Monte Carlo Option Pricer
Price options by simulation under risk-neutral GBM: a European call with standard errors benchmarked against Black-Scholes, antithetic variance reduction, then a path-dependent Asian option with no closed form.
The scenario
The desk's exotic book has payoffs with no closed-form price, so everything is valued by simulation. Before you touch the exotics, the team wants to see you can build a Monte Carlo pricer that agrees with Black-Scholes on a vanilla, knows its own error bars, and uses a basic variance-reduction trick — then extend it to a path-dependent Asian option.
Where this shows up
A Monte Carlo pricer with error bars and variance reduction is a staple quant-dev coding assessment at firms of this type.
Firms such as Mako, Jump, IMC.
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Task brief
# Monte Carlo Option Pricer **Role relevance:** A core quant-dev coding assessment - price by simulation with error bars. **Estimated time:** 60-75 minutes **Difficulty:** Advanced **Format:** Python (.py), requires numpy ## What you are given - `monte_carlo_pricer_starter.py` - `bs_call` provided for benchmarking; the MC functions are left to you ## What you must deliver 1. A European call by Monte Carlo, with its standard error 2. A Black-Scholes benchmark and a convergence check 3. Antithetic variates and the variance reduction they buy 4. An arithmetic-average Asian call priced from simulated paths ## Constraints - Vectorise with numpy; report standard errors, not just point estimates. ## Submission note Implement the MC functions, run the script, then compare against the mark scheme.
Your tasks
- 01Simulate terminal GBM prices and price a European call by Monte Carlo, reporting the standard error of the estimate.
- 02Benchmark against the Black-Scholes closed form and show the estimate converges as the path count grows.
- 03Add antithetic variates and quantify the variance reduction at a fixed path count.
- 04Price an arithmetic-average Asian call by simulating full paths, and report price ± standard error.
How you're assessed
The full points-based mark scheme is included with the pack.
What you'll learn
- How Monte Carlo approximates a risk-neutral expectation, and why the error shrinks like 1/√N.
- How antithetic variates cut variance for free by pairing each draw with its mirror.
- How to price path-dependent payoffs that have no closed-form solution.