Monte Carlo Errors in Arithmetic Asian Option Valuation

# Monte carlo simulation for arithmetic average price asian option


# Monte carlo simulation for arithmetic average price asian option












I am trying to construct a method in python that evaluates the value of an Arithmetic Asian Option using standard Monte Carlo simulation (without control variates). However, I am not getting the correct option values. The code is adapted from MATLAB source provided here: http://personal.strath.ac.uk/d.j.higham/ch22.m

Here is my implementation: (Key => S0 = stock value, K = strike price, v = volatility, r = risk-free interest rate, T = time to maturity, N = # of observations, M = # of paths in MonteCarlo simulation)

```
def arithmeticAsianCallValue (S0, K, v, r, T, N, M):

    dt = T*1.0/N
    drift = exp((r-0.5*v*v)*dt)

    Spath = numpy.empty(M, dtype=float)
    arithPayOff = numpy.empty(M, dtype=float)

    scipy.random.seed([100])

    for i in range(0,M,1):
        growthFactor = drift * exp(v*sqrt(dt)*scipy.random.randn(1))
        Spath[i] = S0 * growthFactor
        for j in range(i+1,N,1):
            growthFactor = drift * exp(v*sqrt(dt)*scipy.random.randn(1))
            Spath[j] = Spath[j-1] * growthFactor

        arithMean = numpy.mean(Spath)
        arithPayOff[i] = exp(-r*T)* math.max(arithMean-K, 0)

    # Standard Monte Carlo
    Pmean = numpy.mean(arithPayOff)
    Pstd = numpy.std(arithPayOff)

    confmc = [Pmean-1.96*Pstd/sqrt(M), Pmean+1.96*Pstd/sqrt(M)]

    return confmc
```

## Answer by SmallChess (score 1)

https://quant.stackexchange.com/a/33645

- `numpy.max` wouldn't work in this case. Try `Math.max`. If you don't believe me, try this:

> print(numpy.max(-100, 0))

gives

> -100

- You're supposed to draw from random Gaussian, not uniform.

> https://docs.scipy.org/doc/numpy/reference/generated/numpy.random.rand.html Create an array of the given shape and populate it with random samples from a uniform distribution.

Adivice for programming: you're not using the vectorized implementation offered by numpy. If you aren't, forget about it. Mixing looping code with numpy like in this case would just introduce unnecessary bugs.

EDITED

`Spath` is a single dimensional numpy array for a single path. You should have initialized it with `N` not `M`. Making it `M` means you'd average the uninitialised elements (0 by default in Python), and thus very low option value.

@Bob_Jansen and other mods: I'm tempted to close the question off-topic. This is is clearly homework. The finance concepts is fine, it's the actual implementation (e.g. python loops) that's creating incorrect outputs. When I wrote my response, I thought the error was just like misunderstanding in Gaussian. We're here to answer about finance, not python looping.