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, we are going to discuss…
Read More Implied Volatility of Options-Volatility Analysis in PythonLast 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 consulting and research firm Cerulli…
Read More Are AI-Powered Hedge Funds Outperforming?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. Recall that, In finance, the beta (market beta or beta coefficient) is a measure of how…
Read More How to Calculate Stock Beta in Excel-Replicating Yahoo Stock BetaExecutive 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 the option’s contractual term, including…
Read More Valuation of Executive Stock Options Using a Closed-Form FormulaIn 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 privilege of redeeming the bond…
Read More Valuation of Callable Putable Bonds-Derivative Pricing in PythonWith 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 right to sell at a…
Read More Short Volatility Funds Lost Money During The PandemicThe 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 the chaotic first half of…
Read More Banks Hold Many Illiquid AssetsConvertible 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 attractive to investors owing to…
Read More Convertible Bond Issuance Has IncreasedHow do you determine the volatility of an unlisted entity, and more generally, how do you forecast volatility? These are non-trivial questions. There is an interesting discussion on Stackexchange: Here is a question I had for a long time but I never asked. Let’s take an easy example, AirBnb will likely have an IPO soon,…
Read More How to Forecast Implied VolatilityA warrant is a financial derivative instrument that is similar to a regular stock option except that when it is exercised, the company will issue more stocks and sell them to the warrant holder. Warrants and options are similar in that the two contractual financial instruments allow the holder special rights to buy securities. Both…
Read More Valuation of Warrants-Derivative Pricing in Python