REAL OPTIONS AND PATENT DAMAGES: THE LEGAL TREATMENT OF NON-INFRINGING ALTERNATIVES, AND INCENTIVES TO INNOVATE

Abstract.  Patent litigation has become an increasingly important consideration in business strategy. Damage awards in patent litigation are supposed to compensate the patent owner for economic harm created by infringement and are therefore important for protecting returns to innovation. We analyze the effects that a recent court decision in the United States, called Grain Processing , has had on the incentives of potential infringers to infringe and innovators to innovate. We find that Grain Processing has decreased the expected value of damages awards in patent cases by conferring a 'free option' on infringers. Grain Processing also concluded that the patent owner in the case did not suffer lost profits due to the infringement because the infringer would have adopted an (inferior) non-infringing technology had it not infringed. We demonstrate that this conclusion is inconsistent with standard economic models.     

Implied volatilities,stochastic interest rates,and currency futures options valuation: an empirical investigation

Different models of pricing currency call and put options on futures are empirically tested. Option prices are determined using different models and compared to actual market prices. Option prices are determined using historical as well as implied volatility. The different models tested include both constant and stochastic interest rate models. To determine if the model prices are different from the market prices, regression analysis and paired t-tests are performed. To see which model misprices the least, root mean square errors are determined. It is found that better results are obtained when implied volatility is used. Stochastic interest rate models perform better than constant interest rate models.     

No-dynamic-arbitrage and market impact

Starting from a no-dynamic-arbitrage principle that imposes that trading costs should be non-negative on average and a simple model for the evolution of market prices, we demonstrate a relationship between the shape of the market impact function describing the average response of the market price to traded quantity and the function that describes the decay of market impact. In particular, we show that the widely assumed exponential decay of market impact is compatible only with linear market impact. We derive various inequalities relating the typical shape of the observed market impact function to the decay of market impact, noting that, empirically, these inequalities are typically close to being equalities.     

Pricing exotic options using MSL-MC

Today, better numerical approximations are required for multi-dimensional SDEs to improve on the poor performance of the standard Monte Carlo pricing method. With this aim in mind, this paper presents a method (MSL-MC) to price exotic options using multi-dimensional SDEs (e.g. stochastic volatility models). Usually, it is the weak convergence property of numerical discretizations that is most important, because, in financial applications, one is mostly concerned with the accurate estimation of expected payoffs. However, in the recently developed Multilevel Monte Carlo path simulation method (ML-MC), the strong convergence property plays a crucial role. We present a modification to the ML-MC algorithm that can be used to achieve better savings. To illustrate these, various examples of exotic options are given using a wide variety of payoffs, stochastic volatility models and the new Multischeme Multilevel Monte Carlo method (MSL-MC). For standard payoffs, both European and Digital options are presented. Examples are also given for complex payoffs, such as combinations of European options (Butterfly Spread, Strip and Strap options). Finally, for path-dependent payoffs, both Asian and Variance Swap options are demonstrated. This research shows how the use of stochastic volatility models and the θ scheme can improve the convergence of the MSL-MC so that the computational cost to achieve an accuracy of O(ε) is reduced from O(ε^?3) to O(ε^?2) for a payoff under global and non-global Lipschitz conditions.     

A perturbative approach to Bermudan options pricing with applications

In this paper we address the problem of the valuation of Bermudan option derivatives in the framework of multi-factor interest rate models. We propose a solution in which the exercise decision entails a properly defined series expansion. The method allows for the fast computation of both a lower and an upper bound for the option price, and a tight control of its accuracy, for a generic Markovian interest rate model. In particular, we show detailed computations in the case of the Bond Market Model. As examples we consider the case of a zero coupon Bermudan option and a coupon bearing Bermudan option; in order to demonstrate the wide applicability of the proposed methodology we also consider the case of a last generation payoff, a Bermudan option on a CMS spread bond.     

The term structure of S&P 100 model-free volatilities

We develop an improved method to obtain the model-free volatility more accurately despite the limitations of a finite number of options and large strike price intervals. Our method computes the model-free volatility from European-style S&P 100 index options over a horizon of up to 450 days, the first time that this has been attempted, as far as we are aware. With the estimated daily term structure over the long horizon, we find that (i) changes in model-free volatilities are asymmetrically more positively impacted by a decrease in the index level than negatively impacted by an increase in the index level; (ii) the negative relationship between the daily change in model-free volatility and the daily change in index level is stronger in the near term than in the far term; and (iii) the slope of the term structure is positively associated with the index level, having a tendency to display a negative slope during bear markets and a positive slope during bull markets. These significant results have important implications for pricing and hedging index derivatives and portfolios.     

非木材林产品可持续利用与乡村社会林业的协调发展

本文分析了非木材林产品开发利用的重要性及其潜在价值,认为非木材林产品可持续利用的最佳选择是建立农林复合生态系统,培育非木材林产品产业是实现乡村社会林业持续发展的必然选择,并进一步提出发展非木材林产品产业的指导性原则及政府政策选择。     

存在即期收益时房地产开发的投资时机与可达性问题研究

本文在房地产价格与建设成本均随机以及二者存在相关性的条件下，运用期权分析技术建模，研究了存在即期收益情形下的房地产最优投资时机及其可达性问题，指出投资规则中应当包含期权价值。此外，比较静态的数值分析表明，当相关性存在时，不确定性不一定提高期权价值反而会抑制房地产投资。该结论与不确定性提高期权价值，从而抑制投资的经典结果相反。同时，我们也指出，即期收益提高了投资的临界水平并赋予了投资期权以更大的价值，这表明即期收益抑制了投资水平。特别地，我们对结果亦给出了经济与政策含义。     

An options-based approach to evaluating the risk of Fannie Mae and Freddie Mac

Fannie Mae and Freddie Mac assume a significant amount of interest and prepayment risk and all of the credit risk for about half of the $8 trillion U.S. residential mortgage market. Their hybrid government-private status, and the perception that they are too big to fail, make them a potentially large, but largely unaccounted for, risk to the federal government. Measuring the size and risk of this liability is technically difficult, but important for the debate over the appropriate regulation of these institutions. Here we take an options pricing approach to evaluating these costs and risks. Under the base case assumptions, the estimated value of the guarantees is $7.9 billion over 10 years, with a combined .5 percent value at risk of $122 billion. We evaluate the sensitivity of these estimates to various modeling assumptions, and also to the regulatory regime, including forbearance policies and capital requirements. The analysis highlights the benefits, but also the challenges, of taking an options-based approach to evaluating the value of federal credit guarantees.