Option Pricing and Timberland's Land-Use Conversion Option: Reply
回应Thomson对Zinkhan林地转换期权定价模型的批评，指出Thomson模型低估了转换的机会成本，并论证Zinkhan模型通过使用出价而非林地期望值部分避免了这一问题。
Thomson's response to my recent article (Zinkhan 1991) in this journal proposes an alternative approach for valuing a timberland land-use conversion option. The most significant distinction between the Zinkhan model (ZM) and the Thomson model (TM) is the selection of different analogies for two Black-Scholes option pricing model parameters: the underlying asset price and the exercise price. Thomson defines the adjusted price of the alternative land use (S in his response) to be the underlying asset price; the sum of the land expectation value for continuous forest production (LEV) and the physical costs associated with converting from timber to the alternative land use (CC) is treated as the exercise price (X). In contrast, the gap (SADJ' in Zinkhan) between the price of the alternative land use (PAL To), after adjustment, and the highest bid received for the given tract (POFFo), after adjustment, serves as the underlying asset price in the ZM. Zinkhan assumes that the exercise price (X') is the sum of two values (as of the time of expiration of the option, t'): CC,, and the absolute value of the negative impact on LEV resulting from a deviation (if any) from the optimal rotation age (I,,). There are several serious problems associated with the TM. First, the TM does not recognize the landowner's forfeiture of the land-use conversion option (from timber production to some alternative use) if the tract is converted. Thus, the opportunity cost associated with conversion is underestimated. Given Thomson's framework for estimating the land-use conversion option's value, a solution to the problem would be indeterminable if the exercise price was simply modified through the addition of an estimate of the land-use conversion option. A solution would be unattainable since exercise price is an input in the process of calculating the same land-use conversion option. Zinkhan partially avoids this problem by utilizing POFFo rather than LEVo when estimating SADJ', where a bid is considered by the landowner only if POFF >LEVo. POFFo, which is subtracted from PALTo (after necessary adjustments) in order to maintain the ZM analogy for underlying asset price, might at least partially reflect the value of the land-use conversion option. In contrast, the TM's LEV does not reflect this option value. Because of the possibility that the market-clearing price of the cutover timberland tract at time 0 will