Monte Carlo Valuation of Conditional Multi-Asset Options

Summary

The document considers an option whose payoff depends on several assets meeting exercise conditions together. Its example combines a call on one stock, a put on another, and a call on an index. The response distinguishes this structure from a conventional basket option and describes the other assets’ conditions as external barriers.

For more than two underlyings, it recommends Monte Carlo valuation using a chosen market model, ideally a stochastic local volatility model when available. It proposes calculating Greeks by bumping inputs and repricing. The answer does not provide a payoff formula, implementation details, calibration guidance, numerical results, or a worked example. It also cautions that the shapes of the Greeks are difficult to generalize because they depend on multiple factors, including volatility and cross-asset dependence.

Key ideas

• A conditional option on several assets can be viewed as an option with external barriers rather than a standard basket option.
• Monte Carlo simulation can handle structures with more than two underlyings.
• A stochastic local volatility model is suggested when suitable market data and infrastructure are available.
• Greeks can be estimated by changing an input and repricing the structure.
• Greek behavior depends on several interacting factors and is not characterized in detail.

Tags

# Valuing Conditional "All Or Nothing" Multi Asset Options


# Valuing Conditional "All Or Nothing" Multi Asset Options












I would like some insight as to how to value modified rainbow options on multiple assets:

For example: A multi asset option, Call GOOG with $S_t$ \$1600 that you may exercise if and only if you also exercise a put on TSLA with $S_t$ \$600 and a call on the SPY with $S_t$ \$400, I have read Jan Stuller's answer to a similar question, but not exactly sure how to generalize this for the option structure above on $n$ securities.

As well, how would a pricing model for a option such as the one above model changes in the correlations of the underlying securities and their volatilities? How would one define the Greeks for an option like this one?

## Answer by AKdemy (score 1, accepted)

https://quant.stackexchange.com/a/64189

For more than two underlyings, look here.

It is not a traditional basket option, just external barriers. Usually modelled with Monte Carlo (and a model of choice, or whatever is available). Ideally, SLV.

Greeks will be bump and reprice. In terms of the shape of greeks, this is difficult to answer as there is a number of factors affecting this. You can find simple and intuitive charts here.

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