Monte Carlo Flashcards
Standard error of MC estimate of a RV
RMSE
Error of Euler scheme discretization method
O(delta*t) which means that the error disappears at the same spped of the decline in time increments
If underlying is assumed to follow Lognormal random walk. Is the discrete-time process exact?
Yes -> no approximation is needed -> if payoff is NOT path-dependent, it is sufficient to simulate only final price
Option is path-dependent and underlying follow lognormal random walk. Error?
Exact but still =(delta*t) error
Error if discretization is approximate
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
Simplest way to calculate delta with MC
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
Simple way of calculating greeks for lognormal RW
multiply final value of S with (1+epsilon)
How to generate correlated RVs
Choleski factorization
Disadvantages of MC
1) Slow compared to analytical solution
2) American options difficult (must calculate price for ALL values of S and t)
Longstaff Schwartz
use regression on sample paths for american options