Monte Carlo Valuation of a Payoff on Traded and Nontraded Assets

Summary

The document considers a security that pays the product of two asset values at maturity, where one asset is traded and the other is not. It assumes the assets follow geometric Brownian motion and are uncorrelated. The proposed approach is to specify a theoretical price process and model inputs for the nontraded asset, then simulate the joint payoff distribution and discount the expected maturity payoff to value the security.

For a nontraded stock, the response suggests using book value per share and historical data to estimate its return, payout, and volatility characteristics. It says a similar theoretical price proxy is needed if the nontraded asset is not a stock. These suggestions are conditional on available data and do not establish that book value is a reliable market value or that the resulting model is arbitrage-free. The answer also leaves key assumptions, including the discount rate and risk adjustment for the nontraded asset, unspecified, so the valuation recipe is incomplete without further modeling.

Key ideas

• The security's maturity payoff is the product of the traded and nontraded asset values.
• The suggested valuation models both asset processes and simulates the payoff distribution.
• The response proposes book value per share and historical observations as possible inputs for a nontraded stock.
• A nonstock nontraded asset requires a suitable theoretical price proxy based on available data.
• The answer leaves risk adjustment and other valuation assumptions unresolved.

Tags

# Security value based on futures contracts of a traded and non-traded assets


# Security value based on futures contracts of a traded and non-traded assets












S1 - index with dividend a,

S2 - non-traded asset.

A security pays off $S_{1T}S_{2T}$ upon its maturity

S1 and S2 are uncorrelated and follow geometric brownian motion.

What is the value of security at time t?

## Answer by alexbougias (score 1)

https://quant.stackexchange.com/a/45471

You could assume that the stock price of S2 is the book value of equity divided by outstanding shares (as long as S2 is a stock). From the previous financial statements, you can find the dividend payout ratio, the rate of return from the change in book price and the standard deviation from the sample standard deviation of the book price series. For S1, you can follow the known steps, mentioned in the literature. For defining contract's value, a simple monte Carlo simulation should provide you with the distribution of S1*S2 at any give time t. Calculate the mean price at time t=T and discount it at time t=0. That is the value of the security.

Note: If S2 is not a stock, you should find a similar a theoretical price, given your data availability.

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