPY GK_OPTION_CV_OUT_REC_TYPE);
95
96 /*-----------------------------------------------------------------------
97 Calculates the FX Spot Rate for different currencies exchange.
98
99 Formula:
100 * If the BASIS_CONTRA/BASE is not 'C' (Commodity Unit Quote) then convert with FX FORWARD (HLD) Formula 1
101 * Check CURRENCY_CONTRA and CURRENCY_BASE if cross-currency pair is involved then use FX FORWARD (HLD) Formula 2
102
103 Formula 1 is converting from Base Unit Quote to Commodity Unit Quote, and vice versa.
104 Formula 2 is to calculate the SPOT RATE(=Cross Rate)
105
106 Assumption: p_RATE_ CONTRA and p_RATE_ BASE have the same day count basis.
107
108 For IRS: BASE = Receive Leg
109 CONTRA = Pay Leg
110 Example for FX:CHFGBP -> CHF = Base Currency
111 GBP = Contra Currency
112
113 IF there is a notion of BID and ASK then:
114 To find p_SPOT_RATE (BID/ASK):
115 FOR CONTRA:
116 IF p_BASIS_CONTRA = 'C' THEN
117 p_RATE_CONTRA (BID/ASK) = BID/ASK Rate of
118 Contra Currency
119 ELSE
120 p_RATE_CONTRA (BID/ASK) = ASK/BID Rate of
121 Contra Currency
122 FOR BASE:
123 IF p_BASIS_BASE = 'C' THEN
124 p_RATE_BASE (BID/ASK) = ASK/BID Rate of Base
125 Currency
126 ELSE
127 p_RATE_BASE (BID/ASK) = BID/ASK Rate of Base
128 Currency
129
130 * p_RATE_CONTRA/BASE = FX rate of the contra/base side against USD
131 (p_RATE_CONTRA = Rate vs. USD Contra, p_RATE_ BASE = Rate vs. USD Base).
132 If the currency is USD then p_RATE = 1;
133 * p_CURRENCY_CONTRA/BASE = the currency for contra/base.
134 * p_BASIS_CONTRA/BASE indicates the quotation basis against USD for the CONTRA
135 BASE side, 'C' for Commodity Unit Quote (=USDGBP) and 'B' for Base Unit Quote=
136 GBPUSD) (Definitions are in FX Calculator HLD)
137 * p_SPOT_RATE = fair exchange rate of two different currencies.
138 -----------------------------------------------------------------------*/
139
140 PROCEDURE FX_SPOT_RATE (p_currency_contra IN VARCHAR2,
141 p_currency_base IN VARCHAR2,
142 p_rate_contra IN NUMBER,
143 p_rate_base IN NUMBER,
144 p_basis_contra IN CHAR,
145 p_basis_base IN CHAR,
146 p_spot_rate IN OUT NOCOPY NUMBER);
147
148
149
150 /*-------------------------------------------------------------------------
151 Calculates the FX Forward Rate
152
153 Formula:
154 FX FORWARD (HLD) Formula 3
155
156 Example for FX: CHFGBP -> CHF = Base Currency
157 GBP = Contra Currency
158
159 IF there is a notion of BID and ASK then:
160 To find p_FORWARD_RATE (BID):
161 p_SPOT_RATE = BID FX Spot Rate
162 p_BASE_CURR_INT_RATE = ASK Base Currency risk free interest rate.
163 p_CONTRA_CURR_INT_RATE = BID Contra Currency risk free interest rate.
164
165 To find p_FORWARD_RATE (ASK):
166 p_SPOT_RATE = ASK FX Spot Rate
167 p_BASE_CURR_INT_RATE = BID Base Currency risk free interest rate.
168 p_CONTRA_CURR_INT_RATE = ASK Contra Currency risk free interest rate.
169
170
171 * p_SPOT_RATE = fair exchange rate of two different currencies.
172 * p_BASE/CONTRA_CURR_INT_RATE = risk free interest rate for the base/contra
173 currency.
174 * p_DAY_COUNT_BASE/CONTRA = number of days between the spot date and the
175 forward
176 date.
177 * p_ANNUAL_BASIS_BASE/CONTRA = number of days in a year of which the
178 * p_DAY_COUNT_BASE/CONTRA and the p_BASE/CONTRA_CURR_INT_RATE are based on.
179 -------------------------------------------------------------------------*/
180
181 PROCEDURE FX_FORWARD_RATE (p_spot_rate IN NUMBER,
182 p_base_curr_int_rate IN NUMBER,
183 p_contra_curr_int_rate IN NUMBER,
184 p_day_count_base IN NUMBER,
185 p_day_count_contra IN NUMBER,
186 p_annual_basis_base IN NUMBER,
187 p_annual_basis_contra IN NUMBER,
188 p_forward_rate IN OUT NOCOPY NUMBER);
189
190
191 /*---------------------------------------------------------------------------
192 FX Option Pricing (Garman Kohlagen's Method)
193 Calculates the price and sensitivity of a currency option and its associated greek ratio's using Garman-Kohlhagen formula, which is the extension of Black-Scholes formula.
194
195 Formula:
196 Taken from Currency Option Pricing Formula in Hull's Option, Future, and Other Derivatives, Third Edition p.272, p. 317.
197 (Defined in xtrprc2b.pls)
198
199 Currently used in xtrrevlb.pld
200
201 Call XTR_RATE_CONVERSION.rate_conversion to convert day counts and/or between compounded and simple interest rates.
202
203 * l_days = time left to maturity in days(assuming 30/360 day count basis).
204 * l_base_int_rate = annual risk free interest rate for base currency.
205 * l_contra_int_rate = annual risk free interest rate for contra currency.
206 * l_spot_rate = the current market rate for the exchange.
207 * l_strike_price = the strike price agreed in the option.
208 * vol = volatility
209 * l_call_price = theoretical fair value of the call.
210 * l_put_price = theoretical fair value of the put
211 * l_fwd_price = the forward rate of the exchange calculated from the l_spot_rate
212 * l_delta_call/put = delta of the call/put
213 * l_theta_call/put = theta of the call/put
214 * l_rho_call/put = rho of the call/put (with respect to the change in base interest rate)
215 * l_gamma = gamma
216 * l_vega = vega
217 * l_nd1/2 = cumulative normal probability distribution value = N(x) in Black Formu
218 la
219 * l_nd1/2_a = N'(x) in Black Formula
220
221
222 gamma, theta, delta, vega are sensitivity measurements of the model relatives to its different variables and explained extensively in Hull's Option, Future, and Other Derivatives.
223 ----------------------------------------------------------------------------*/
224 -- modified fhu 6/13/01
225 PROCEDURE FX_GK_OPTION_PRICE(
226 l_days IN NUMBER,
227 l_base_int_rate IN NUMBER,
228 l_contra_int_rate IN NUMBER,
229 l_spot_rate IN NUMBER,
230 l_strike_rate IN NUMBER,
231 vol IN NUMBER,
232 l_call_price IN OUT NOCOPY NUMBER,
233 l_put_price IN OUT NOCOPY NUMBER,
234 l_fwd_rate IN OUT NOCOPY NUMBER,
235 l_nd1 IN OUT NOCOPY NUMBER,
236 l_nd2 IN OUT NOCOPY NUMBER,
237 l_nd1_a IN OUT NOCOPY NUMBER,
238 l_nd2_a IN OUT NOCOPY NUMBER );
239 --added by sankim 9/10/01
240 /*
241 FX_SPOT_RATE_CV (FUNCTION)Cover routine that calculates the FX Spot Rate for
242 bid and ask side of different currencies exchange.In order to make the cover
243 routine easier to be called from Java (middle tier) directly, the record type
244 is not used to encapsulate the arguments. Moreover, function is used instead of
245 procedure since function can be called from SQL.
246 Parameters
247 * p_RATE_CONTRA/BASE_BID/ASK = FX rate of the contra/base currency against USD
248 for bid/ask side (p_RATE_ CONTRA = Rate vs. USD Contra, p_RATE_ BASE = Rate vs.
249 USD Base). If the currency is USD then use the default rate (=1).
250 * p_CURRENCY_CONTRA/BASE = the currency for contra/base.
251 p_QUOTATION_BASIS_CONTRA/BASE indicates the quotation basis against USD for
252 the CONTRA /BASE side, 'C' for Commodity Unit Quote (=USDGBP) and 'B' for Base
253 Unit Quote (= GBPUSD) (Definitions are in FX Calculator HLD)
254 * Returned: p_SPOT_RATE (BID/ASK) = fair exchange rate of two different
255 currencies of side bid/ask.
256 */
257 FUNCTION FX_SPOT_RATE_CV( p_currency_contra IN VARCHAR2,
258 p_currency_base IN VARCHAR2,
259 p_rate_contra_bid IN NUMBER DEFAULT 1,
260 p_rate_contra_ask IN NUMBER DEFAULT 1,
261 p_rate_base_bid IN NUMBER DEFAULT 1,
262 p_rate_base_ask IN NUMBER DEFAULT 1,
263 p_quotation_basis_contra IN VARCHAR2 DEFAULT 'C',
264 p_quotation_basis_base IN VARCHAR2 DEFAULT 'C')
265 RETURN XTR_MD_NUM_TABLE;
266 --added by sankim 9/10/01
267 /*
268 FX_FORWARD_RATE_CV (FUNCTION)A cover routine that calculates the FX Forward
269 Rate for exchange that has USD as the base.In order to make the cover routine
270 easier to be called from Java (middle tier) directly, the record type is not
271 used to encapsulate the arguments. Moreover, function is used instead of
272 procedure since function can be called from SQL.
273 Parameters
274 * p_SPOT_RATE_BASE_BID/ASK = fair exchange rate of between the base currency
275 against USD. If the base currency is USD, then the default value of 1 should be
276 used.
277 * p_SPOT_RATE_CONTRA_BID/ASK = fair exchange rate of between the contra
278 currency against USD. If the contra currency is USD, then the default value of
279 1 should be used.
280 * p_BASE_CURR_INT_RATE_BID/ASK = bid/ask risk free interest rate for the base
281 currency. This parameter should be null if the base currency is USD.
282 * p_CONTRA_CURR_INT_RATE_BID/ASK = bid/ask risk free interest rate for the
283 contra currency. This parameter should be null if the contra currency is USD.
284 * p_USD _CURR_INT_RATE = risk free interest rate for the USD.
285 * p_DAY_COUNT_BASE/CONTRA = number of days between the spot date and the
286 forward date. If the contra currency is USD, then p_DAY_COUNT_CONTRA should be
287 null, and vice versa in the case of base is USD.
288 * p_ANNUAL_BASIS_BASE/CONTRA = number of days in a year of which the
289 p_DAY_COUNT_BASE/CONTRA and the p_BASE/CONTRA_CURR_INT_RATE are based on. If
290 the contra currency is USD, then p_ANNUAL_BASIS_CONTRA should be null, and vice
291 versa in the case of base is USD.
292 * p_DAY_COUNT_USD = number of days between the spot date and the forward date.
293 = number of days in a year of which the p_DAY_COUNT_USD and the
294 p_USD _CURR_INT_RATE are based on.
295 * p_ANNUAL_BASIS_USD = number of days in a year of which the p_DAY_COUNT_USD
296 and the p_USD _CURR_INT_RATE are based on.
297 * p_CURRENCY_CONTRA/BASE = the currency for contra/base.
298 * p_QUOTATION_BASIS_CONTRA/BASE indicates the quotation basis against USD for
299 the CONTRA /BASE side, 'C' for Commodity Unit Quote (=USDGBP) and 'B' for Base
300 Unit Quote (= GBPUSD) (Definitions are in FX Calculator HLD). This parameter is
301 required if base/contra is non-USD accordingly.
302 * Returned: p_FORWARD_RATE (BID/ASK) indicates the bid/ask side of forward rate
303 results.
304 */
305 FUNCTION FX_FORWARD_RATE_CV( p_spot_rate_base_bid IN NUMBER DEFAULT 1,
306 p_spot_rate_base_ask IN NUMBER DEFAULT 1,
307 p_spot_rate_contra_bid IN NUMBER DEFAULT 1,
308 p_spot_rate_contra_ask IN NUMBER DEFAULT 1,
309 p_base_curr_int_rate_bid IN NUMBER,
310 p_base_curr_int_rate_ask IN NUMBER,
311 p_contra_curr_int_rate_bid IN NUMBER,
312 p_contra_curr_int_rate_ask IN NUMBER,
313 p_usd_curr_int_rate_bid IN NUMBER,
314 p_usd_curr_int_rate_ask IN NUMBER,
315 p_day_count_base IN NUMBER,
316 p_day_count_contra IN NUMBER,
317 p_day_count_usd IN NUMBER,
318 p_annual_basis_base IN NUMBER,
319 p_annual_basis_contra IN NUMBER,
320 p_annual_basis_usd IN NUMBER,
321 p_currency_base IN VARCHAR2,
322 p_currency_contra IN VARCHAR2,
323 p_quotation_basis_base IN VARCHAR2 DEFAULT 'C',
327 END XTR_FX_FORMULAS;
324 p_quotation_basis_contra IN VARCHAR2 DEFAULT 'C')
325 RETURN XTR_MD_NUM_TABLE;
326
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