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Libor Market Model

I try to simulate forward rates with the Libor Market Model (LMM). Unfortunately, I just have data for normal vols instead of lognormal vols which are assumed in the LMM. Is there a way I can adjust ...
Marc157's user avatar
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Interpreting parameters on Matlab from Patons code on time varying copulas

I ran Andrew pattons code(2006) for Markov switching time varying copulas with an example code given in the Matlab tool box. This is the equation for Markov switching time varying normal copulas I ...
nadeem's user avatar
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Is this equation correct for portfolio optimization for CARA normal with N risky and one riskless asset?

Suppose the consumer Solves $\max -e^{-\gamma W}$ where $W=X^T D -X^Tp R_f$ where $X$ is the vector invested in a risky asset and $D\sim N(E[D],\Sigma^2_D)$ and $R=\sim N(E[R],\Sigma^2_R)$. Then ${ X=(...
John Williams's user avatar
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1 answer
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Verify numerically relation between mean deviation and standard deviation

I was reading "We Don’t Quite Know What We Are Talking About When We Talk About Volatility" by Goldstein and Taleb, and I was trying to quickly verify numerically the relation between mean ...
EC_crypto's user avatar
0 votes
2 answers
558 views

VaR using normal vol vS lognormal

We are using a vendor's software to calculate the Parametric VaR (using RiskMetrics approach) that take as input the volatility figure of the risk factors. The volatility used so far was the lognormal....
tgeorge's user avatar
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1 answer
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Calculating the Value-at-Risk when changing the confidence level

If I have a VaR estimate at a 95% confidence interval is 10, how do I calculate the approximate level of the VaR if the confidence level was raised to 99%, assuming a one-tailed normal distribution?
May's user avatar
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2 votes
1 answer
214 views

What is the industry standard model for pricing Swaptions during this time of negative interest rates, normal model or shifted log-normal model?

I have referred to the some of the well known papers but none of them has a clear answer for my question. I know that both of these models have some disadvantages but, what is the industry standard ...
Urja's user avatar
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2 votes
1 answer
548 views

SABR Normal Volatility when F = K

Looking at the papers Arbitrage free SABR (Hagan) Managing Smile Risk (Hagan) Explicit SABR Calibration through simple expansions (Floch) all 3 papers have similar forms for expression for implied ...
Benedict's user avatar
  • 326
9 votes
1 answer
205 views

Basic question on Ito integrals

$Let \space X(t) =\begin{cases} 2, \qquad\text{if} \space 0\le t \le 1 \\ 3, \qquad\text{if} \space 1 < t \le 3 \\ -5, \qquad\text{if}\space 3 < t \le 4 \end{cases} $ or in one forumala $...
FFSU's user avatar
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1 answer
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What is the distribution of percentage return in general?

In finance, we often assume that the log-returns $\ln(1+R(t))$ follow a normal distribution. Since $\ln(1+R(t)) \approx R(t)$ when $R(t)$ is small, \begin{equation*} dS/S \sim \text{Normal}. \end{...
Jason chiu's user avatar
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1 answer
3k views

Bachelier option delta = probability of exercise?

Under the Black-Scholes model, the delta of a call option is sometimes interpreted as the probability for the option to end in the money. If I assume that the underlying follows a normal distribution ...
ettlich's user avatar
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7 votes
4 answers
4k views

Downward sloping smile in normal model

We consider an stock price $S$ following a normal model: $dS_t = \sigma dW_t$ We can write this as $\frac{dS_t}{S_t}=\frac{\sigma}{S_t}dW_t$ Hence we can see that $S$ follows a "log-normal" ...
Dark's user avatar
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