Option Valuation

On Thursday, September 2, 2010, Svetlana A. Sigalova will present a free live webcast entitled. "The Use of the DecisionTools Suite in Biotechnology Project and Portfolio Decision Making "

Given the uncertainty of outcomes in the biotech industry, consideration of variability is an inherent part of the decision process. Often, the mean (average) is not a relevant decision criteria. This is especially true for smaller biotech companies like Vertex – the opportunity costs are extremely high because scarce capital resources would be invested elsewhere, with a higher probability of realistic return. For example, a company may reject a project which is profitable on average (positive Net Present Value) because some of the possible outcomes are unacceptable to the decision maker. Consideration of variability allows a decision maker to bring in their own risk tolerance into the decision. A similar argument applies when estimating a safety margin above a base case (e.g. in cost budgeting).

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Vertex Pharmaceuticals, Inc. is a global biotechnology company based out of Cambridge, MA. The Company's strategy is to commercialize its products both independently and in collaboration with major pharmaceutical companies. Vertex's product pipeline is focused on viral diseases, cystic fibrosis, inflammation, autoimmune diseases, cancer, and pain.

Given the uncertainty of outcomes in the biotech industry, consideration of variability is an inherent part of the decision process. Often, the mean (average) is not a relevant decision criteria. This is especially true for smaller biotech companies like Vertex – the opportunity costs are extremely high because scarce capital resources would be invested elsewhere, with a higher probability of realistic return. For example, a company may reject a project which is profitable on average (positive Net Present Value) because some of the possible outcomes are unacceptable to the decision maker. Consideration of variability allows a decision maker to bring in their own risk tolerance into the decision. A similar argument applies when estimating a safety margin above a base case (e.g. in cost budgeting).

Vertex’s strategy and analytics group within the corporate finance division seeks to provide the senior management with dynamic revenue and profit forecasting methodology that helps to identify types of drugs that should be developed given a finite amount of cash and resources. A traditional financial view allows the user to identify scenarios and potential outcomes, but lacks the ability to show the range of potential values within each and every outcome. Vertex’s team uses the DecisonTools Suite to establish the average outcome, the variability of outcomes and to pressure-test risk and uncertainty of a particular scenario throughout the decision process.

Vertex’s team built a complex financial risk analysis model using @RISK to enhance its portfolio process. Monte Carlo simulation and optimization are used to analyze and optimize project and portfolio decisions, given short and long-term corporate strategy. @RISK is also frequently used throughout the business development process: simulating across multiple sales forecasts provides BD team with a range of potential outcomes, making it easy to pinpoint a particular scenario on a curve, along with its probability and value. TopRank turns the sensitivity analysis into a quick and seamless exercise, answering multiple what-if questions within minutes. Franchise and program leaders can now see a dollar effect of their program being delayed or advanced, adding supplementary indications to the development plan and even addressing the price uncertainties all at the same time. The simple interface of PrecisionTree along with tornado chart outputs makes it easy to explain the effect and importance of a particular assumption / decision to an audience with no finance background.

As the company continues to grow, adding more drugs and collaborations to its development pipeline, we will see in this free live webcast how the DecisionsTools Suite remains one of Vertex’s analytical tools of choice to enhance and guide the decision making process.

» Register now (FREE)
» View archived webcasts

The UK's new coalition government has said that, as part of its 'Green Deal', it will encourage home energy efficiency improvements paid for by savings from energy bills. It seems likely that, in the year that energy regulator Ofgem warned of 20 percent electricity price hikes by 2020, this initiative will include solar panel technology

Currently the UK still lags behind many other countries in Europe and the rest of the world when it comes to harnessing solar power. Not only do we have less hours of sunshine than many regions, but there is a lack of clarity as to the 'payback' time when it comes to users seeing a return on investment.

This is where Palisade customer, the California-based Tioga Energy, makes an interesting case study. Whilst it may seem unfair to compare the UK with the west coast of America when talking about solar-related matters, the sunnier climate does not reduce the need to prove ROI for customers with solar energy agreements.

Tioga Energy provides project financing through its solar Power Purchase Agreements (PPAs), and maintains and operates solar systems on behalf of its customers. Tioga’s offering delivers predictably priced power and enables organisations to to both 'green' their operations and reduce energy costs. To illustrate the benefits of solar, estimating future electricity prices and making comparisons by showing the savings from a new solar system, Tioga enlisted the help of @RISK for risk analysis solutions.

To forecast possible price increases, Tioga Energy inputs California's historical electricity rate data into a quantitative risk analysis model developed using @RISK. This generates a probability distribution for electricity rate rises over the 20-year PPA period, which shows that there is a 25 percent likelihood that price increases will be less than 4.8 percent, and a 25 percent chance that rate rises would be more than 8.7 percent.

The @RISK risk analysis model therefore helps Tioga Energy evaluate the likelihood that a customer will save money for a variety of PPA scenarios (i.e. the rate at which electricity would initially be charged and the amount by which it would then increase each year). It also calculates the magnitude of savings for the different combinations of first year costs and subsequent rises. Consumers are therefore able to better understand the pricing and make an informed decision about whether to sign up for a PPA.

Using historical data and @RISK's risk modelling software capacity, Tioga offers consumers a robust view of the potential benefits of a solar PPA. This enables them to hedge against rising electricity rates, as well as feel confident that they are playing a part in tackling global warming.

» Read the Tioga Energy case study

Craig Ferri
EMEA Managing Director of Risk & Decision Analysis

@RISK's use of Monte Carlo simulation allows for powerful features, like RiskSimtable.

The RiskSimtable feature can be used to run multiple simulations to test the sensitivity of the risk analysis model, for example to changes in the parameters of a distribution. This model is of a business with a base case expected revenue of 100 and cost of 80, giving a profit of 20.

The risk model assumes that the revenue and cost distributions are determined from a mean and standard deviation. The RiskSimtable feature is used to test the sensitivity of the distribution of profit to changes in the standard deviation of the revenues. Three values are tested of which the first is our original @RISK model. The number of simulations is therefore set at 3. A RiskSimtable can be set up either by directly typing in the required format, or by inserting it as for other Excel functions via the Insert Function menu option. The model also uses some @RISK statistical analysis functions to report the probability for each simulation that the profit exceeds 50.

» Download the example: BasicBusiness.Simtable.xls

This financial risk analysis example demonstrates the use of the Corrmat function to correlate multiple @RISK distributions. The distributions are correlated using a matrix of coefficients that specify the relationship between each pair of functions. The coefficients must be between -1 and +1, with a value of +1 indicating a perfect correlation, 0 indicating no correlation, and -1 indicating a perfect negative correlation. In this example three variables, the current US interest rate, the Pound/$ exchange rate, and the Euro/$ exchange rate, are correlated using a 3x3 matrix. Correlation matrix inconsistency occurs when a matrix that is mathematically impossible to realize is entered. If this happens, @RISK will try to adjust your matrix. However, you may have some correlation coefficients that you do not wish to be adjusted, while others are more or less free to be changed. This information may be entered using an adjustment weight matrix. 

» Download the example:
   CorrmatWithAdjustmentWeightMatrix.xls
» See more Financial Risk Analysis models here
 » Case Study: FiduciaryVest uses @RISK's correlation
    matrices in asset allocation modeling

@RISK, risk analysis software using Monte Carlo simulation, has many powerful features that help you create powerful models for decision making under uncertainty.

For example, you can use the RiskTheo function in @RISK to determine the parameters of a discrete distribution based on a continuous one. In this example, the RiskTheo functions of @RISK work out the P10, P50, and P90 percentiles of a continuous distribution (in this case the LogNormal), and the Mean and Standard Deviation of a RiskDiscrete distribution which has these X-values and some assumed probabilities (or weights). It then uses Excel's Solver to work out the probabilities required so that the discrete distribution based on these percentiles and probabilities would have the same mean and standard deviation as the continuous distribution.

» Download the example: CtsToDiscrete.xls
» See "Uses of the RiskTheo functions in
   @RISK to match distributions"
 » See "DMAIC Failure Rate using RISKTheo" for a
    Six Sigma application of the RISKTheo function

We are pleased to welcome back to my blog consultant and trainer David Roy from Six Sigma Professionals, Inc.

 

 

Oops! Didn’t see that coming! Part 3
 

 

As a continuation from the June blog, we are now covering the “Conceptualize” phase of the ICOV framework of a rigorous new design process as explained in “Services Design for Six Sigma – A Roadmap for Excellence”.

 

This phase is important because it conceives, evaluates and selects good design solutions through robust process methodology which ensures alignment to the customer and the business needs.

 

Many design solutions skip this phase and become typically named as “Launch and Learn”.

 

The Conceptualize phase consists of two stages and associated Tollgates to validate successful completion of the requirements. 

 

The Concept Development stage involves translating Customer requirements into solution free Functional requirements, developing the System Level Conceptual Design, generating Concepts for required functions, Concept selection and translation of the Functional Requirements to Design Parameters.

An example of a Functional Requirement for a Customer Want of “Speedy Service” could be “Speed of Service” and a Design Parameter could be “Waiting Time”

 

Tollgate 3 Exit Criteria:

• Assessment that the Conceptual Development Plan & Cost will satisfy the customer base
• A Decision the design represents an economic opportunity (if appropriate)
• Verification adequate funding will be available to perform Preliminary Design
• Identification of the Tollgate Keeper & the appropriate staff
• An action plan to continue flow-down of the design Functional Requirements

 

The Preliminary Design stage involves creating the design documentation and configuration management, performing design analysis and testing, translating the Design Parameters into Process Variables and formulating the Production strategy.

An example of further mapping the Design Parameter of “Waiting Time” to a Process Variable could be “Number of Phone Lines”

 

Tollgate 4 Exit Criteria:

• Acceptance of the selected Solution/Design
• Agreement the Design is likely to satisfy all Design Requirements
• Agreement to proceed with the next stage of the selected Solution/Design
• An action plan to finish the flow-down of the design Functional Requirements to design parameters and process variables

 

Formal tools which can be used in this phase are QFD, TRIZ/Axiomatic design, Measurement System Analysis (MSA), Failure Mode effect Analysis (FMEA), Design scorecard, Process mapping, Process management, Pugh Concept Selection, Robust Design, Design Scorecards, Design for X and Design reviews.

 

The next and final blog will cover the Optimize and Validate phases.

 

BIO:

 

David Roy is an integral part of the Six Sigma community. He taught GE’s Jack Welch and entire staff Six Sigma, as well as served as Senior Vice President of Textron Six Sigma. He is a Certified GE Master Black Belt, was instrumental in developing GE’s DMADV (DFSS) methodology, and has taught 3 waves of DFSS Black Belts. David holds a BS in Mechanical Engineering from The University of New Hampshire. He is also the co-author “Services Design for Six Sigma – A Roadmap for Excellence”

 

 » Part 1
 » Part 2

@RISK has many applications for oil and gas exploration and production. This quantitative risk analysis model forecasts production, revenues, and present value based on exponential decline. Uncertain input factors include yearly production, decline rate, GOR, price of gas, price of oil, and rate of increase in oil and gas prices.

A SimTable function is also used in the Discount Rate input that is used to calculate Total NPV. This contains two possible values for Discount Rate – 12% and 14% - enabling you to run two back-to-back simulations to compare the effect of different discount rates on your Total NPV.

» Download the example: Declin.xls

Just after I posted my last blog questioning a recent Investopedia column in the San Francisco Chronicle, I had a congenial note from the author of that column, David Harper.  His column compared Monte Carlo Simulation with two other methods of calculating Value-at-Risk, and I was concerned that its view of risk and risk analysis techniques was overly simplified. David   was surprised to discover that column had just appeared because he wrote it five years ago!

The five-year lag explains a lot--Monte Carlo simulation was not nearly so widely adopted or carried about by so many software tools as it is today--and I should have suspected the article was a vintage piece before I started carping.

So I happily retract my concerns to introduce to you David Harper, CPA and certified Financial Risk Manager.  In response to my comment about the attitudes and techniques that led to last year's collapse of the financial markets, David says that, now that the black swan has flown, "the crisis should implicate both HistoricalSim VaR and parametric VaR (at least multivariate normal!) and point toward Monte Carlo Sim. I've been thinking for a while that all of this [I think he means lack of accuracy in specifying risk] should really boost Monte Carlo."

Investment commentary is only one of David's activities.  He is the founder of Bionic Turtle, a business devoted to e-learning about financial risk and preparation for the certification exam for financial risk managers. This is a worthy enterprise--I was relieved to discover that there are hoops financial risk managers have to got through to be called that--and for anyone who would like to know more about quantitative techniques for risk analysis, its website is worth prowling. 

Thank you, David, for setting me straight.  

If you missed Palisade trainer Rishi Prabhakar's webcast "Customised Solutions Using @RISK and VBA for Excel," you can still view it in our archive.

The hour-long presentation explores the use of VBA for Microsoft Excel to control @RISK functionality, to simplify the process of risk analysis for resource-strapped businesses. Rishi explains the advantages (and limitations) of macro control for modelling and running simulations.

Simple examples are worked through to show the XDK (@RISK’s automation library) in action, from generic examples to a cost estimation model. This addresses elements of model construction, various simulation settings and finally reporting. The emphasis is on exposing the viewer to the various possibilities the XDK lends to the user rather than an in-depth VBA for Excel coding session.

Rishi Prabhakar holds a BSc in Mathematics from the University of Technology, Sydney Australia. Rishi has experience in the resources, infrastructure and primary industries, telecommunications, scientific research, banking and finance with an emphasis on operational risk.

With technical skills in the areas of modelling, simulation, statistical analysis, cost estimation, time series forecasting, customised solutions utilising VBA for Excel, and extreme value theory, Rishi has provided training and consulting services in risk and decision analysis for Palisade’s Asia Pacific office since 2005.


» Customised Solutions Using @RISK and VBA for Excel
» Webcast archive

Modeling Uncertain Number of Events, Each with Uncertain Parameters
@RISK (risk analysis software using Monte Carlo simulation) is widely used in insurance and reinsurance for premium pricing and loss reserves modeling. A 2006 survey identified @RISK as the third most widely-used software by actuaries, after Microsoft Office and in-house actuarial tools.

@RISK's RiskCompound function allows for the sampling of frequency-severity distributions. This is often required in insurance modelling, as well as in some operations management situations. For example, to determine the total insurance claims payout, one must account for the uncertainty in both the total number of claims (frequency) and the dollar amount of each claim made (severity). 

A powerful feature of the function is that the argument that corresponds to the severity may be a reference to a cell containing a formula (rather than just a single distribution function). 

For example, one could use the function in the form RiskCompound(RiskPoisson(5), A10). The Poisson distribution would describe the frequency (occurrence) of events (e.g. an individual sample may determine that three events occur), and cell A10 would contain a formula that is separately evaluated for each of these three events (before returning the sum of these three as the sampled value of RiskCompound). 

A simple example could be A10 = RiskLognorm(10000,1000)/(1.1^RiskWeibull(2,1)), with the Weibull distribution representing the time to settlement of an insurance claim, which is used to discount the basic claim value sampled from the Lognormal distribution of severity. For example, once a claim is filed for a nominal amount, the actual payment may be delayed due to court actions or disputes, which may reduce the cost of the claim to the insurer.

» Download the model: RiskCompoundCellReferencing.xls

Variance-covariance assumes volatility only in terms of standard deviation, and volatility doesn't come in one flavor or standard deviation.  Neither does risk.   

@RISK risk modeling software is used for a wide variety of applications in financial risk analysis forecasting, investments, and banking. This model is one example of how @RISK can help in risk analysis decision making.

Models of the prices of assets (stocks, property, commodities) very often assume a random walk over time, in which the periodic price changes are random, and in the simplest models are independent of each other. The future price level of the asset may result in some contract or payoff becoming valuable, such as in the case of financial market options. In these cases, the value of the contract (contingent payment or option) is calculated as the average discounted value of the future payoff. In the special case of European options on a traded underlying asset, the value calculated from the simulation may be compared with mathematical formulas that analytically provide the valuation, such as the Black-Scholes equation. In many more complex cases, the pertinent analytic formulas may be unknown or very complex to derive, and one may wish to rely on simulation techniques. This particular model compares the average simulated payoff for European Call and Put options with the Black-Scholes valuation.

» Download the example: AssetPrices.Options.BS.Multi.xls

@RISK risk modeling software is used for a wide variety of applications in financial risk analysis forecasting, investments, and banking. Below is an application of a discounted cash flow analysis.

Discounted cash flow (DCF) calculations are a frequent example of the use of @RISK. In the example model, the sources of risk are the revenue growth rate and the variable costs as a percentage of sales. After taking into account the assumed investment, and applying a discount factor, the DCF is derived. Following the simulation, the average (mean) of the DCF is known as the net present value (NPV).

In this example, the results show that the average DCF is positive (about 40), whereas the probability of a negative DCF is about 15%. The decision as to whether to proceed or not with this project will therefore depend on the risk perspective or tolerance of the decision-maker.

This example has also been extended to calculate the distribution of bonus payments on the assumption that a bonus is paid whenever the net DCF is larger than a fixed amount (such as 50). It also uses some of the @RISK Statistics functions RiskMean, RiskTarget, and RiskTargetD to work out the average net DCF, the probability that the net DCF is negative and the probability that a bonus is paid.

» Example model: CashFlow.xls

The decisions-by-the-numbers guys certainly had their day in court.  The free advertising wasn't bad either.

As a small--very small--shareholder, discovering that there is such a tipping point and that Karame knows how to locate it is reassuring.  Makes me feel there's someone on my side.   

Example Model: SENSIM.XLS

Sensitivity analysis in @RISK (risk analysis software using Monte Carlo simulation) lets you see the impact of uncertain risk analysis model parameters on your results. But what if some of the uncertain model parameters are under your control? In this case the value a variable will take is not random, but can be set by you. For example, you might need to choose between some possible prices you could charge, different possible raw materials you could use or from a set of possible bids or bets. To properly analyze your model, you need to run a simulation at each possible value for the "user-controlled" variables and compare the results. A Sensitivity Simulation in @RISK allows you to quickly and easily do this - offering a powerful analysis technique for selecting between available alternatives.

In @RISK any number of simulations can be included in a single Sensitivity Simulation. The RiskSimtable function is used to enter lists of values, which will be used in the individual simulations, into your worksheet cells and formulas. @RISK will automatically process and display the results from each of the individual simulations together, allowing easy comparison.

» Click here to see how to run a Sensitivity Simulation
» Click here to download the example file SENSIM.XLS