We’re rewarding the question askers & reputations are being recalculated! Read more.

# Questions tagged [differential-equations]

The tag has no usage guidance.

54 questions
Filter by
Sorted by
Tagged with
159 views

### Evaluating the SDE $dX_t = t\,dS_t$

The process $S$ is a geometric Brownian motion with an SDE: $dS_t = S_t(\sigma\, dB_t + \mu\, dt)$. I'm stuck evaluating $E(X_t)$ and $V(X_t)$, where $dX_t = t\,dS_t$.
33 views

### B-S derivative with another boundary condition

I want to use the derivation of BS for another type of derivative, not an option. Known the derivation of the Black-Scholes differential equation, is it possible to use in the same equation when my ...
54 views

44 views

### Functional Analysis or Ordinary Differential Equations? [closed]

I am a current undergraduate and will be looking to apply to Quant Programs next year. This semester I have the choice between selecting Functional Analysis and Ordinary Differential Equations. I have ...
137 views

### Black-Scholes to Diffusion Initial Condition

I'm having troubles with the transformation from the Black-Scholes PDE and transforming it to the diffusion equation. I read this other stackexchange post (Here) and I understand most of the process, ...
70 views

### Differential product Correlated processes

I am trying to derive the differential of the product of two processes, but I got stuck. This is what I have until now: We have the following two stochastic processes: $dX_t= \mu_t dt +\sigma_t dW_t$...
701 views

### Market Making Strategies Found by Hamilton-Jacobi-Bellman Equation

Im working my way through the book "Algorithmic and High-Frequency Trading" (AHFT) by Cartea, Jaimungal and Penalva and i'm curious to see how the market making model with an exponential utility ...
41 views

97 views

### Why do we have to use discretization methods for SDE?

I haven't found the answer for the question above in google. Why can't we just discretize the equation instead of using methods like euler or milstein for the discretization.
323 views

### Differential Sortino Ratio

I'm attempting to optimize a reinforcement learning system to maximize risk adjusted returns. I have currently defined the reward as the differential Sharpe ratio at each step: the influence of the ...
295 views

### Riccati Equation in spot rate model

Given that $dr=(\eta-\gamma r)dt+\sqrt{\alpha r+\beta}dW$ Let $Z(r,t)=e^{A(t;T)-rB(t;T)}$, \begin{matrix} \frac{dA}{dt}=\eta B-\frac{1}{2}\beta {{B}^{2}} \\ \frac{dB}{dt}=\frac{1}{2}\alpha {{...
299 views

### Pricing the Passport option

Suppose underlying asset $S$ $$dS = \mu Sdt + \sigma Sd W$$ our portfolio $\pi$ consist with $q(t)$ stock $S$ and cash $\pi - qS$...
2k views

### How to understand the market price of risk

Consider the stochastic vol: $$dS = \mu Sdt + \sigma SdW_1$$ $$d\sigma = p(\sigma,S,t)dt + q(\sigma,S,t)dW_2$$ $$dW_1dW_2 = \rho dt$$ We want to obtain the price of option $V(\sigma,S,t),$ we use the ...
54 views

196 views

710 views

### How to solve this PDE using Feynman-Kac?

I have the following problem right now: solve $$F_t(t,x) + rxF_x(t,x) + \frac{\sigma^2}{2}F_{xx}(t,x) = rF(t,x), \\ F(T,x) = (x - K)^2.$$ How do I solve this? There exists a theorem to solve this, ...
417 views

151 views

1k views

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

I'm attempting to implement aforementioned SVCJ model by Duffie et al in MATLAB. so far without success. It's supposed to price vanilla (european) calls . parameters provided, the expected price is: ~...
12k views

371 views

### Can we explain physical similarities between Black Scholes PDE and the Mass Balance PDE (e.g. Advection-Diffusion equation)?

Both the Black-Scholes PDE and the Mass/Material Balance PDE have similar mathematical form of the PDE which is evident from the fact that on change of variables from Black-Scholes PDE we derive the ...
So, any European type option we can characterize with a payoff function $P(S)$ where $S$ is a price of an underlying at the maturity. Let us consider some model $M$ such that within this model \$V(S,\...