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A risk-neutral measure is a probability measure that yields an expected present value (discounted at the risk-free rate) which is equal to the current market price. The risk-neutral measure is also called an equivalent martingale measure.

5 votes
1 answer
3k views

Why must a riskless portfolio earn the risk-free rate?

In Options, Futures and Other Derivatives when Hull introduces the risk-neutral approach to pricing European options in the one-step binomial model, he claims that Riskless portfolio must, in the …
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4 votes
1 answer
355 views

Do *all* non-dividend paying assets have the risk-free instantaneous return rate under the r...

For simplicity let's consider a 1D BS world. The only source of randomness comes from the Brownian motion dynamics $dB_t$. The risk-free rate is $r$ (one may assume it as constant for the time being). …
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2 votes
2 answers
546 views

Why can only non-dividend paying assets serve as numeraire?

In Kerry Back, A Course in Derivative Securities, Sect. 1.4 (page 29), the author stated the FTAP in the following form (in boldface): If there are no arbitrage opportunities, then for each (non …
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7 votes
1 answer
2k views

How to determine the risk-neutral measure in a Heston model?

To clarify, I'm quite familiar with the risk-neutral pricing framework, and I know one can efficiently Monte-Carlo a Heston model via the non-central $\chi^2$ distribution approach. But so far we're o …
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