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As a financial innovation, the options market is introducing Options contracts based on California Earthquakes. In your own words, discuss the following:

True or False? “The sellers of Options on California Earthquakes should perform option pricing based on the real world probabilities of Earthquakes.”

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    $\begingroup$ It is a question about Risk Neutral Probabilities versus Real World Probabilities. Trying to probe whether you understand the distinction between them. Which do you think should be used here and why? (See also the related question linked on the right.). $\endgroup$
    – nbbo2
    Commented May 16, 2021 at 0:53
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    $\begingroup$ Did you just copy and paste your homework question here? You may want to consider that 1) you will learn a lot more if you try to answer the question by going through your course notes, and 2) you are probably violating your course instructor's copyright (and possibly their explicit course rules). Best of luck with your learning! $\endgroup$
    – user2705196
    Commented May 16, 2021 at 14:01

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The heart of option pricing is the ability to replicate. If you can make a mango from apple and orange, the price of the mango is determined by the cost of an apple and an orange. People may value the mango less or more than that, but the market price is already constrained and there is no scope for pricing in these (real world) preferences. No replication means people can opine on the value of a mango and that value has a way of sneaking into the mango price.

If one sells options on earthquake events, there is no way to replicate that payoff so there is scope for subjective assessment (real world probabilities) driving the price. There is no concept of risk neutral probability here because there is no replication of the option payoff.

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  • $\begingroup$ I think you can still create a martingale measure as with other incomplete markets (since the underlying “earthquake” itself is not traded). You will have to create a constant market price of risk. For example to value temperature derivatives, the risk free asset is defined as the one that gives one dollar for every unit increase in degree C. So it might be possible to value Earthquake derivatives in Q similar to weather derivatives. $\endgroup$
    – Dhruv Mahajan
    Commented May 17, 2021 at 5:28
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    $\begingroup$ This would be equivalent to the development of a liquid apple (or orange) market in @Arshdeep Singh Duggal's answer. If it happens, you can indeed calibrate your models to these quotes and get the market implied price of the mango by replication (i.e. absence of arbitrage opportunities). But to quote these contracts in the first place he is right, we are back at the original question and the above answer in my opinion too: historical probabilities + participants risk aversion. Unless there is a causality/structural relationship between the price of a mango and a potato (weather derivative). $\endgroup$
    – Quantuple
    Commented May 17, 2021 at 5:53

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