# Questions tagged [expected-value]

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### Why is logarithmic mean equal to the arithmetic expectation less one-half its variance?

I've taken it as gospel that the following equality is true: $$\mathbb{E}[\mu_x] = m_x - \frac{1}{2}\sigma_x^2$$ where: $\mathbb{E}[\mu_x]$ is the expected value of the logarithmic mean of some ...
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### Intuitive explanation for expectiles

I am looking for an intuitive explanation for expectiles. Here is a link to a paper about expectiles: Bellini and Di Bernardino: Risk Management with Expectiles, European Journal of Finance, May ...
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### How to calculate the expected stock returns for an individual stock?

I know about CAPM. My question is if this method is also viable: Calculate monthly logReturns ...
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### Expectation of option value

Say we are in a BS world where the (conditional on t) price of a call is given by the usual $$V(S_t)=V(S_t;K,r,\sigma,T|F_t) = \Phi(d_1)S_t - \Phi(d_2)Ke^{-r(T-t)}$$ Now, what about the ...
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### Determining the No Arbitrage price of max[B(T), S(T)]

Following is given, $dB(t)=rB(t)dt$ $dS(t)= (r-\delta)S(t)dt+\sigma S(t)dW(t)$ where, $r$ is the risk-free interest rate, $\delta$ the continous dividend yield $\sigma$ is the stock asset ...
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### change of measure expectation

How to find expectation of this stochastic process? Also, to show that the expectation of a stochastic process expression [Xt - St] in one measure is equal to expectation of another expression (of the ...
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### Expectation and variance of standard brownian motion

Assuming that the price of the stock follows the model $S(t) = S(0) exp ( mt − (σ^2/ 2) t + σW(t) ) ,$ where W(t) is a standard Brownian motion; σ > 0, S(0) > 0, m are some ...
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### Can the value of a swaption at any time become more negative than the swaption premium?

I am interpolating swaption values as a function of parallel shifts in interest rate and have come across some peculiar shaped options among the data I have at hand. Here is an example of a simple ...
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Let $W_t$ be a Brownian motion, so $W_t=z_t \sqrt{t}$ where $z_t \in N(0,1)$ and the pdf of $z$ is $f(z)=\frac{e^{-\frac{z^2}{2}}}{\sqrt{2\pi}}$. So $$E(W_t)=\int_{-\infty}^{\infty} W_t f(z) dz =\... 0answers 66 views ### Expected value and variance of the stock log-returns under Local Volatility framework I want to calculate the expected value and the variance of the stock process log-returns in the Local Volatility setting (and the realized/terminal correlation but let us begin in the one-dimentional ... 1answer 109 views ### What's the expected value of a repeated game with 50% chance to win 0.5 and 50% to lose 0.5? Assume we start with 1. In the first bet the expected value of remained balance is 1.5 * 0.5 + 0.5 * 0.5 = 1 For N times, is it still 1 according to E(XYZ)=E(X)E(Y)E(Z)? But 1.5^50 * 0.5^50 is not 1. ... 1answer 53 views ### Condition expectation calculation examples and theory [closed] I want to ask you an advice about reading theory and examples of conditional expectation and conditional variance. I want to have my understanding deeper, because sometimes I can't understand ... 1answer 190 views ### Reference material (EV/ betting game questions) for Quant Hedge Funds Interviews [closed] I need material to practice EV games questions.But I lack practice in betting questions where a set-up of a game is given and one has to respond to the best strategy or best bet to take. A good book ... 0answers 28 views ### Intuitive explanation for - Shreve Vol 1 Ch 3 Lemma 3.2.6 I need help in getting a more intuitive understanding of this lemma 3.2.6 in Vol 1 of Shreve's Stochastic Calculus for Finance: Here, in the context of multi-period binomial pricing model, Y is a ... 0answers 23 views ### Order of expectation versus expectation of order (error terms in Taylor expansion) Given a payoff function F(X) of a random variable X, and a Taylor expansion of F(X) around X=a, then the expecation of F(X) can be written as$$ E[F(X)] = F(a) + E[ O((X-a))]  Under what ...
I have discrete time series financial data, with time($u$), price($S$) and someVariable($q$) which looks something like this. ...
$I(t)=\int_0^t \sqrt sdW_s$ What is $E(I(t)^4)$