# Questions tagged [expected-value]

The tag has no usage guidance.

46 questions
Filter by
Sorted by
Tagged with
1 vote
36 views

556 views

### How to compute $E[W(T)\exp(W(T)]$

I have got this interview question twice. Does anyone know from which interview question book or another source this question comes from? It may be some well known source as two different interviewers ...
1 vote
36 views

### Calculating E^2[σ^2] where σ is a GARCH(1,1) Proces

Given that α =0,113079 β = 0,873884 ω = 0,0000081 Need the calculate a call price using garch volatility I alsa calculated the kurtosis = 235 enter image description here: https://www.researchgate.net/...
1 vote
155 views

209 views

### Proof that we can price any derivative as the discounted value of its expected return under the risk neutral measure

I am reading a paper which tries to convey the intuition behind the Black-Scholes pricing formula. In that paper, the author states the following two things without proof, and I would like to know why ...
136 views

### 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 ...
70 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 ...
132 views

### Expected value of stochastic optimization

I have a optimization problem where the SDE is: $$dX(t) = [X(t)(u(t)-\beta(t))+\theta(t)]dt+X(t)u(t)\sigma dW(t), t \in [0,T], X(0) = X_0$$ where $\beta(t)$ and $\theta(t)$ are deterministic ...
1 vote
151 views

### 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 ...
513 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 ...
1 vote
161 views

### 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 ...
1 vote
555 views

### 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 ...
$dY_t=2Y_tdt+2\sqrt{1+Y_t^2}dW_t$ where $W_t$ is $P-$Brownian motion (Wiener process). I have defined a new measure $Q$ where the Kernel density (In Girsanov theorem) is $$\phi_t = \frac{Y_t}{\sqrt{... 2 votes 0 answers 724 views ### Expectation of option value Say we are in a BS world where the (conditional on t) price of a call is given by the usual$$V(S_t)=V(S_t;K,r,\sigma,T|F_t) = \Phi(d_1)S_t - \Phi(d_2)Ke^{-r(T-t)}$$Now, what about the ... -1 votes 2 answers 117 views ### Fourth moment of a itos integral I(t)=\int_0^t \sqrt sdW_s What is E(I(t)^4) 3 votes 0 answers 969 views ### Properties of Geometric Brownian Motion Integrated w.r.t. Time (i.e., distribution of a Yor Process) Let S_t be a process which follows a Geometric Brownian Motion: \frac{dS_\tau}{S_\tau} = \mu \,d\tau + \sigma \,dW_\tau By Ito's lemma, we have: S_T = S_t e^{(\mu-{\sigma^2 \over 2})(T-t) + \... 4 votes 1 answer 2k views ### Intuitive explanation for expectiles I am looking for an intuitive explanation for expectiles. Here is a link to a paper about expectiles: Bellini and Di Bernardino: Risk Management with Expectiles, European Journal of Finance, May ... 2 votes 1 answer 3k views ### Expected Value of Stochastic Process Given the following stochastic process:$$ dX = a(X,t)dt + b(X,t)dz $$where:$$ dz = A \sqrt{dt}$$and A is a random variable with mean zero and variance 1. Is there a way to calculate the ... 1 vote 1 answer 557 views ### Write expectation of brownian motion conditional on filtration as an integral? Let W_t be a Brownian motion, so W_t=z_t \sqrt{t} where z_t \in N(0,1) and the pdf of z is f(z)=\frac{e^{-\frac{z^2}{2}}}{\sqrt{2\pi}}. So$$E(W_t)=\int_{-\infty}^{\infty} W_t f(z) dz =\...
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 ...