# Tag Info

## Hot answers tagged martingale

### Explaining the Risk Neutral Measure

Life Without a Risk-Neutral Measure How would we price assets without the measure $\mathbb Q$? Well, we would start with some version of the Euler equation $P_t=\mathbb{E}_t[M_{t+1}P_{t+1}]$, where $M$...
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### Strictly local martingales: what is the intuition behind them?

I think to understand the martingale/local martingale distinction, it helps to bring in a third class of processes, the uniformly integrable martingale. I would argue that the local martingale and ...
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### Intuitive Explanation for Shannon's Demon?

Whether it's called volatility pumping, rebalancing premium, or Shannon's Demon it would just be a form of replicating a short gamma option strategy (eg. selling straddles). Intuitively, you are ...
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### How do we determine the "correct measure"?

Recall that any traded asset divided by a numéraire is a martingale under the measure associated to that numéraire. For the 3 interest rates you mention, the natural measure (namely the one that makes ...
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### Intuition for Stock Price Numeraire Drift

As a general principle, I would be wary of economic or financial interpretations of change of measure techniques. Changing numéraires is merely a mathematical tool to ease pricing, see for example the ...
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### Numeraire correlated to the traded asset

As @ilovevolatility explains, the seminal reference for this matter is Geman, El Karoui & Rochet (1995). We assume none of the assets are dividend paying, and they are strictly positive. There are ...
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### Why is this stochastic integral a martingale?

I aim to give a careful mathematical treatment to this answer, whilst following the fantastic book "Basic Stochastic Processes" by Brzezniak and Zastawniak. The reason I am putting this answer on is ...
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### Heston stochastic volatility, Girsanov theorem

Consider the Heston (1993) model under the real world measure ($\mathbb{P}$) \begin{align*} \mathrm{d}S_t&=\mu^\mathbb{P} S_t\mathrm{d}t+\sqrt{v_t}S_t\mathrm{d}B_{S,t}^\mathbb{P}, \\ \mathrm{d}v_t&...
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