Question 4: Can you price options using Arithmetic Brownian motion?

hello fellow quants,
Today’s question is:
Q4: “Can you price options using Arithmetic Brownian motion?”


1. Can we use the same pricing models for different asset classes?
2. How is the money savings account related to a zero-coupon bond?
3. What are the challenges in the calculation of implied volatilities?
4. Can you price options using Arithmetic Brownian motion?
5. What is the difference between a stochastic process and a random variable?
6. What are the advantages and disadvantages of using ABM/GBM for modelling a stock process?
7. What sanity checks can you perform for a simulated stock process?
8. What is the Feynman-Kac formula?
9. What is the implied volatility term structure?
10. What are the deficiencies of the Black-Scholes model? Why is the BS model still used?
11. How does the Ito’s table look like if we include the Poisson jump process?
12. What is the impact of jumps on implied volatility?
13. How to derive a characteristic function for a model with jumps?
14. Is the Heston model with time-dependent parameters affine?
15. Why is adding more and more factors to the pricing models not the best idea?
16. Can you interpret the Heston model parameters and their impact on the volatility surface?
17. Can we model volatility with the Arithmetic Brownian Motion process?
18. What are the benefits of FFT compared to a “brute force” integration?
19. What to do if the FFT/COS method does not converge for increasing expansion terms?
20. What is a standard error? How to interpret it?
21. What is weak and strong convergence in Monte Carlo pricing?
22. What are the challenges of discretizing the CIR process using the Euler method?
23. Why do we need Monte Carlo if we have FFT methods for pricing?
24. How to hedge Jumps?
25. What is pathwise sensitivity?
26. What is the Bates model, and how can it be used for pricing?
27. What is the relation between European and Forward-start options?
28. What instruments to choose to calibrate your pricing model?
29. How to calibrate a pricing model? How to choose the objective function?
30. What are the Chooser options?

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