From Ratings to Historical Default Probabilities
A credit rating — AAA, BBB, and so on — is a compact measure of relative credit risk. It shows how risky one debtor is compared with another. […]
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A credit rating — AAA, BBB, and so on — is a compact measure of relative credit risk. It shows how risky one debtor is compared with another. […]
Standard diversification models have a fundamental weakness: during periods of large market fluctuations and crises, historical relationships stop working. This happens because correlations between assets tend to increase, […]
The value formula from Valuation: Measuring and Managing the Value of Companies by McKinsey & Company (also referred to as the Tao of Corporate Finance) is: Value=NOPAT×(1−g/ROIC)WACC−gValue = […]
🎯 GARCH is not just a descriptive model — its purpose is to forecast the volatility of future returns on invested capital. In previous posts, we: Now we […]
1. Second-Level Thinking Successful investing begins where obvious thinking ends. It is not enough to say that an asset, company, or market is good. The real question is […]
Models of return volatility such as EWMA and GARCH aim to explain volatility clustering. In real markets, calm periods tend to be followed by calm periods, while turbulent […]
The maximum likelihood method is used in modeling to estimate the parameters that make historical events most probable. Suppose an event has occurred. If we assume that this […]
GARCH (1,1) and Volatility Clustering Financial markets exhibit an important property: volatility clustering and reversion toward a long-run average. In other words, large movements tend to be followed […]
Volatility is such an overused term that we may forget how important the assumptions are that lead to the final number. Let us start with the basics. When […]
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In previous posts, I covered the calculation of portfolio Value at Risk (VaR) and Expected Shortfall using the historical simulation and linear modeling methods. Now, in order to […]
In the previous note about VaR, I discussed and showed how it is calculated using simulation of historical data. Now I will demonstrate how it is calculated using […]
While the Greek letters view portfolio risk from multiple angles and generate numerous risk measures, the VaR (Value at Risk) metric is an attempt to express portfolio risk […]
The finite difference method, beyond finance, is actively used in physics and engineering fields, such as: The method involves breaking down a continuous differential equation into a system […]
The main advantage of the Monte Carlo simulation method over binomial trees is that it can be used to price options whose payoff depends not only on the […]
One method used to value an American option is the construction of a binomial tree. I have written about this before (Binomial Trees), so here I will focus […]
It turns out that the option price calculated using the Black–Scholes–Merton (BSM) model differs from the price formed in the real market. The reason is that the market […]
The presence of a risk-free asset portion in a portfolio can insure its value with almost the same precision as purchasing put options. The value of a diversified […]