Chapter 19 Monte Carlo Valuation

Question 1

Monte Carlo simulations is based on the idea that we can

Answer 1

simulate the stock prices to get option prices and then discount those on the risk free rate to get the value of the options

Question 2

Using a uniform distribution to simulate a lognormal can be done by

Answer 2

use uniform as generating the quantiles, then take the inverse normal functions, so if you got 0.1 then N(0.1), and finally raise it by e to get to a lognormal distribution

Question 3

Standard deviation of a group of estimates is

Answer 3

1/(sqrt(n)) * sqrt of 1 sample

which can be found using sqrt over the whole sample

Question 4

Antihectic Monte Carlo

Answer 4

for each draw, you pull the opposite, so for 0.5, you also draw -0.5 can reduce variance as the each draw is normaled out by the other.

Question 5

Stratified Sampling Monte Carlo

Answer 5

take one draw randomly from each part of niform distribution i.e. one from [0, 0.01] , one from [0.01, 0.02] and so forth

Question 6

Control Variate Monte Carlo Method

Answer 6

pg. 585
Choose correlated option that there is a formula for and instead calculate A + B(g - G) = a

B is cov(A, G) / Var(G)

Question 7

Control Variate Monte Carlo Method Variation

Answer 7

var(A) = Var(a)(1 - p^2)