Monte Carlo Pricing for a Multi-Currency Basket Option

Summary

The document presents a Monte Carlo setup for pricing a basket option on nine currency crosses. It updates each cross over multiple time steps using lognormal dynamics, with correlated normal draws supplied in a simulation array. At each simulation’s end, it multiplies the cross values to form the basket, calculates the call payoff, and averages payoffs to estimate value. The author notes that pricing is needed repeatedly to calculate implied correlation.

The question focuses on reducing the cost of nested loops in Python and asks about importance sampling. It supplies no answer, benchmark, optimized implementation, or importance-sampling method, so it does not establish which optimizations work best. The code and description are useful as a concrete example of a path-dependent simulation workload, but they do not discuss variance reduction, memory use, discounting, or validation of the model assumptions. Readers would need additional material to assess numerical accuracy and practical performance.

Key ideas

• The example prices a basket call by simulating nine correlated currency crosses across multiple time steps.
• Each path’s terminal cross values are multiplied to obtain the basket value and option payoff.
• The author seeks faster repeated pricing for implied-correlation calculations.
• The document asks about importance sampling but gives no method or performance evidence.

Tags

# Optimizing monte carlo code in python


# Optimizing monte carlo code in python












What are they key points to use while coding a monte carlo simulation in python?

I have the following monte carlo code :

```
payoff = 0    
for i in range(0,n_sim):
    s = x_o.copy()
    for j in range(0,n_steps):
        for l in range(0,9):
           z = z_net[i][j]
           s[l] = s[l]*math.exp(sig[l]*math.sqrt(delT)*z[l] - (sig[l]**2)*delT/2) 
    s_net= np.prod(s)
    payoff = payoff + max(s_net-k,0)

value = payoff/n_sim
```

Here I have 9 currency crosses each with a correlation structure, so the innermost loop handles that, then I am running n steps each with delT time interval, that is the second loop and the outermost loop is for simulations.

Here x_o are the initial values of currency pairs and z_net is n_sim X n_step X 9 matrix with multivariate normal random numbers

As you can see the time complexity of this code is very high due to three loops. What are the best practices to optimize this. I need to because I have to calculate implied correlation which depends on pricing the option multiple times

Apart from this, can someone provide me a coded blog/article with importance sampling in monte carlo?

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