3
$\begingroup$

I am currently working on Benth and Benth "THE VOLATILITY OF TEMPERATURE AND PRICING OF WEATHER DERIVATIVES" and i am stuck at following paragraph at page 10, which is about risk-neutral measures in incomplete markets of weather derivatives:

"In order to derive a more explicit expression for the futures price, we need to specify the risk-neutral probability $Q$. Since temperature is not a storable commodity, the futures contracts can not be hedged and the market is therefore incomplete. A risk-neutral probability is by definition a probability measure $Q\sim P$ such that all tradeable assets in the market are martingales after discounting. Thus, all equivalent probabilities $Q$ will become risk-neutral probabilities. We specify a sub-family of probability measures $Q$ using the Girsanov transform: [...]"

Problem:
I do not understand why all equivalent probabilities are risk-neutral probabilities in incomplete markets?!

Thank you very much for your help!

$\endgroup$

1 Answer 1

0
$\begingroup$

That is my solution:

The price of weather derivatives cannot simply be calculated using a hedging strategy, since the underlying is not tradable. We are therefore in an incomplete market. If we restrict the market to weather derivatives, the treasury bill with a risk-free interest rate $r\in\mathbb{R}$ is the only tradeable asset in the market. The discounted treasury bill price is $1$ and it is therefore a trivial martingale with respect to all equivalent measures. Thus, all equivalent probability measures $\mathcal{Q}\sim \mathcal{P}$ will become risk neutral probabilities.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.