# Tag Info

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### Transformation of local volatility model

Yes it is called the Lamperti transform. This document, in particular Theorem 2, page 7, describes what the Lamperti transform is.
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### Riccati Equation in spot rate model

As you noted, this is a Riccati type ODE and it can thus be simplified using the standard transformations for this class - see e.g. Wikipedia. We start by defining \begin{equation} C(t, T) = \frac{1}{...
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### 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 ...

### 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 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 ...
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### SVCJ (SVJJ) Duffie et. al Model implementation in Matlab

About the integration problem: Your integrand is highly oscillatory, and the adaptive quadrature of Matlab doesn't handle such integrands very well. In general, I would recommend Mathematica when ...
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### Differential of time over Browninan motion

Edits have been made, but the original question asked about $\frac{\mathrm{d}t}{W_t}$. The random variable does exist In your [original] question you ask about $\frac{\mathrm{d}t}{W_t}$, although I ...
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### What are the advantages and limitations of predicting future stock prices using stochastic differential equations?

The SDE you are describing is called the Geometric Brownian Motion. In the end its just a model, which underlies certain assumptions, which are usually not met in the real world scenarios. There are ...

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

Take the analogy of equations modelling something in physics. Just because you write down an equation, it does not mean it has to be connected to anything in reality. It only do so to the extent you ...