# Questions tagged [pde]

The tag has no usage guidance.

24 questions
Filter by
Sorted by
Tagged with
13 views

### Continuous flows Perpetual maturity cap on Exchange Options PDE Change of variable

Im trying to do a change of variable on the following PDE Using the following change of variable $$V(P^1,P^2) = P^2 W(C), C=\frac{P^1}{P^2}$$ I get this for the homogeneous part of the equation: ...
50 views

### Areas of research in calibration of stochastic volatility models

I am working on a thesis in deep calibration of the Heston model, and I wanted to include a section on the historical work, before the use of neural networks in this area. Thus, I was wondering what ...
• 33
61 views

### How are opitons greeks computed for models that require numerical PDE solving [closed]

I am often told that options priced under SLV models, the Greeks cannot be exactly replicated by finite differences, but are computed at the level of the grid used to solve the PDE. Can someone please ...
• 21
94 views

### Option pricing boundary condition

I am currently working on this paper "https://arxiv.org/abs/2305.02523" about travel time options and I am stuck at Theorem 14 page 20. The proof is similar to Theorem 7.5.1, "...
• 135
148 views

### Pricing PDE of Asian option by Shreve

I am currently working on "Stochastic Calculus for finance II, continuous time model" from Shreve. In chapter 7.5 Theo 7.5.1 he derives a pricing PDE with boundary conditions for an Asian ...
• 135
224 views

### Kou model — solving PIDE for European and American options in Python

Toivanen proposed$^\color{magenta}{\star}$ a method to solve the partial integro-differential equation (PIDE) with a numerical scheme based on Crank-Nicolson. In particular, he proposed an algorithm ...
• 96
1 vote
66 views

### Singular Perturbation in Hagan's 2002 SABR paper "Managing Smile Risk"

I'm reading Hagan's 2002 paper Managing Smile Risk originally published on the WILMOTT magazine, and got something confusing. The set up: $P(τ,f,α,K)$ is the solution of the problem as in Equation (A....
• 2,231
72 views

### When to use total derivative and when not to?

as I was trying to teach myself financial mathematics, I came across this topic on transforming black scholes pde to a heat equation. I had the exat same question as this post Black Scholes to Heat ...
1 vote
292 views

### Is stochastic control with the HJB equation used in market making/algo trading at institutions?

In chapter 5 of https://www.maths.ed.ac.uk/~dsiska/LecNotesSCDAA.pdf, they use stochastic control and the Hamiltonian Jacobi Bellman (HJB) equation in attempt to measure bid-ask spreads and optimal ...
45 views

### Pricing equation with two correlated states

Consider the following asset pricing setting for a perpetual defaultable coupon bond with price $P(V,c)$, where $V$ is the value of the underlying asset and $c$ is a poisson payment that occurs with ...
• 327
193 views

### What are the parallels between the Black-Scholes equation and the heat equation?

I'm trying to understand the analogy between the Black-Scholes equation (1) and the heat partial differential equation (2). I understand that (1) can be written in the form of (2) mathematically, but ...
240 views

### What is the PDE for this interest rate derivative?

We have the following model for the short rate $r_t$under $\mathbb{Q}$: $$dr_t=(2\%-r_t)dt+\sqrt{r_t+\sigma_t}dW^1_t\\d\sigma_t=(5\%-\sigma_t)dt+\sqrt{\sigma_t}dW^2_t$$ What is the PDE of which the ...
• 41
1 vote
237 views

• 21
142 views

### Power option's PDE

I am looking to understand the PDE of Power Options in Paull Willmot on Quantitative Finance (2nd Ed), Ch. 8.9 - Formulae for Power Options (p. 149). Suppose the payoff depends on the asset price at ...
1 vote
615 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 ...
• 47
635 views

### Any book which is intro to PDEs but prioritises techniques useful for solving Black-Scholes?

Summary: Can you recommend any book which is: Intro/first course in PDEs Covers solution methods useful for Black-Scholes model? Background I have just started learning about PDEs (after studying ...
90 views

### What is the difference between "stochastic" heat equation and just heat equation?

I am trying to understand the difference between the "stochastic" heat equation and the heat equation. Will i be wrong to say the stochastic heat equation is just the heat equationg with the ...
88 views

• 111
1 vote
138 views

### Canonical text on numerical PDEs in finance

I am looking for a text similar to Glasserman's Monte Carlo Methods in Financial Engineering, but with a focus on numerical methods for PDEs. Glasserman's book seems to cover a lot for what is ...
• 747