# Questions tagged [stochastic-calculus]

A branch of mathematics that operates on stochastic processes.

90 questions with no upvoted or accepted answers
Filter by
Sorted by
Tagged with
77 views

### Valuation of Callable Bonds

Is there any way to price American Callable Bonds (those which can be called on any date before expiration) other than basic CRR interest rate trees, since they won't be accurate enough to give ...
32 views

### Stochastic process with determinstic frequency of regime changes

Suppose that I have an OU process. For instance, assume that I want to model the interest rates. Suppose that regime change is known ex ante, and is deterministic in terms of frequency (For instance, ...
92 views

### Log Contract payoff function

I can’t get where Dr. Rouah gets payoff function of log contract. Could you please take a look at that? https://frouah.com/finance%20notes/Variance%20Swap.pdf It’s on page 2, section 3. I couldn’t ...
78 views

### Unconditional Expectation vs. Conditional Expectation at time $0$

In most mathematical finance books I have read (all of them actually), the expectation, with respect to the sigma algebra at time $0$, $\mathcal F_0$, is considered the same as the unconditional ...
88 views

### The conditional expectation of a geometric brownian motion

In this question it states that $$\mathbb{E}[e^{\sigma(W_t-W_s)}|\mathcal{F}_s] = \mathbb{E}[e^{\sigma(W_t-W_s)}],$$ and I assume that $0 \leq s \leq t$. The accepted answer states that this step is ...
54 views

### Self financing strategy and repo rate

I was wondering how to adjust the self financing condition when cash borrowing cas be secured by the stock. Suppose the risk-free money account is $B_t$ and there is a risky asset $S_t$. One have ...
54 views

26 views

133 views

58 views

58 views

### Using malliavin derivative to find the worst Delta-positive hedge?

Background: I've heard that Malliavin Calculus can be used to show the explicit form of a delta-neutral hedge (given an SDE driven market model). For example, here is a sketch here on page 21 on how ...
496 views

102 views

### Intensity Function of Stochastic Processes

I'm fitting some financial data to a model based on a stochastic process and evaluating the fit of it by looking at the compensator. However, I cannot understand well what does it mean to take the ...
25 views

### Call Option on the Square of a Log-Normal: Process of Underlying under Stock Measure and Risk Neutral Measure

I'm working on some quant interview questions from the book called Quant Job Interview Questions And Answers (by Mark Joshi and other authors). Here are the questions from the bookd, and the answers ...
48 views

85 views

### Approximating an SDE for Volatility Estimation

Consider the SDE $$dT(t) = ds(t) + a(s(t) - T(t))dt + \sigma dW(t)$$ where $s(t)$ is a deterministic function that turns out to be the long-term mean (this SDE is used to model daily temperature, so ...
### When $E[f(\alpha,X)] = f(\alpha, E[X])$
When $E[f(\alpha,X)] = f(\alpha,E[X])$, where $f$ is some convex function of the first and second variables, except when the first variable takes the value $\alpha$ in which case the equality holds, ...
I have a very fundamental problem, please help me out. I am little confused with the derivation for the close form solution for the Geometric Brownian Motion, from the very fundamental stock model: \...