dS = mu S dt + sigma S dW
setting mu to r sets the risk measure as though there weren't any arbitrage opportunities
can analytical solution from this:
St/S0 ~logN(f(r,t),f(sigma,t))
St ~ logN
logSt ~ N
therefore, can use this instead of MC simulation, because distribution of St is known and we sample from it
dS = mu S dt + sigma S dW setting mu to r sets the risk measure as though there weren't any arbitrage opportunities can analytical solution from this: St/S0 ~logN(f(r,t),f(sigma,t)) St ~ logN logSt ~ N therefore, can use this instead of MC simulation, because distribution of St is known and we sample from it