# Tag Info

Accepted

### Book/reference to practice stochastic calculus and PDE for interviews

You may like: Probability and Stochastic Calculus Quant Interview Questions by Ivan Matić, Radoš Radoičić, Dan Stefanica 150 Most Frequently Asked Questions on Quant Interviews, Second Edition by Dan ...
• 12.4k

• 514

### Is there an intuitive explanation for the Feynman-Kac-Theorem?

Let's approach this answer in two steps. First, I find it quite intuitive, that for a given stochastic PDE there exists a deterministic PDE that evolves the density to a later time. This equation is ...
• 348

### How to understand the market price of risk

I think you misunderstood the underlying idea of the risk-neutrality and the market price of risk. The basic idea is to price the option with a portfolio consisting of the underlying asset $S$ and ...
• 267
Accepted

### The PDE of caplet and floors

It must be a typo for the equation in the book. That is, the equation for a caplet is of the form \begin{align*} \frac{\partial V}{\partial t} + LV - r_t V +\max(r_t-r^*, 0) = 0, \end{align*} which ...
• 21.1k

### Prove that $E[g(X_T)|\mathscr F_t] = E[g(X_T)|X_t]$

This is a corollary of Feynman-Kac theorem. For self-containedness, I re-produce the proof as follows. Assume that there exists a $C^{1,2}$-function $F=F(t,x)$ defined on $[0,T]\times\mathbb{R}$ that ...

### How to apply the chain rule for partial derivatives to transformations?

As you state in your comment, you only have trouble with the second partial derivative w.r.t. the spot. So you understand how the first partial derivative is obtained \frac{\partial ...
• 6,044

### The PDE of the probability hitting the barrier before T

May be I have overlooked something, but I believe that \begin{align*} Q(t, S) = \mathbb{P}\left(\tau_{B} \le T \mid \mathcal{F}_t\right). \end{align*} Then $\{Q(t, S), \, 0<t < T\}$ is a ...
• 21.1k

### why futures contract has no value

The mathematical analysis above is correct, but to understand WHY we say that "a futures has no value" it is helpful to understand how a Futures Exchange works. When you enter into a position (for ...
• 11.4k
Accepted

### How to price the American style Asian option with recent N day average

In convertible bond pricing there is something similar called a "soft call" with similar properties so you might want to search for literature on them. The main difference is that soft calls are an ...
• 14.9k

### What are the advantages and limitations of predicting future stock prices using stochastic differential equations?

The GBM model is liked by practitioners for the modelling of stock prices for the following reasons: (i) The solution is log-normal, so the stock price distribution varies between zero and infinity: ...
• 6,118
Accepted

### Approximating Sharpe and Sortino ratios from Exponential moving averages

For anybody still following this: I figured out that the equations and my code work fine; the problem was that I had to scale the returns before doing the risk calculations to avoid float32 precision ...
Accepted

### Using the risk neutral version of the First Fundamental Theorem of Asset Pricing to derive a partial differential equation

In the answer to a related question of yours it was shown that under the risk-neutral measure $\mathbb Q$ the process $$S_te^{-rt}=S_0e^{-\frac{\sigma^2t}{2}+\sigma W^{\mathbb Q}_t}$$ is a ...
• 2,033