1. Pricing Asian Basket Multi-Digital Options
with interest rate and underlying assets
as stochastic processes
Artem Rybakov
Simon Porras

2. Key points Asian Basket Multi-Digital
Modeling underlying assets’ trajectories
Modeling stochastic interest rate
Monte-Carlo simulations
Model tests
Conclusions

3. Asian Basket Multi-Digital
Asian Part
Digital Part
One Simulation
Underlying
Average Price over last month
Strike
Condition
  Pay off
Stock 1 A1 K1
A1>K1
If 5 or more stocks > strike
1 if condition=true;
0 otherwise
Stock 2 A2 K2
A2>K2
Stock 3 A3 K3
A3>K3
Stock 4 A4 K4
A4>K4
Stock 5 A5 K5
A5>K5
Stock 6 A6 K6
A6>K6
Stock 7 A7 K7
A7>K7
Stock 8 A8 K8
A8>K8
Stock 9 A9 K9
A9>K9
Stock 10
A10
K10
A10>K10

4. Brownian Motions (1827) Robert Brown (1773–1858)
A single realization of a three-dimensional Wiener process

5. Norbert Wiener (1894 – 1964)

6. Underlying assets

7. Vasicek Model b: long term mean level a: speed of reversion
σ: instantaneous volatility
Oldrich Vasicek

8. Fitting short rate to yield curve using Maximum Likelihood Estimation

9. Interest rate dynamics for various simulations

10. Price dynamics of ABMD for different volatilities

11. Price dynamics of ABMD for different volatilities

12. Thank you for attention
Mucho gracias
Thank you for attention
Спасибо