# Questions tagged [merton-model]

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### Understanding the application of Asset-Correlation to credit risk models

Suppose we have a portfolio of $n$ credits. In order the estimate the Portfolio Value at Risk (99,9) we use a standard vasicek model with the Ability to pay variable $A_i=\sqrt{\rho}x+\sqrt{1-\rho}z_i$...
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### Can someone provide an example of how arbitrage would be used when an american call option can be bought for less than max(final stock - strike,0)? [closed]

"Final stock" means the stock price at expiration, and "strike" means strike price. If a call option had to be purchased for more than the max(final stock - strike,0)then you would ...
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### Solving Equation for estimation risk averse parameter

Let the portfolio value follow the SDE: $$V_t=(\mu w+r(1-w))\cdot V_t\cdot dt +\sigma \cdot w\cdot V_t \cdot dB_t$$ where $\mu$ = drift of the portfolio, $\sigma$=standard deviation of the portfolio, ...
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### Maximum Likelihood Estimation for Merton's Jump Diffusion Model

I'm wondering if there is a consensus about the a) most accurate and b) most computationally efficient way to estimate parameters for Merton's (1976) jump diffusion model. In this model, the ...
1 vote
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### Does Gordy Formula measure default risk & downgrade risk?

The Gordy Formula used for measuring Credit Risk as proposed in Basel Rules is based on the asymptotic single risk factor model. It is derived from a Merton Model. The Merton Model only knows to stati,...
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### How can you interpret one of the parameters of optimal consumption at the Merton portfolio problem?

Statement: Let the dynamics of wealth of the agent satisfy $$dX_{t} = \pi_tX_t\Big(\mu dt+\sigma dB_{t}\Big)- c_t X_t dt, \qquad \textrm{with}\quad X_0=x_0 \in \mathbb{R},$$ where $(\pi,c)$ is an ...
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### Use of PIT vs TTC PD in a Merton one-factor model

Under one-factor Merton framework, like Basel, you use unconditional PDs as input of the portfolio model and this "unconditional" means it is a TTC-PD. Given a i-th borrower, the default ...
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From Lando (2004)* I am trying to replicate the following figure (Section 2.6 Default Barriers: The Black-Cox Setup): The spreads are computed as follows: $$s(T) = \frac{1}{T}\ln\frac{D}{B_0}-r$$ ...
1 vote
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### Relationship between asset volatility and debt and equity value

So how I understand it, higher asset volatility implies a higher call option price. The Merton Model holds that the value of equity is a call option. This therefore implies that the equity value must ...
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### Hedging jump models with a infinite number of derivatives

First of all, I inform you that I am not a financial mathematician and have vague knowledge about an incomplete market. Stochastic volatility models are incomplete so derivatives cannot be ...
1 vote