Question

A forward rate is the mathematical expectation of a future spot rate in risk neutral world.

True

False

Answer 1

True.

A forward rate is the mathematical expectation of a future spot rate in risk neutral world as the forward rate takes into account the discounted value of what the spot rate will be in the future (since other risk factors are constant - it is a risk neutral world)

To elaborate:

a risk-neutral measure is a probability measure such that each share price is exactly equal to the discounted expectation of the share price under this measure.

As per the fundamental theorem of asset pricing, in a complete market, a derivative's price is the discounted expected value of the future payoff under the unique risk-neutral measure. Such a measure exists if and only if the market is arbitrage-free.