DLOM Chaffee Model

The Chaffee Model, also known as the “European Put Option Model,” estimates the DLOM as the value of a European-style put option on the common shares with a strike price equal to the share price on the valuation date. The Black-Scholes-Merton model is used to calculate the put option price. In order to apply the model. In practice, the strike price is set equal to the share price on the valuation date, while the expected option life or term is the estimated holding period or delay incurred in selling the shares. Dividend yield will reflect any dividends paid by the actual shares under consideration. The risk-free interest rate over the option term may be estimated from the yield of US Treasury of other Sovereign debt issues. Determination of expected volatility is more problematic. Since the subject stock does not actively trade, the expected volatility must be estimated from the data of “comparable” publicly traded companies.

Function Description: The Chaffee model requires these inputs to estimate the Discount for Lack of Marketability (DLOM):

1. Time (T)

   Definition: This input represents the length of the period during which the asset or stock is expected to be held before it can be freely traded or sold, usually measured in years.

   Significance: The duration of the holding period directly influences the valuation of the put option used in the Chaffe model. The longer the holding period, the greater the potential for the underlying asset's price to fall below the strike price (typically the current price), increasing the value of the put option and hence the DLOM.

   Application: In practice, this would be estimated as the expected time until an exit scenario is likely, such as a sale or IPO, or until restrictions on sale after a vesting period are lifted.

2. Expected Volatility (σ)

   Definition: This measures the expected annualized standard deviation of the returns of the underlying asset. It is a gauge of the asset's price variability or risk.

   Significance: Volatility is a critical factor in any option pricing model because it affects the likelihood that the option will end in-the-money at expiration. Higher volatility increases the option's value by increasing the probability that the asset’s price will deviate significantly from its current price, thus increasing the DLOM.

   Application: For publicly traded stocks, volatility can be estimated from historical market data. For private companies, volatility might be estimated by looking at similar public companies (peer group analysis) or industry volatility averages.

3. Interest Rate (r)

   Definition: This is the risk-free rate applicable over the holding period of the asset. It represents the return that investors would expect from a risk-free investment for the same duration.

   Significance: The interest rate affects the present value calculations within the option pricing model. It is used to discount the expected payoff of the put option, affecting its value. Lower interest rates tend to increase the value of options, and vice versa.

   Application: Typically, the yield on U.S. Treasury securities matching the holding period of the asset is used as a proxy for the risk-free rate.

4. Dividend Yield (q)

   Definition: This is the expected annual dividends paid by the asset as a percentage of its current price.

   Significance: Dividends reduce the expected future price of the asset because they represent a payout of assets which reduces the equity value. In the context of the Chaffe model, expected dividends reduce the value of the underlying asset, potentially increasing the value of the put option and thereby the DLOM.

   Application: For dividend-paying stocks, the yield can be estimated based on historical dividend payments and expected future dividends. For stocks that do not pay dividends, this value would be set to zero.

These inputs are crucial for accurately modeling the DLOM using the Chaffe approach. They collectively influence how the European put option, representing the lack of marketability, is valued, which in turn determines the size of the discount applied to the asset’s value due to its illiquidity.