Economic Scenario Generator

Using Geometric Brownian Motion to model stocks $dS = \mu S dt + \sigma S dB$
and Ornstein–Uhlenbeck for interest rates $dr = a(\mu - r) dt + \sigma dB$
Driving Brownian process is generated from correlation-matrix that need not be wellconditioned since truncated singular value decomposition is used. Interdependence between paths is captured with Gaussian copula, which is easily modified to model more realistic interdependencies.

References

Ornstein–Uhlenbeck process https://en.wikipedia.org/wiki/Ornstein%E2%80%93Uhlenbeck_process

Singular value decomposition https://en.wikipedia.org/wiki/Singular_value_decomposition

Copula https://en.wikipedia.org/wiki/Copula_(probability_theory)

FastAPI in Docker

docker run -d --name my_esg -p 8000:80 holmen1/economic-scenario-generator-api

curl -X POST "http://localhost:8000/api/scenarios" -H "accept: application/json" -H "Content-Type: application/json" -d "{\"samples\":2,\"years\":1,\"s0\":[224.0,0.03],\"a\":[0.0,0.09],\"mu\":[0.094,-0.007],\"sigma\":[0.16,0.007],\"corrmatrix\":[[1.0,0.2],[0.2,1.0]]}" 

Returns 2 samples each of stock and interest rate paths with correlation 0.2

{
  "gbm":
  [
    [
      [224.0,233.24412013814867,229.18547108835241,201.21767138237402,197.79405885872166,204.47744632258156,205.55080360971866,197.35847765423307,186.42121736135533,181.7706511859549,173.90476702243666,163.2463116308496]
    ],
    [
      [224.0,245.87642132422636,222.14745917168156,232.9024969635743,229.74452566362092,212.972579510549,220.10836429078336,225.67609603841169,219.71785863011573,224.02066532753028,236.47170360973624,233.02408676476088]]
  ],
  "vasicek":
  [
    [
      [0.03,0.0317490993624826,0.031126022475785314,0.028784999428232854,0.02386318403273988,0.02339283297432511,0.022223960080312615,0.02372984522270116,0.022343614082276548,0.022403681819454593,0.020849847246733787,0.01836709280417392]
    ],
    [
      [0.03,0.03175193924876177,0.029062422938180357,0.028804540622892057,0.030073175655091995,0.02909048927411122,0.030467152357563074,0.02833432423517005,0.027626317877791372,0.02643795243414647,0.026070559942345636,0.025927968228109975]
    ]
  ],
  "processors": 12,
  "duration": 0.04755851699997038
}

curl -X POST "http://localhost:8000/api/scenarios" -H "accept: application/json" -H "Content-Type: application/json" -d "{\"samples\":2000,\"years\":5,\"s0\":[224.0,0.03],\"a\":[0.0,0.09],\"mu\":[0.094,-0.007],\"sigma\":[0.16,0.007],\"corrmatrix\":[[1.0,0.2],[0.2,1.0]]}" 

Time to run 2000 monthly samples for 5 years on 12 processors is 0.37 seconds

{
  [...],
  "processors":12,
  "time":0.3729823819999183
}

From A to Z

• Preprocessing of data

• Parameter estimation

• Plot realizations

• Validation

Suggested extensions

• Reallocation s_t+1 += μ(s_t + s_r)dt + σ(s_t + s_r)db
• Black-Litterman
• Non-Gaussian Copula

TODO

• RequestModel parameter validation
• Add documentation
• Add GitHub Actions