Monte Carlo

Question 1

Standard error of MC estimate of a RV

Answer 1

RMSE

Question 2

Error of Euler scheme discretization method

Answer 2

O(delta*t) which means that the error disappears at the same spped of the decline in time increments

Question 3

If underlying is assumed to follow Lognormal random walk. Is the discrete-time process exact?

Answer 3

Yes -> no approximation is needed -> if payoff is NOT path-dependent, it is sufficient to simulate only final price

Question 4

Option is path-dependent and underlying follow lognormal random walk. Error?

Answer 4

Exact but still =(delta*t) error

Question 5

Error if discretization is approximate

Answer 5

O(delta*t) AND O(N^-0.5) due to N being finite. The error in the price is then the max out of these two

Question 6

Simplest way to calculate delta with MC

Answer 6

estimate options value twice, with S+h and S-h. Errot is then O(h^2). However: maginify error -> solve by using same values for random numbers

Question 7

Simple way of calculating greeks for lognormal RW

Answer 7

multiply final value of S with (1+epsilon)

Question 8

How to generate correlated RVs

Answer 8

Choleski factorization

Question 9

Disadvantages of MC

Answer 9

1) Slow compared to analytical solution

2) American options difficult (must calculate price for ALL values of S and t)

Question 10

Longstaff Schwartz

Answer 10

use regression on sample paths for american options