Simulating Geometric Brownian Motion Efficiently in R

Summary

The article presents two R approaches for simulating geometric Brownian motion price paths. A nested-loop version generates one random shock at a time for each path and time step. A vectorized version draws the shocks in a matrix, applies the per-step growth factors, and uses cumulative products to construct paths from the starting price. The article also illustrates plotting simulated paths and comparing their terminal prices with a density plot.

For the stated example of 50,000 simulations, the reported vectorized run took about 0.9 seconds, compared with about 10 seconds for the loop-based version. It then demonstrates using the simulated terminal-price distribution to calculate a probability-weighted payoff for a call-like payoff above a strike. These examples show a coding technique and a possible use in payoff analysis, not a validated market forecast or option valuation model. The document does not discuss calibration to market data, discounting, or model risk, and its illustrative payoff calculation should not be treated as a complete pricing framework.

Key ideas

• A loop-based GBM simulator draws a random shock for each path and time step.
• The vectorized approach generates shocks in a matrix and compounds growth factors across time.
• The article reports a faster runtime for its vectorized example than for its loop-based example.
• Simulated terminal prices can be used to estimate a payoff distribution under the chosen model inputs.
• The illustrated payoff calculation does not include a full option valuation framework.

Tags

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.