Monte Carlo Barrier Pricing with Serially Dependent Returns

Summary

The document asks how to estimate the payoff or expected return of a path-dependent barrier strategy when short-interval returns are serially correlated. The motivating example places both a stop-loss and a stop-return after a liquidity shock, then considers simulating several successive price steps from historical return data. The central issue is that an independent and identically distributed return assumption may not fit the data, while barrier outcomes depend on the sequence of returns and whether a threshold is crossed.

The brief answer suggests fitting a statistical distribution to historical returns, such as a beta or lognormal form, or specifying a distribution by its mean, variance, skewness, and kurtosis, then sampling in Monte Carlo. This gives a possible way to represent non-normal marginal behavior, but it does not explain how to preserve serial dependence or calibrate a path model. Matching four moments alone does not determine the joint dynamics needed for barrier pricing. No empirical results, model comparison, or treatment of jump and liquidity effects is supplied, so the proposal is incomplete for the stated path-dependent problem.

Key ideas

• Barrier strategy outcomes depend on the sequence of returns, not only the terminal return.
• The question highlights serial correlation in returns sampled at short intervals.
• The suggested approach fits a distribution to historical returns or specifies selected moments for simulation.
• A marginal distribution fit alone does not preserve serial dependence between successive returns.
• The response provides no complete path-generation method or evidence of pricing accuracy.

Tags

# How to price a barrier using monte carlo when return distribution is not iid?


# How to price a barrier using monte carlo when return distribution is not iid?












this question is actually related to set the stop loss and stop return. Say after a liquidity shock, I want to place two stops, one being stop loss and another being stop return. If I use, say 10 seconds return for the next one minute to collect historical data, I am pretty sure the return is not iid, most likely serial correlated.

If return is iid, I believe I can simulate 6 step price using monte carlo simulation to find return expectation for different stop loss and stop return pair.

But in this case, it is not iid, what is the approach to find the return expectatoin based on historical data, when the expectation is like barrier option that is path dependent?

## Answer by Kiann (score 1)

https://quant.stackexchange.com/a/42691

perhaps you can fit the historical return data into best-fit statistical profile; such as beta, lognormal, or even specifying the 4-moments for the distribution directly.

You can then generate a monte-carlo run where the sample draws from a 4-moment distribution (by 4-moment, I refer to specifying the mean, variance, skew, and kurtosis directly).

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