# Questions tagged [risk-neutral-measure]

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.

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### ATM Implied Volatility and Expected Variance

This answer claims that $$\sigma^2_{ATM}\approx E^Q\left(\frac{1}{T}\int_0^T\sigma^2_t dt\right)$$ ie implied ATM vol = risk-neutral expectation of integrated variance. Is there some proof available? ...
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### Estimating market price of interest rate risk under CIR model

My goal is to find the market price of risk associated with the interest rate under the CIR model whose stochastic differential equation under the physical measure is given: \begin{eqnarray}\label{...
45 views

### Some thoughts over risk-neutral pricing vs real world expectations

I am trying to connect risk-neutral and physical measure expectations, to understand the difference between a no-arbitrage price and an expected terminal value. Imagine I have a European derivative ...
76 views

### Implication of unique risk neutral measure

I'm reading Shreve Stochastic Calculus II, theorem 5.4.9 (Second fundamental theorem of asset pricing), This is the part that confuses me : suppose there is only one risk-neutral measure. This ...
1 vote
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### BKM risk neutral moments in python

I am trying to compute the BKM implied moments (Bakshi, Kapadia and Madan 2003) in python by following this paper: Neumann, Skiadopoulos: Predictable Dynamics in Higher Order Risk-Neutral Moments: ...
1 vote
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### Dividend Dynamics under Q Measure / Using Girsanov Theorem with Covariance

I want to find the value of a dividend stream. I can do it under the P-measure, but now I would also like to do it under the Q-measure but cant figure out how to derive the dynamics of the dividend ...
63 views

### Is the market price of an asset always lower than the expected discounted value under the REAL WORLD measure?

The risk neutral measure is often said to reflect the risk aversion of investors. So intuitively, I would think that an asset's expected discounted value should be lower under the risk neutral measure ...
40 views

### Equivalent martingale measure and derivative pricing [duplicate]

So I just recently saw in class that to price a derivative you use what is called an equivalent martingale measure which allows you to compute the price of the contract which then will be the expected ...
73 views

### GARCH option pricing

I have been trying to implement GARCH(1,1) model for pricing call options. Suppose I have calibrated Garch(1,1) model for modelling the conditional volatility using the historical data of an equity ...
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### Risk premium of insurance risk

I recently came across an equation in a paper. In short, suppose that $I(t)$ denotes a longevity index at time $t$. An informative indicator that is useful in the absence of any information about the ...
74 views

### Option implied risk neutral distribution vs BKM risk neutral moments

I am doing some research on the option implied risk neutral distribution and methods calculate it, and so far have come across two ways to do so. The first way is through the Breeden-Litzenberger ...
105 views

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### Risk Neutral Change of Measure: Intuition for Adding in Market Price of Risk

In effecting a risk neutral change of measure for Brownian motion of stock prices, can anyone share the intuition behind subtracting the market price of risk from the risk neutral in order to obtain ...