Black-Scholes Merton

The Black-Scholes model is a mathematical formula used to estimate the price of financial options. In simple terms, it helps investors determine how much an option - a contract that gives the right to buy or sell an asset (in this case a call option to convert to equity) at a predetermined price - should be worth. Factors that impact this include the current price of the asset, the time until option expiry and the volatility.

When it comes to pricing convertible bonds, the Black-Scholes model can be a bit more complex, but in simple terms:

1. Convertible Bonds: a type of bond that can be converted into a pre-determined number of shares (the “conversion ratio”) of the underlying stock. Hence they have characteristics of both bonds (debt) and stocks (equity).

2. Why use Black-Scholes? Convertibles have an embedded call option - the option to convert the bond into stock if/when the conversion price is reached. Black-Scholes helps in pricing this option component of the bond.

3. Factors to consider:

   • the current stock price

   • the conversion price (otherwise known as the “strike price” in traditional options speak)

   • the time until the bond matures or can be converted

   • the risk-free interest rate (a theoretical return on an investment with no risk)

   • the volatility of the stock (how much the stock price fluctuates around the mean, or “standard deviation”).

4. Calculating the price: using these factors the Black-Scholes formula calculated the theoretical or “fair” value of the conversion option embedded in the bond. This helps determine how much the convertible bond should be worth in the market.

This valuation is crucial because it affects the decision to buy, hold or sell the bond, and whether the equity optionality is well-priced.

Historically this calculation would be done by hand, however, fortunately we are assisted by tools such as Bloomberg’s CVNI and OVCV functions.