In a previous post, we presented an example of volatility analysis using Close-to-Close historical volatility. In this post, we are going to use the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model to forecast volatility. In econometrics, the autoregressive conditional heteroscedasticity (ARCH) model is a statistical model for time series data that …

Volatility measures market expectations regarding how the price of an underlying asset is expected to move in the future. There are two types of volatility: historical volatility and implied volatility. In a series of previous posts, we presented methods and provided Python programs for calculating historical volatilities. In this post, …

Last month, institutionalinvestor.com reported that AI-powered hedge funds outperformed their peers, Hedge funds with artificial intelligence capabilities showed a huge competitive edge over investors that didn’t use AI, new research indicates. AI-led hedge funds produced cumulative returns of 34 percent in the three years through May, a report Tuesday from …

Convertible bonds are complex financial instruments. However, the accounting treatment for convertible bonds has been simplified. The Financial Accounting Standards Board (FASB) released new guidance last month on accounting for convertible instruments and contracts in an entity’s own equity… Convertible instruments are debt or equity instruments (or features) that either …

In a previous post, we presented a method for calculating a stock beta and implemented it in Python. In this follow-up post, we are going to implement the calculation in Excel. We continue to use Facebook as an example. What is beta? Recall that, In finance, the beta (market beta …

Executive stock options usually have complex payoffs. To price them, we often use the binomial tree method or Monte Carlo simulations. … a lattice model can be designed to accommodate dynamic assumptions of expected volatility and dividends over the option’s contractual term, and estimates of expected option exercise patterns during …

In a previous post, we presented a method for pricing a fixed-rate bond. In this post, we are going to discuss valuation of a callable bond. A callable bond (also called redeemable bond) is a type of bond (debt security) that allows the issuer of the bond to retain the …

With a sudden increase in volatility during the pandemic, many volatility funds lost money. Many funds were struck because they adopted a strategy known as shorting volatility — betting that it will fall or remain low. Such funds sell derivative protection such as put options, which give the buyer the …

The trend in the increased holding of risky assets continues. Because of Covid-19, the big banks now hold more illiquid, opaque assets than before. Lenders including Barclays Plc, Citigroup Inc., BNP Paribas SA and Societe Generale SA reported a surge of more than 20% in their most opaque assets during …

Convertible bond issuance has increased during the Covid 19 pandemic. From a funding perspective, convertible bonds have many attractive features for corporates, which have become more important during the pandemic. …In volatile markets, the value of the embedded option in a convertible bond increases. The asset class also becomes more …