# Questions tagged [feynman-kac]

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### Why is Feynman-Kac formula applicable in Burgard-Kjaers PDE paper?

In the paper Partial Differential Equation Representation of Derivatives with Bilateral Counterparty Risk and Funding Costs by Burgard and Kjaer, they say we may formally apply the Feynman-Kac theorem ...
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### Is there a Black Scholes PDE for a GBM with path-dependent volatility?

Question: Is there a known path-dependent Black-Scholes PDE? To be a little more precise, let $S$ be a stock price under a risk-neutral measure such that $S$ satisfies the SDE with path-dependent ...
354 views

### The derivation of vega/gamma relationship

In Lorenzo Bergomi, Stochastic Volatility Modeling, Chapter 5 Appendix A.1, Equation (5.64), as shown below, seems to assume $\hat\sigma$ to be constant. If that is the case, why do we bother to ...
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### Feymann Kac pde with correlated process

I have to solve the following PDE: \begin{equation} \begin{cases} \dfrac{\partial F}{\partial t}+\dfrac{1}{2}\dfrac{\partial^2 F}{\partial x^2}+\dfrac{1}{2}\dfrac{\partial^2 F}{\partial y^2}+\dfrac{1}{...
1 vote
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### Feymann Kac for multidimensional pde

I Have to solve the following PDE: \begin{equation} \begin{cases} \dfrac{\partial F}{\partial t}+\dfrac{1}{2}\dfrac{\partial^2 F}{\partial x^2}+\dfrac{1}{2}\dfrac{\partial^2 F}{\partial y^2}+\dfrac{\...
71 views

### Can the Feynman-Kac formula be used for asset classes that don’t have options?

So rather than a call option C(S_t,t) we have some type of asset with asset price is given by S(x,t) where x is any type of variable that the asset price depends on. I.e Price of wooden desks, W(x,t) ...
180 views

### Hitting time of Brownian motion with drift using Feynman-Kac

I was studying this question from "A Practical Guide to Quantitative Finance Interviews" and was having some trouble understanding one solution. Please advise if misunderstood anything or if ...
1 vote
498 views

### Black Scholes PDE in forward log space

In BS world, we have the stock process in log space $dS_t=(r-\frac{1}{2}\sigma^2)dt+\sigma dW$. Let's say we want to price $f(t,x)=\mathbb{E}_{t,x}[h(S(T)]$. Using Feynman-kac, we get \begin{equation} ...
527 views

### Deriving the Heston-Hull-White PDE

I'm trying to derive the Heston-Hull-White PDE. The correct backwards PDE is equation (1.3) of this paper on page (2). I will begin deriving the forward PDE, but switching between the two is trivial. ...
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### Explicit form for forwards Feynman-Kac formula

This might be a simple question, but I'm having trouble with it. Consider the Cauchy problem with final condition. \begin{equation} \begin{cases} \frac{\partial u}{\partial t}(t,x) + \mathcal{L}u(t,x) ...
966 views

### Hyperbolic and Elliptic PDEs in Quant Finance

Parabolic PDEs (e.g. heat equation) are closely linked to finance via the Feynman Kac Theorem. Do other types of PDEs appear in quant finance? Elliptic PDEs don't contain a time dimension (so perhaps ...
1 vote
58 views

### Feynman Kac: Perpetual Bond

I would like to derive a PDE for a perpetual bond. Suppose we have a bond that will pay a coupon $C$ until there is a default event that occurs. Take the time of default as $\tau$ and consider the ...