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Pricing and Risk

Measures

Measures

A measure is a metric that can be calculated on an instrument, like a dollar price. Below is a table of supported measures and their definitions.

MeasureDefinition
Dollar PricePrice of the instrument in US Dollars
Price*Price of the instrument (In local currency unless currency specified in parameters)
ForwardPricePrice of the instrument at expiry in the local currency
CDDeltaChange in option Dollar Price relative to the change in underlying index Dollar Price, due to a 1bp shift in the underlying index spread
CDGammaChange in option Delta relative to the change in underlying index Delta, due to a 1bp shift in the underlying index spread
CDThetaChange in option Dollar Price over one day
CDVegaChange in option Dollar Price due to a 1bp shift in the implied volatility of the underlying index
EqDelta*Change in Dollar Price (USD present value) due to individual 1% move in the spot price of underlying equity security
EqGamma*Change in EqDelta for a 1% move in the price of the underlying equity security
EqVega*Change in Dollar Price (USD present value) due to individual 1bp moves in the implied volatility of the underlying equity security
FXDelta*Dollar Price sensitivity of the instrument to a move in the underlying spot such that dSpot * FXDelta = PnL
FXGamma*FXDelta sensitivity of the instrument to a move in the underlying spot such that dSpot * FXGamma = dDelta
FXAnnualImpliedVolFX daily implied volatility (in percent)
FXAnnualATMImpliedVolFX daily implied volatility (in basis points)
FXSpotFX spot reference
FXVega*Change in Dollar Price due to a 1 vol move in the implied volatility of ATM instruments used to build the volatility surface
IRBasis*Change in Dollar Price (USD present value) due to individual 1bp moves in the interest rate instruments used to build the basis curve(s)
IRDelta*Change in Dollar Price (USD present value) due to individual 1bp moves in the interest rate instruments used to build the underlying discount curve
IRGamma*Change in aggregated IRDelta for a aggregated 1bp shift in the interest rate instruments used to build the underlying discount curve
IRVega*Change in Dollar Price (USD present value) due to individual 1bp moves in the implied volatility (IRAnnualImpliedVol) of instruments used to build the volatility surface
IRAnnualImpliedVolInterest rate annual implied volatility (in percent)
IRAnnualATMImpliedVolInterest rate annual implied at-the-money volatility (in percent)
IRDailyImpliedVolInterest rate daily implied volatility (in basis points)
IRSpotRateInterest rate at-the-money spot rate (in percent)
IRFwdRateInterest rate par rate (in percent)
IRXccyDelta*Change in Price due to 1bp move in cross currency rates.
InflationDelta*Change in Price due to 1bp move in inflation curve.

Note - * indicates parameterised risk measures. See Parameterised Risk Measure section below.

Calculating Price Measures

Let's price an instrument. For information on how to define an instrument, please refer to the Instruments tutorial.

Note, below we resolve the swaption parameters that will be used to price the swaption, thereby mutating the swaption object. If resolve(), is not called prior to calling price(), the object will be copied and resolved on the fly without mutating the original swaption object. The preferred behavior may depend on the PricingContext - more on this in the Pricing Context guide.

price() method will return price in the local currency.

IR Swaps

from gs_quant.instrument import IRSwap
from gs_quant.common import PayReceive, Currency
# Creating Swaps - spot starting, forward starting
swap = IRSwap(PayReceive.Receive, '10y', 'GBP', fixed_rate='atm+50', notional_amount=1e8)  # running
swap_fwd_start = IRSwap(PayReceive.Pay, '5y', 'EUR', fixed_rate='atm+20', effective_date='3y')  # fwd starting
# View Instrument w/ specified relative parameters
swap_fwd_start.as_dict()

Output:

{'asset_class': Rates,
 'fee': 0,
 'termination_date': '5y',
 'fixed_rate': 'atm+20',
 'pay_or_receive': Pay,
 'notional_currency': EUR,
 'type': Swap,
 'effective_date': '3y'}
 
# Resolve Instrument, View fixed parameters
swap_fwd_start.resolve()
swap_fwd_start.as_dict()

Output:

{'fixed_rate_day_count_fraction': 30/360,
 'principal_exchange': None,
 'fixed_rate_frequency': '1y',
 'notional_amount': 100000000.0,
 'roll_convention': 'Default',
 'floating_rate_business_day_convention': Modified Following,
 'fee_payment_date': datetime.date(2020, 10, 29),
 'floating_rate_designated_maturity': '6m',
 'fixed_last_stub': datetime.date(2028, 10, 30),
 'asset_class': Rates,
 'fixed_first_stub': datetime.date(2023, 10, 30),
 'floating_hols': 'Target',
 'floating_rate_option': 'EUR-EURIBOR-Telerate',
 'floating_rate_day_count_fraction': ACT/360,
 'fixed_rate_business_day_convention': Modified Following,
 'floating_rate_spread': 0.0,
 'floating_rate_frequency': '6m',
 'fee': 0.0,
 'termination_date': datetime.date(2028, 10, 30),
 'fixed_rate': -0.0003280328013176625,
 'floating_first_stub': datetime.date(2023, 10, 30),
 'pay_or_receive': Pay,
 'fee_currency': EUR,
 'fixed_hols': 'Target',
 'notional_currency': EUR,
 'type': Swap,
 'clearing_house': NONE,
 'effective_date': datetime.date(2023, 10, 30),
 'floating_last_stub': datetime.date(2028, 10, 30)}

Calculating Risk Measures

We can also calculate risk measures for the defined instrument. Please refer to the Risk Package for the available risk measures. Calling calc(risk_measure) calculates the value of the risk measure and can return a float, a dataframe or a future thereof, depending on how PricingContext is being used - more on this in the Pricing Context tutorial.

Calculate a scalar value like implied volatility:

import gs_quant.risk as risk

swaption.calc(risk.IRAnnualImpliedVol) * 10000

Output:

65.75327244844051

Calculate a structured value like vega:

swaption.calc(risk.IRVega)

Output:

 marketDataType	      assetId	pointClass	point	      value
0       IR VOL	USD-LIBOR-BBA	SWAPTION	5Y;9M	-833.270880
1	    IR VOL	USD-LIBOR-BBA	SWAPTION	5Y;1Y	11436.482786
2	    IR VOL	USD-LIBOR-BBA	SWAPTION	5Y;15M	6506.953414
3	    IR VOL	USD-LIBOR-BBA	SWAPTION	5Y;18M	-881.193556

Calculate IR Delta (Aggregated Scalar and Ladder) for Swaps

ir_risk = swap.calc((risk.IRDelta(aggregation_level=AggregationLevel.Type), risk.IRDelta(aggregation_level=AggregationLevel.Type, currency='local'), risk.IRDelta))

# Print Risks
print(ir_risk[risk.IRDelta(aggregation_level=AggregationLevel.Type)])
print(ir_risk[risk.risk.IRDelta(aggregation_level=AggregationLevel.Type, currency='local')])
print(ir_risk[risk.IRDelta])

Output:

-126266.81091040764
-96980.10870167123
   mkt_type mkt_asset mkt_class  mkt_point         value
0        IR       GBP      CASH      1 DAY  1.739874e+00
1        IR       GBP      CASH  CASH STUB  1.759617e+03
2        IR       GBP       FRA      DEC20  3.164005e+03
3        IR       GBP       FRA      MAR21  1.459212e+03
4        IR       GBP       FRA      JUN21 -3.191050e+01
5        IR       GBP       FRA      SEP21 -2.765180e+01
6        IR       GBP       FRA      DEC21 -2.575705e+01
7        IR       GBP       FRA      MAR22 -1.708280e+01
8        IR       GBP       FRA      JUN22 -1.008386e+01
9        IR       GBP       FRA      SEP22 -1.347198e+01
10       IR       GBP  SWAP OIS         3Y -1.644059e+02
11       IR       GBP  SWAP OIS         4Y -3.068205e+02
12       IR       GBP  SWAP OIS         5Y -1.554243e+02
13       IR       GBP  SWAP OIS         6Y -4.754207e+02
14       IR       GBP  SWAP OIS         7Y -3.978586e+02
15       IR       GBP  SWAP OIS         8Y -4.717499e+02
16       IR       GBP  SWAP OIS         9Y -6.641736e+02
17       IR       GBP  SWAP OIS        10Y -1.298433e+05
18       IR       GBP  SWAP OIS        12Y -4.921439e+01
19       IR       GBP  SWAP OIS        15Y  7.086755e+00
20       IR       GBP  SWAP OIS        20Y -5.343531e-01
21       IR       GBP  SWAP OIS        25Y -1.732565e-03
22       IR       GBP  SWAP OIS        30Y  2.842251e-04
23       IR       GBP  SWAP OIS        40Y -8.279800e-06
24       IR       GBP  SWAP OIS        50Y -7.247925e-08
25       IR       GBP  SWAP OIS        60Y  1.945496e-08
26       IR       GBP  SWAP OIS        70Y  3.051758e-08
27       IR       GBP  SWAP OIS        80Y  1.564026e-08
28       IR       USD      CASH        O/N -1.800790e+00
29       IR       USD      CASH  CASH STUB -1.800005e+00
30       IR       USD       FRA      DEC20  8.923584e-04
31       IR       USD       FRA      MAR21 -2.621010e-04
32       IR       USD       FRA      JUN21  2.066803e-06
33       IR       USD       FRA      SEP21  1.328514e-04
34       IR       USD       FRA      DEC21 -3.990868e-04
35       IR       USD       FRA      MAR22  3.143867e-04
36       IR       USD       FRA      JUN22  1.238235e-04
37       IR       USD       FRA      SEP22  0.000000e+00
38       IR       USD       FRA      DEC22  0.000000e+00
39       IR       USD       FRA      MAR23  0.000000e+00
40       IR       USD       FRA      JUN23  3.814697e-10
41       IR       USD       FRA      SEP23  0.000000e+00
42       IR       USD      SWAP         4Y  0.000000e+00
43       IR       USD      SWAP         5Y  3.814697e-10
44       IR       USD      SWAP         6Y -3.814697e-10
45       IR       USD      SWAP         7Y  0.000000e+00
46       IR       USD      SWAP         8Y  3.814697e-10
47       IR       USD      SWAP         9Y -7.629395e-10
48       IR       USD      SWAP        10Y -7.629395e-10
49       IR       USD      SWAP        12Y  3.814697e-10
50       IR       USD      SWAP        15Y  0.000000e+00
51       IR       USD      SWAP        20Y -3.814697e-10
52       IR       USD      SWAP        25Y  3.814697e-10
53       IR       USD      SWAP        30Y  0.000000e+00
54       IR       USD      SWAP        35Y  7.629395e-10
55       IR       USD      SWAP        40Y  3.814697e-10
56       IR       USD      SWAP        45Y  0.000000e+00
57       IR       USD      SWAP        50Y -7.629395e-10

Calculate a conditional risk measure. Show IRDelta Ladder only where exposure >1e-2

ird_ladder=ir_risk[risk.IRDelta]
print(ird_ladder[abs(ird_ladder.value)>1e-2])

Output:

   mkt_type mkt_asset mkt_class  mkt_point          value
0        IR       GBP      CASH      1 DAY       1.739874
1        IR       GBP      CASH  CASH STUB    1759.617323
2        IR       GBP       FRA      DEC20    3164.005345
3        IR       GBP       FRA      MAR21    1459.211995
4        IR       GBP       FRA      JUN21     -31.910504
5        IR       GBP       FRA      SEP21     -27.651800
6        IR       GBP       FRA      DEC21     -25.757052
7        IR       GBP       FRA      MAR22     -17.082804
8        IR       GBP       FRA      JUN22     -10.083864
9        IR       GBP       FRA      SEP22     -13.471984
10       IR       GBP  SWAP OIS         3Y    -164.405861
11       IR       GBP  SWAP OIS         4Y    -306.820500
12       IR       GBP  SWAP OIS         5Y    -155.424287
13       IR       GBP  SWAP OIS         6Y    -475.420745
14       IR       GBP  SWAP OIS         7Y    -397.858642
15       IR       GBP  SWAP OIS         8Y    -471.749941
16       IR       GBP  SWAP OIS         9Y    -664.173632
17       IR       GBP  SWAP OIS        10Y -129843.283225
18       IR       GBP  SWAP OIS        12Y     -49.214390
19       IR       GBP  SWAP OIS        15Y       7.086755
20       IR       GBP  SWAP OIS        20Y      -0.534353
28       IR       USD      CASH        O/N      -1.800790
29       IR       USD      CASH  CASH STUB      -1.800005

See measures table for information on units.

Parameterised Risk Measures

Some risk measures now support extra parameters

You can now specify which currency you want the price of an instrument to be expressed in

eur_swap = IRSwap(PayReceive.Pay, '5y', 'EUR', fixed_rate='atm+20')
price = eur_swap.price(currency='PLN')
print(f'{price} {list(price.unit.keys())[0]}')

Output:

-4634381.565442756 Polish Zloty

For some finite difference risk measures (noted * in the table above), you can now pass in the specifics of the calculation methodology.

Parameters supported in finite difference risk measures

Parameter nameTypeDescription
currencystringCurrency of risk result
aggregation_levelgs_quant.target.common.AggregationLevelLevel of aggregate shift
local_curveboolChange in Price (present value in the denominated currency)
finite_difference_methodgs_quant.target.common.FiniteDifferenceParameterDirection and dimension of finite difference
mkt_marking_modestringMarket marking mode
bump_sizefloatBump size
scale_factorfloatScale factor
print(swap.calc(risk.IRDelta))

Output:

-4634381.565442756 Polish Zloty
 
print(swap.calc(risk.IRDelta))

Output:

mkt_type mkt_asset mkt_class  mkt_point mkt_quoting_style         value
0        IR       GBP      CASH      1 DAY                    3.975320e+01
1        IR       GBP      CASH  CASH STUB                   -1.712791e+01
2        IR       GBP       FRA      SEP21                   -3.340941e+01
3        IR       GBP       FRA      DEC21                   -3.304035e+01
4        IR       GBP       FRA      MAR22                   -3.388328e+01
5        IR       GBP       FRA      JUN22                   -2.238591e+01
6        IR       GBP       FRA      SEP22                   -1.839452e+01
7        IR       GBP       FRA      DEC22                   -1.489927e+01
8        IR       GBP       FRA      MAR23                   -1.882270e+01
9        IR       GBP       FRA      JUN23                   -4.702490e+00
10       IR       GBP  SWAP OIS         3Y                   -1.963525e+02
11       IR       GBP  SWAP OIS         4Y                   -2.661177e+02
12       IR       GBP  SWAP OIS         5Y                   -3.323207e+02
13       IR       GBP  SWAP OIS         6Y                   -3.993289e+02
14       IR       GBP  SWAP OIS         7Y                   -4.709492e+02
15       IR       GBP  SWAP OIS         8Y                   -5.330585e+02
16       IR       GBP  SWAP OIS         9Y                   -6.006114e+02
17       IR       GBP  SWAP OIS        10Y                   -1.356210e+05
18       IR       GBP  SWAP OIS        12Y                    1.755524e-05
19       IR       GBP  SWAP OIS        15Y                   -1.166458e-05
20       IR       GBP  SWAP OIS        20Y                    4.046631e-06
21       IR       GBP  SWAP OIS        25Y                   -5.867004e-07
22       IR       GBP  SWAP OIS        30Y                    2.937317e-08
23       IR       GBP  SWAP OIS        40Y                    6.866455e-09
24       IR       GBP  SWAP OIS        50Y                   -2.162933e-07
25       IR       GBP  SWAP OIS        60Y                   -2.059937e-08
26       IR       GBP  SWAP OIS        70Y                    3.128052e-08
27       IR       GBP  SWAP OIS        80Y                   -3.433228e-08
28       IR       USD      CASH        O/N                   -1.874307e+00
29       IR       USD      CASH  CASH STUB                   -5.621533e+00
30       IR       USD       FRA      SEP21                    7.039375e-05
31       IR       USD       FRA      DEC21                   -4.110413e-05
32       IR       USD       FRA      MAR22                    1.529045e-05
33       IR       USD       FRA      JUN22                   -9.892464e-05
34       IR       USD       FRA      SEP22                    1.229893e-04
35       IR       USD       FRA      DEC22                    1.500053e-04
36       IR       USD       FRA      MAR23                   -1.602684e-04
37       IR       USD       FRA      JUN23                   -1.144409e-09
38       IR       USD       FRA      SEP23                    0.000000e+00
39       IR       USD       FRA      DEC23                    0.000000e+00
40       IR       USD       FRA      MAR24                    0.000000e+00
41       IR       USD       FRA      JUN24                   -3.814697e-10
42       IR       USD      SWAP         4Y                    1.525879e-09
43       IR       USD      SWAP         5Y                    0.000000e+00
44       IR       USD      SWAP         6Y                    3.814697e-10
45       IR       USD      SWAP         7Y                   -3.814697e-10
46       IR       USD      SWAP         8Y                   -7.629395e-10
47       IR       USD      SWAP         9Y                    0.000000e+00
48       IR       USD      SWAP        10Y                   -1.144409e-09
49       IR       USD      SWAP        12Y                   -3.814697e-10
50       IR       USD      SWAP        15Y                   -3.814697e-10
51       IR       USD      SWAP        20Y                    1.525879e-09
52       IR       USD      SWAP        25Y                    0.000000e+00
53       IR       USD      SWAP        30Y                    1.144409e-09
54       IR       USD      SWAP        35Y                    0.000000e+00
55       IR       USD      SWAP        40Y                    3.814697e-10
56       IR       USD      SWAP        45Y                    0.000000e+00
57       IR       USD      SWAP        50Y                   -3.814697e-10
 
# Calculate delta calculated due to change in Price only in the denominated currency
print(swap.calc(risk.IRDelta(currency='local')))

Output:

mkt_type mkt_asset mkt_class  mkt_point mkt_quoting_style         value
0        IR       GBP      CASH      1 DAY                   -1.068222e+00
1        IR       GBP      CASH  CASH STUB                   -1.641412e+01
2        IR       GBP       FRA      SEP21                   -2.409039e+01
3        IR       GBP       FRA      DEC21                   -2.382426e+01
4        IR       GBP       FRA      MAR22                   -2.443204e+01
5        IR       GBP       FRA      JUN22                   -1.614180e+01
6        IR       GBP       FRA      SEP22                   -1.326354e+01
7        IR       GBP       FRA      DEC22                   -1.074325e+01
8        IR       GBP       FRA      MAR23                   -1.357251e+01
9        IR       GBP       FRA      JUN23                   -3.390803e+00
10       IR       GBP  SWAP OIS         3Y                   -1.415830e+02
11       IR       GBP  SWAP OIS         4Y                   -1.918883e+02
12       IR       GBP  SWAP OIS         5Y                   -2.396250e+02
13       IR       GBP  SWAP OIS         6Y                   -2.879423e+02
14       IR       GBP  SWAP OIS         7Y                   -3.395852e+02
15       IR       GBP  SWAP OIS         8Y                   -3.843700e+02
16       IR       GBP  SWAP OIS         9Y                   -4.330801e+02
17       IR       GBP  SWAP OIS        10Y                   -9.779165e+04
18       IR       GBP  SWAP OIS        12Y                    1.270790e-05
19       IR       GBP  SWAP OIS        15Y                   -8.369064e-06
20       IR       GBP  SWAP OIS        20Y                    2.946854e-06
21       IR       GBP  SWAP OIS        25Y                   -4.714966e-07
22       IR       GBP  SWAP OIS        30Y                    5.264282e-08
23       IR       GBP  SWAP OIS        40Y                    2.021790e-08
24       IR       GBP  SWAP OIS        50Y                   -1.125336e-07
25       IR       GBP  SWAP OIS        60Y                    3.433228e-08
26       IR       GBP  SWAP OIS        70Y                    0.000000e+00
27       IR       GBP  SWAP OIS        80Y                   -8.659363e-08
 
from gs_quant.common import AggregationLevel
# Calculate delta using an aggregated 1bp shift and using change in Price only in the denominated currency
print(swap.calc(risk.IRDelta(aggregation_level=AggregationLevel.Type, currency='local')))

Output:

-100327.21051493683

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