# Tag Info

Accepted

### Solution of Merton's Jump-Diffusion SDE

Let $$dS_t = \mu S_t dt + \sigma S_t dW_t + S_{t^-} dJ_t$$ where $$J_t = \sum_{j=1}^{N_t} (V_j - 1)$$ is a compound Poisson process, with $V_j$ i.i.d. jump sizes (positive random variables) whose ...
Accepted

Accepted

### Use of PIT vs TTC PD in a Merton one-factor model

The first equation is already a PIT PD if $\displaystyle PD_{i}$ is substituted by TTC PD. The challenges of using this model are: (1) $\displaystyle \rho _{i}$, the asset correlation, is very ...

### Merton model d1 and probability of default

Since $d_1 = d_2 + \sigma\sqrt{\tau}$, you need to know the volatility of your asset value process. You typically estimate it from equity prices (see e.g. Hull's book).
Accepted

### Merton portfolio allocation problem proportions/weights >1 or <0?

Your statement should be correct, the weights into the risky asset are not bounded between $0$ and $1$. Essentially, by setting $r=0$ you omit the term which shows that your weights always sum up to ...
1 vote

### Finding Equity Volatility for the Standard Merton Model of Corporate Debt

If the company is publicly traded you can use the current market capitalization and the implied volatility of that stock (a choice must be made here, it seems sensible to use the ATM implied ...
1 vote

1 vote
Accepted

### Cauchy-Euler ODE with indicator function in coefficient

I solved it for the case $\mu = r_1$, the solution in $\mathbb{C}^1$ takes the guessed form F(V) = \begin{cases} A_0 + A_1 V + A_2 V^{-x} \; \text{ if } \; V>k \\ B_0 + B_1 V + B_2 V^{-y} \; \...
1 vote

### Yearly ytm calculation on stock using binomial model

At the terminal date, the value will be: 1.44, 0.84, 0.84, 0.49 in the four states: UU, UD, DU, and DD, respectively. The probability of an up move is: (1.1-0.7)/(1.2-0.7)=0.8 So the probability of ...
1 vote

### What are the best relative value frameworks for Corporate Credit?

Not a complete answer, but some thoughts below - First you need to bifurcate the names into two categories - (1) Traded Credit, (2) Illiquid credit. For Traded credit underliers, fairly reliable ...
1 vote

### Relationship between asset volatility and debt and equity value

You're right about the equity value increasing with higher volatility. You're wrong about the debt value. That decreases with higher volatility, because it is short an option. And yes, equity ...
1 vote

### Model the share price under the Merton Credit model

Your latter statement is correct. Under the Merton model, Firm Value (FV) = Value of Equity + Value of Debt. The percentage changes in FV are then assumed to be GBM. So, the value of equity will be ...
1 vote

### Merton model for Probability of Default - What liabilities?

The Kealhoffer-Merton-Vasicek (KMV) model is derivative of Merton. Essentially, it codifies the calibration process and extends the framework to empirical distributions. The following entry, Modeling ...
1 vote

### Pricing Exotics: Monte-Carlo is too slow?

I assume you are using MatLab. You may consider pre-generating all 1,000 random numbers once before for-loop by exploiting array coding. Another approach, have you ever tried using Quasi Monte Carlo?...
1 vote
Accepted

### Numerical Methods for Merton Model

You should take a look at the BENCHOP project. There we benchmarked around 15 different numerical methods against 6 option pricing problems. One of the problems was the Merton model. The methods were ...

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