# Questions tagged [heath-jarrow-morton]

The tag has no usage guidance.

41 questions
Filter by
Sorted by
Tagged with
113 views

### What does volatility process mean and how is it different from volatility?

I have been reading the paper "Bridging P-Q Modeling Divide with Factor HJM Modeling Framework" by Lyashenko and Goncharov (2022). On Equation 5 of page 4 of the paper, I came across the ...
1 vote
54 views

### Interest rate models history

I am familiar with some interest rate models, such as the Vasicek, CIR. I also have an understanding of the basic formalization of other models such as Ho-Lee, Hull-White, HJM, Libor market model (LMM)...
138 views

402 views

1 vote
148 views

### HJM model, existence of arbitrage:

The Setup: Suppose I know the yield curve of a Bond satisfies: f (0, t) = 0.04 for t ≥ 0 and f (ω, 1, t) = 0.06, t ≥ 1, ω = ω 1 , 0.02, t ≥ 1, ω = ω 2 , where Ω = {ω 1 , ω 2 } with P[ω i ] > 0, i = 1,...
122 views

### Vol specifications under Heath Jarrow Morton framework

What are some of the common forward vol specifications under HJM framework used in the industry. I guess most common would be 2 and 3 factor models, but any pointers to more details would be very ...
954 views

### Stochastic Leibniz rule

We have the following single-factor HJM model $$d_tf(t,T)=\sigma(t,T)dW_t+\alpha(t,T)dt$$ $$f(t,T)=f(0,T)+\int_0^t\sigma(s,T)dW_s+\int_0^t\alpha(s,T)ds$$ The discounted T bond is then \begin{align} Z(...
1 vote
942 views

### Understanding the HJM drift condition's dimensions

In an HJM model the forward rate dynamics follow $$df_t(T) =a_t(f_t(T))dt+b_t(f_t(T))dW_t$$ where $W_t$ is a $d$-dimensional brownian motion, $b_t$ takes values in $\mathbb{R}^{d\times d}$ and $a_t$ ...
508 views

### HJM framework problem - showing that HJM drift condition implies that $b(z)=b+βz$ and $(ρ)^2=α$

Hi I am looking for some general clarification to Heath–Jarrow–Morton framework. I am analyzing a problem where the forward rate is modeled as $$f(t,T)=e^{\beta(T-t)} Z_t+h(T-t) \tag{1}$$ for some ...
1 vote
I'm using Glasserman 3.16 and 3.17 algorithm to price bonds. The algorithms evaluates the forward rates and the discount factor $B(0,t_j)$. My question is: How can I price bonds in a future time? I ...
I'm trying to simulate a 3-factor HJM model. I got the algorithms from Glasserman book. In my case, I have $3$ maturity:$0.25y, 0.5y, 0.75y$. So my time grid is: $t_0=0,t_1=0.25,t_2=0.5,t_3=0.75$. ...