MATLAB European Call antithetic Flashcards
1
Q
Generate M samples from N(0,1)
A
X = randn(M,1)
2
Q
Simulate first set of M trajectories in one step that are negatively correlated
A
ST_plus = S0exp((r-0.5sigma^2)T+sigmasqrt(T)*X)
3
Q
Simulate second set of M trajectories in one step that are negatively correlated
A
ST_minus = S0exp((r-0.5sigma^2)T-sigmasqrt(T)*X)
4
Q
Define payoff from the first set
A
payoff_plus = max(ST_plus-K,0)
5
Q
Define payoff from the second set
A
payoff_minus = max(ST_minus-K,0)
6
Q
Define average payoff for each trajectory
A
payoff = 0.5*(payoff_plus+payoff_minus)
7
Q
Discount Factor
A
discountFactor = exp(-r*T)
8
Q
MC price
A
price_MC = discountFactor*mean(payoff)
9
Q
Standard deviation of MC estimate
A
stdev_MC = discountFactor*std(payoff)/sqrt(M)
