Pricing Options In The Real-World Measure

Option pricing is usually carried out in the risk-neutral world where the market participants are assumed to be indifferent between taking a certain payoff or investing in an asset with that same expected return. Mathematically, an option's price is the expected value of its payoff in the risk-neutral measure discounted to the present at the risk-free rate.  The risk-neutral measure is also known as the equivalent martingale measure or equilibrium measure.

Reference [1] argued that the risk-neutral world is not always realistic,

…the risk-neutral world does not actually exist and reality may be quite different. As is the case in any financial transaction, the views of seller and buyer about reality and its relation to a risk-neutral world are likely to be radically different. To cover his real position the writer may use a value for the volatility parameter 𝜎𝜎 that is larger than anything approximating what the risk-neutral world may presuppose. The buyer may expect the price growth rate of the underlying to be larger than that described by the risk neutral process and therefore try to take advantage of the perceived opportunity to profit by buying the option. Thus, the use of risk neutral arguments in the pricing of an option is rather debateable and at most serves as an indication of the possible value of an option.

The authors proposed an alternative option pricing method based on the real-world expected loss and profit. This pricing scheme can be operated in both real and risk-neutral worlds,

In this paper we formulated option pricing for option traders using expected profit and expected loss, the EP-EL approach. One of the appealing aspects of this approach is that it links directly to concrete metrics familiar to traders, such as profit to loss ratio and average profitability... This approach has a “real world” character and as such differs in principle from the so-called “risk-neutral world “(or no arbitrage) approach that underlies the Black-Scholes methodology.

We find the authors’ arguments valid. However, as in the case of risk-neutral pricing, their real-world approach also contains a lot of assumptions. Using this pricing model to develop trading strategies is not a trivial task.

Let us know what you think in the comments below or in the discussion forum.

References

[1] JH Venter and PJ de Jongh, Pricing options using expected profit and loss measures, 2022

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