Separate Option Fair Value from a Subjective Price Forecast
Summary
The response distinguishes an option's no-arbitrage fair value from an investor's forecast of the underlying asset. In the standard replication framework, fair value is the cost of establishing a hedging portfolio and equals the discounted expected payoff under a risk-neutral measure. A personal forecast of the stock's future price distribution uses a subjective measure and does not redefine that replication-based value.
The forecast can still inform a trading decision: an investor can estimate the distribution of returns from buying or selling the option under their own model and use that analysis to shape a strategy. The example asks how to price a short-dated call given a predicted normally distributed terminal stock price, but the answer does not provide a payoff-integration formula or address American exercise in detail. Its key caveat is that any strategy based on the forecast depends on the model being sufficiently accurate; the subjective forecast should be treated as an investment view rather than substituted for risk-neutral valuation.
Key ideas
- Replication-based option fair value is determined under a risk-neutral measure, not an investor's personal forecast.
- A subjective underlying-price distribution can be used to estimate the investor's expected option returns.
- A trading strategy may compare forecast-based return distributions with market prices while accounting for risk.
- The suggested use of a forecast depends on its accuracy and does not establish a new no-arbitrage option value.
- The response gives the conceptual distinction but does not supply a numerical valuation method for the example.
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Full text
# Valuing an option when we have a view on future price of underlying # Valuing an option when we have a view on future price of underlying I have a model that predicts the future price of a stock, and would like to incorporate this information to value the option. Lets take an example. AAPL stock is trading at 151.89 US dollars today (Sep 22, 2017). I would like to compute the fair value of the call option with a strike of 149 that expires on Oct 20, 2017. From the market I can get the current mid price of the option and its implied volatility. However, lets say my model predicts that the value of AAPL on Oct 20, 2017 is normally distributed with a mean of 145 dollars and a standard deviation of 1 dollar. How could I use this information to compute the value of the option? For the purposes of this question, we can assume the dividend yield is 0 and we know the risk free rate. If somebody has a way to do this for a European option instead of an American that would probably be close enough for my purposes. The purpose of computing the value is so I can buy or sell the option where market price is most different from the value computed above thus maximizing risk adjusted return. The assumption, of course is that my model is accurate. ## Answer by Antoine Conze (score 0, accepted) https://quant.stackexchange.com/a/36179 You cannot incorporate your own prediction into the "fair value" of the option. "Fair value" of the option is the initial amount required to set up the replication hedging portfolio, and is shown to be equal to the discounted expectation of the option payoff under the risk neutral measure, not the subjective measure that comes out of your "personal" model. You can however compute the distribution of return of buying or selling an option under your "personal" model and build your investment strategy accordingly.
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