DLOM Longstaff

The Longstaff model provides an estimate of the DLOM assuming the seller of the shares has perfect market knowledge, and is able to time his sale to maximize the proceeds. The so-called “look-back put option” allows the seller to exercise his put at the end of the holding period at the highest or best price attained by the stock in the period from valuation date to expiration.

Function Description: The Longstaff model requires three key inputs to estimate the Discount for Lack of Marketability (DLOM):

1. Time (T)

   Definition: This is the duration until the option expires, generally matching the holding period during which the asset cannot be sold.

   Significance: The time input is crucial because it defines the window during which the option holder can observe and select the highest price at which to exercise the look-back put option. The longer the time period, the greater the chance that the asset will reach a higher peak price, potentially increasing the DLOM as the model assumes the ability to capitalize on this peak.

   Application: In practical terms, this would be the expected holding period of the shares or assets from the date of valuation to the potential sale or liquidity event.

2. Expected Volatility (σ)

   Definition: This is the expected standard deviation of the returns of the underlying asset, expressed on an annual basis.

   Significance: Volatility is a critical factor because it influences how much the price of the asset is expected to fluctuate during the holding period. Higher volatility increases the potential range of prices that the asset might achieve, which directly affects the valuation of a look-back option. In the Longstaff model, high volatility can significantly increase the DLOM since the model capitalizes on the highest price achieved.

   Application: Expected volatility would typically be estimated based on historical price movements of the asset or comparable assets, or it could be implied by the market prices of options if available.

3. Dividend Yield (q)

   Definition: This represents the dividends expected to be paid on the underlying asset, expressed as a percentage of its current price.

   Significance: While dividends provide a return to the holder, in the context of the Longstaff model, they are less significant in terms of their direct impact on the option pricing. However, dividends can influence the asset's price trajectory, potentially lowering the peak prices achievable during the holding period since dividends typically reduce the price of the underlying asset when paid.

   Application: If the underlying asset pays dividends, this yield needs to be factored into the model. For assets that do not pay dividends, this would be set to zero.

These inputs—time, volatility, and dividend yield—are essential for calculating the value of the look-back put option in the Longstaff model, which then helps estimate the DLOM by assuming an idealized scenario of perfect market timing. This assumption allows the model to potentially provide an upper limit or a very aggressive estimate of the DLOM, making it particularly useful in scenarios where the highest possible marketability discount needs to be justified or explored.