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Intuitively, they should both be short correlation, that is the less correlated the assets are the higher the value of the worst of/best of option. The best of option payoff is sandwiched by an exchange option payoff (plus other vanilla forward/option payoffs on single stock, insensitive to correlation): $$ X_T -K + (Y_T-X_T)^+ \leq \max(X_T - K ,Y_T - K,0) \...


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The GBM model can be written as: $$ \delta S_t= \mu S_t \delta t+\sigma S_t\delta t $$ The above is short-hand for the following SDE: $$ S(t)=S(0)+\int^{t}_{0}\mu S(h)dh+\int^{t}_{0}\sigma S(h)dW(h) $$ Solving the above SDE yields an expression that you implemented in your code: $$ S(t)=S_0exp\left((\mu-0.5 \sigma^2)t+\sigma \sqrt{t} Z\right) $$ The Black-...


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We recently released qmcpy which does both Monte Carlo and quasi-Monte Carlo with guaranteed accuracy. For a MC/qMC problem in our framework you need to define your function, measure, discrete distribution (iid standard uniform, iid standard Gaussian, ...), and an algorithm to determine the number of points needed to meet your error tolerance. Lots of ...


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Your simple approach is perfectly reasonable for (somewhat rough) single-period risk. However, when you compound it (via the random walk/brownian motion) you are not accounting for mean reversion of rates and will get risks that are too high, as you have found. Reasonable stochastic models for rates have mean-reversion terms in them that, at their simplest,...


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Best-of + Worst-of = Call1 + Call2 The right hand side is independent of correlation (and you can check it in your model). Therefore if Best-of is short correlation, worst-of must be long correlation. Increasing correlation makes the two assets more similar and therefore makes the best-of more like a vanilla. This is why a best-of is short correlation. (Hope ...


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