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Butsomesituationswarrantagreaterdegreeofskepticismthanothers.Thereareproblemsoftwokin...
But some situations warrant a greater degree of skepticism than others. There are problems of two kinds: The model can be wrong, so that the theoretical value is not the true option value, or the model may give the correct value, but the market price the option differently.
In the first category we include situations in which the model assumptions are violated (to a larger extent than normal). This is true for long-maturity options, where parameters such as volatility and interest rates (which one can treat as being fairly constant over a month) can vary widely and unpredictably over longer periods. We can have confidence in a valuation model only to the extent that we are confident of our forecasts of its parameters out to option expiration, which may be many years in the future.
We can also expect inaccuracies arising from errors in modeling security prices as geometric brownian motion. There is considerable evidence that actual price changes have "fat tails”一 that is, there is a greater probability of a large change in a short interval than the model assumes, leading to hedging problems and undervaluation of short-maturity options. There is also growing evidence that over both long and short horizons, there is some non-randomness in stock price movements.
There is certainly reason to doubt an arbitrage-based model's valuation of an option on an underlying asset that is not traded, even though theorists routinely apply the Black-Scholes for mina to all manner of cases in which the arbitrage is impossible, or essentially so. For example, it is an important theoretical insight that limited 1iability in bankruptcy makes the equity of a firm with outstanding debt similar to a call option to buy the firm's assets from the bondholders by paying the debt. But the firm as a whole is not an asset that can be traded independently from its securities, so there is no way investors could arbitrage the stock against the underlying firm if they
thought the market was mispricing its option value.
The same problem applies to options on any non traded asset, or on anything that is not an asset at all, such as the "option" to abandon an investment project. Even valuing an option on a marketable but indivisible asset, such as a unique piece of property, causes difficulty when there is no way to form a hedge portfolio that can be rebalanced. There are clearly many cases in which one must be skeptical about deriving an option s value from an arbitrage strategy that cannot be done.
The second category of problems pertains when the model gives the true value of an option, but the market prices it differently. The more difficult and costly the arbitrage trade is to do, the greater the scope is for factors not covered in the model to move the market price away from its theoretical value. Several situations have proved particularly difficult for arbitrage based models 展开
In the first category we include situations in which the model assumptions are violated (to a larger extent than normal). This is true for long-maturity options, where parameters such as volatility and interest rates (which one can treat as being fairly constant over a month) can vary widely and unpredictably over longer periods. We can have confidence in a valuation model only to the extent that we are confident of our forecasts of its parameters out to option expiration, which may be many years in the future.
We can also expect inaccuracies arising from errors in modeling security prices as geometric brownian motion. There is considerable evidence that actual price changes have "fat tails”一 that is, there is a greater probability of a large change in a short interval than the model assumes, leading to hedging problems and undervaluation of short-maturity options. There is also growing evidence that over both long and short horizons, there is some non-randomness in stock price movements.
There is certainly reason to doubt an arbitrage-based model's valuation of an option on an underlying asset that is not traded, even though theorists routinely apply the Black-Scholes for mina to all manner of cases in which the arbitrage is impossible, or essentially so. For example, it is an important theoretical insight that limited 1iability in bankruptcy makes the equity of a firm with outstanding debt similar to a call option to buy the firm's assets from the bondholders by paying the debt. But the firm as a whole is not an asset that can be traded independently from its securities, so there is no way investors could arbitrage the stock against the underlying firm if they
thought the market was mispricing its option value.
The same problem applies to options on any non traded asset, or on anything that is not an asset at all, such as the "option" to abandon an investment project. Even valuing an option on a marketable but indivisible asset, such as a unique piece of property, causes difficulty when there is no way to form a hedge portfolio that can be rebalanced. There are clearly many cases in which one must be skeptical about deriving an option s value from an arbitrage strategy that cannot be done.
The second category of problems pertains when the model gives the true value of an option, but the market prices it differently. The more difficult and costly the arbitrage trade is to do, the greater the scope is for factors not covered in the model to move the market price away from its theoretical value. Several situations have proved particularly difficult for arbitrage based models 展开
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但是一些情形跟其它比起来保证一个怀疑论的较棒的程度。 有二个类型的问题: 模型可能是错误的,所以理论上的价值不是真实的选项价值, 或模型可能提供正确的价值, 但是市场不同地定价格选项。
在第一个阶元中,我们包括样板的假定被违犯的情形。 (对较大的范围超过常态) 这对长-成熟选项,叁数 , 像是挥发性和利率 (哪一个能对待当做非常持续在一个月之上 ) 能广泛地而且无法预测地在较长的期数之上改变是真实的。 我们只能有对一个评价模型的信心到那范围我们对选项呼出在外我们的它的叁数的预测是自信的, 未来可能是许多年。
我们也能期待从学名差错在仿制如几何学的 brownian 运动的安全价格方面出现的错误。有真实的价格变化有 " 胖尾部 " 一的相当多的证据哪一是, 超过模型有在一方面的大改变的较棒的可能性一个短间隔承担, 带领到围以树篱问题和短-成熟选项的低估之价值。 也有增加的结束两者的长和短地平线,有存货的价格运动的一些非任意的证据。
无疑地有理由在一个在下面的资产上怀疑以仲裁为基础的模型选项的评价没被交易, 即使理论家通常应用黑色者 - Scholes 为古代希腊的金额单位到仲裁是不可能的情形的所有样子, 或本质上如此。 举例来说,在破产的有限制的 1iability 对鸣叫选项用杰出的债务来制造公司的公正相似藉由支付债务来买来自公司债所有者的公司的资产是重要的理论上的洞察力。 但是公司整体而言不是能被独立地从它的安全交易的一个资产, 没有方法投资者会仲裁对抗在下面的公司群体如果他们
被想的市场正在标错价格它的选项价值。
相同的问题在任何的非交易资产上适用于选项, 或在一点也不是一个资产, 像是 " 选项 " 放弃一个投资计画的任何事上。 甚至评价在一个像一个独特财产这样的可销售的但是不能分割的资产上的选项, 引起困难当没有方法形成能被再平衡的一个树篱文件夹。 在哪一个一定有关源自来自不能够被做的一个仲裁策略的选项 s 价值是怀疑的有清楚许多情形。
当模型提供选项的真实价值的时候,问题的第二个阶元属于,但是市场不同地定价格它。 更困难和更昂贵的仲裁贸易将做, 比较棒的范围是让在模型没被复盖的因素从它的理论上价值把市价移开。 一些情形对于以仲裁为基础的模型是特别地困难的已经证明
在第一个阶元中,我们包括样板的假定被违犯的情形。 (对较大的范围超过常态) 这对长-成熟选项,叁数 , 像是挥发性和利率 (哪一个能对待当做非常持续在一个月之上 ) 能广泛地而且无法预测地在较长的期数之上改变是真实的。 我们只能有对一个评价模型的信心到那范围我们对选项呼出在外我们的它的叁数的预测是自信的, 未来可能是许多年。
我们也能期待从学名差错在仿制如几何学的 brownian 运动的安全价格方面出现的错误。有真实的价格变化有 " 胖尾部 " 一的相当多的证据哪一是, 超过模型有在一方面的大改变的较棒的可能性一个短间隔承担, 带领到围以树篱问题和短-成熟选项的低估之价值。 也有增加的结束两者的长和短地平线,有存货的价格运动的一些非任意的证据。
无疑地有理由在一个在下面的资产上怀疑以仲裁为基础的模型选项的评价没被交易, 即使理论家通常应用黑色者 - Scholes 为古代希腊的金额单位到仲裁是不可能的情形的所有样子, 或本质上如此。 举例来说,在破产的有限制的 1iability 对鸣叫选项用杰出的债务来制造公司的公正相似藉由支付债务来买来自公司债所有者的公司的资产是重要的理论上的洞察力。 但是公司整体而言不是能被独立地从它的安全交易的一个资产, 没有方法投资者会仲裁对抗在下面的公司群体如果他们
被想的市场正在标错价格它的选项价值。
相同的问题在任何的非交易资产上适用于选项, 或在一点也不是一个资产, 像是 " 选项 " 放弃一个投资计画的任何事上。 甚至评价在一个像一个独特财产这样的可销售的但是不能分割的资产上的选项, 引起困难当没有方法形成能被再平衡的一个树篱文件夹。 在哪一个一定有关源自来自不能够被做的一个仲裁策略的选项 s 价值是怀疑的有清楚许多情形。
当模型提供选项的真实价值的时候,问题的第二个阶元属于,但是市场不同地定价格它。 更困难和更昂贵的仲裁贸易将做, 比较棒的范围是让在模型没被复盖的因素从它的理论上价值把市价移开。 一些情形对于以仲裁为基础的模型是特别地困难的已经证明
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