Inferring an Option’s Required Return from Its Underlying Equity

Summary

The document explores whether an option’s required rate of return can be derived from the required return on its underlying equity, using a call option with a known strike as an example. It proposes comparing two Monte Carlo valuations: a risk-neutral simulation with the risk-free rate as the drift, and a real-world simulation with the equity’s cost of equity as the drift. The question then considers which discount rate applied to the real-world expected payoff would reproduce the risk-neutral option value.

This is presented as a proposed approach and request for guidance, not as a validated pricing method. The document supplies no worked example, conclusion, or literature references. It leaves unresolved whether discounting expected option payoffs in this way yields a meaningful required return, and it highlights the need to distinguish risk-neutral pricing from real-world expected returns when valuing derivatives.

Key ideas

• The document asks whether an underlying equity’s required return can imply a required return for an option on that equity.
• It proposes using different drift assumptions in risk-neutral and real-world Monte Carlo simulations.
• The proposed procedure seeks a discount rate that equates real-world expected payoffs with a risk-neutral option value.
• No conclusion, validation, worked example, or supporting literature is provided.

Tags

# Implying a required rate of return on an option from the required rate of return on the underlying


# Implying a required rate of return on an option from the required rate of return on the underlying












Is it possible to imply a required rate of return on an option from a required rate of return on the underlying?

For example, given a known cost of equity, can you calculate the required rate of return on a call option over that equity given a known strike price?

I wondered whether it would make sense to value the call option using Monte Carlo model under a risk neutral framework where the drift term is the risk free rate, and then use a Monte Carlo model under a real world framework where the drift constant is set to the cost of equity. Under the risk neutral framework the simulated proceeds are discounted by the risk free rate and the mean is taken, giving a value V. Under the real world framework you would calculate the discount rate required for the average NPV to also equal V. This discount rate would be the rate of return required on the option.

Does this make sense? Is there a more eloquent way of doing this?

It would be great is someone could point me in the direction of some literature where options are valued under a non-risk neutral/real world framework, which isn't too inaccessible.

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