# Questions tagged [expected-value]

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### 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 ...
108 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 ...
99 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 ...
48 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 ...
85 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 ...
59 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 ...
116 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 ...