PERSPECTIVAS EXÓGENAS SOBRE IDENTIDAD ÉTNICA

The model is discrete as it has a finite number of time intervals, each of the same length. It is referred to as ”binomial” because each node of the decision tree represents the same structure; with either an ”up” or a ”down” movement of the underlying which is determined by the volatility parameter. The nodes are such that each state of the economy can move in one of two directions: either moving to an up state or a down state (Roman, 2004). The movements at each node are independent from the previous ones. The model has been selected to generate scenarios about future peak sales, whose prediction is indeed a challenging task.

Originally developed for financial stock returns, the structure can be easily adapted to simulate scenarios describing the changes in future peak sales. The uncertainty associated with the peak sales dynamic is characterized by using probability theory and is expressed by a random variable (Baz and Chacko, 2004).

Figure 1.1: Binomial tree

with probability p or down with probability 1 − p, in accordance with a Bernoulli scheme:

X =      U with probability p D with probability (1 − p)

where D = 1/U to ensure that the tree is recombinant.

If we consider a two time steps, n = 2 as in figure 1.1 the final economic conditions can be achieved through various routes; either an up state followed by another up (U,U) or an up state followed by a down state (U,D). Alternatively it can take the other direction, for example a down state followed by another down (D,D) or a down state followed by an upstate (D,U).

The final states can be represented by the probability space Ω = {U, D}2 = 4states. We make the assumption that the tree is recombinant, that is the nodes U,D and D,U both identify the same state of nature. The final states therefore reduce themselves to the value of three, as in figure 1.1. The structure can be replicated for an “n” number of steps leading to a cone of uncertainty7that tracks, at each node, the various states an underlying can assume.

After having defined the procedures on how to generate peak sales scenarios, the next step is to define the real world (or objective) probabilities “p” that peak sales will assume an ’up’ movement.

As previously discussed, the framework underlying financial options cannot entirely be applied to real options in the pharmaceutical business because the assumptions underlying financial options, such as the replicating portfolio assumption, do not hold for the pharma- ceutical industry. For real options, the main assumption behind the construction of a risk free portfolio would be that the underlying (the drug) is traded, or other assets are accumulated

that perfectly correlate with the drug so as to exactly “span” the drug asset value (Dixit and Pindyck, 1999). Neither of these conditions can be met in the pharmaceutical business. As a consequence, the risk neutrality change of probability measure and the use of risk free as discount rate do not hold. Instead, real world probabilities must be utilized as well as a risk adjusted discount rate.

In the pharmaceutical business, risk neutral probabilities (q), used to construct a risk free portfolio in the financial options setting, need to be replaced by real world probabilities (p) using real option analysis. This significantly differs from other businesses where the under- lying (price of oil, commodities, gold) is traded therefore permitting the use of risk neutral probabilities (q).

In the context of the pharmaceutical industry, real world probabilities “p” describe how predictions of peak sales are updated over time. Fluctuation in the update of the peak sales dynamic of a drug generates risk for the option holders that need to be rewarded at a risk adjusted rate (ra) which bears a premium for non-diversifiable risk. Non-diversifiable risk

contains a market component that cannot be diversified away by investors‘ decisions. Diversi- fication is important for the investor who should aim at owning a well diversified portfolio. At a firm level a lack of diversification exposes the company to business risk related to possible failure of molecules in the pipeline. In this context, a company working on respiratory drug inhalation devices for asthma could reduce risk by investing resources in other drug delivery devices for the same condition (asthma). A characteristic of the pharmaceutical business is that non-diversifiable market risk is not easily separated from technical diversifiable risk during all the phases of the R&D process. Calculating the risk adjusted rate to discount a project’s cash flows and obtain a real option value at each stage of the R&D process will be later discussed.

In financial options, the strike price represents the fixed price at which the investor can exercise the option and buy (in the case of a call option) or sell (in the case of a put option) the underlying. In comparison, pharmaceutical options use the expected development costs that a company needs to sustain in order to bring a molecule from R&D to market launch. These costs present a low level of uncertainty and assume a deterministic path which runs symbiotically with the conditions experienced at each phase of development of a product within the phar- maceutical industry. For example the experience gained in technical operations, empowers an adequate level of estimation on the costs of goods sold. Similarly, knowledge gained through clinical studies offers further information on how to plan for future development costs.

point in time at which the option is no longer valid. For real options, this time coincides with the life span of the project, which in the pharmaceutical industry averages about 6-8 years and corresponds to the maturity of the option to invest. Contrary to financial options, increasing the time to expiration does not increase the value of the real option. The longer it takes to launch the higher the amount of loss experienced from late market entry, patent expiration and the impact of competition (Brach, 2003).

A closer look at the cone of uncertainty shows that the higher the value σ, the wider the spread at the extreme end of the binomial lattice. If the value σ is very small then the lat- tice tends to approximate a straight line. The parameter σ represents the volatility of update of peak sales scenarios identified by the pharmaceutical managers depending on market and technical uncertainty. The absence of uncertainty implies that optionality has no value, then the business case would be better analyzed via a DCF (Discounted Cash Flow) application (Mun, 2004). Volatility is another parameter that does not share the same impact as it does in financial options, where an increase in volatility increases the value of the option. Volatile mar- ket conditions may increase the value of the real option by increasing the upside potential of the drug on the market, but technical uncertainty tends to reduce the value of the project by in- creasing the time to launch resulting in a lost competitive market advantage. Current existing models do not consider the existence of such volatility determined by technical uncertainty. A numerical example presented in this study covers both kind of uncertainty.

After introducing the theoretical framework underlying the model, it is next possible to specify the parameters the model requires to finalize lattice development:

The up and down steps are defined by: u = eσ

√ ∆t

d = 1/u

That the d (down) factor is the reciprocal of the u (up) factor ensures the recombinant property of the tree. The value of ∆t represents the discrete time interval. The parameter σ appearing in the formula, represents the standard deviation, or uncertainty on peak sales pre- diction. Given the complexity of the forecasting process taking place during the development of a drug that will not be launched for another 6-8 years, the value of σ is kept constant along the tree. An estimation of σ based on actual forecasting data will be later presented.

The real world probabilities “p” in discrete settings is defined by Bodgan and Villiger (2007):

P (P kt+∆t= u · P kt) = (1+µ)

∆t_−d

P (P kt+∆t= d · P kt) = 1 − p

where u and d represent the up and down factors respectively and P k is the expected value of peak sales.

The parameter µ used in the calculation of real world probability represents the drift of the peak sales forecast. Due to the complex and uncertain forecasting process, a simplified approach is applied in modeling the drift. In this case the assumption is that the drift of the market, defined by marketing analysts as the market “regimen growth rate”, is the best proxy for the drift of the peak sales forecast.