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GCBF ♦ Vol. 11 ♦ No. 1 ♦ 2016 ♦ ISSN 1941-9589 ONLINE & ISSN 2168-0612 USB Flash Drive 170 Global Conference on Business and Finance Proceedings ♦ Volume 11 ♦ Number 1 Let’s examine the impact of uncertainty on the value of option. If in the above example, the allowable options NPV will be equal to -10 and 10 million dollars. (in other words, the spread of likely values of the underlying asset value increases) with equal probability of 0.5; value of the option will have $ 5 million. If you have a choice, the increased risk increases cost of real investment project. This fact is well known in the financial options and, as just illustrated, it is true for the options in the real sector as well.

Thus, in this situation, the payment for option will be the volume of investment in the project, which allows the use of competitive environment opportunities in the future. In this respect, the real option is almost identical to the financial call option. The future value of the underlying asset will be the income earned on the project.

Given the positive correlation between the level of uncertainty and the value of the option it should be noted that options lose value if there is no ambiguity since the choice decreases to the one and only possibility.

In general, the conditions of real options that they have a strategic value are:

project operates in an uncertain market conditions;

this uncertainty has an impact on the market value of the project;

project management has managerial flexibility in decision-making;

the bank's management strategy is realistic and feasible;

management must be rational in the implementation of this strategy.

Failure to comply with at least one of these conditions leads to the inability of real option use.

Parameters used in evaluating real options using the Black & Scholes model and other models are similar to the six parameters used in the valuation of financial options. Black & Scholes model is one of the most important concepts in modern financial theory. It was designed in 1973 by Fischer Black, Robert Merton and Myron Scholes, and is still widely used and considered as one of the best ways to determine the fair value of options. The work was published under the title "Assessment of Options and Corporate Liabilities" in the Journal of Political Economy (Journal of Political Economy) in 1973.

In options there is a financial contract that gives the right to buy or sell the underlying asset at the time of exercising the option, and real options possess some asset that allows the company to launch an investment project.

The price paid for the option (premium) is the cost of acquisition of the asset, which enables the implementation of some of the investment project. If the price of the option, in other words, the average projected cash flows from the sale of the option exceeds the fee for the option, its execution is beneficial.

And the exercise price is the value of all costs in the period of the investment. There are a number of

methodologies to evaluate the real options:

using differential equation using formulas assessment as Black & Scholes model and analytical model with binomial or decision tree.

Using the formula for option pricing is a fast, accurate way without complex calculations. But the main disadvantage is the difficulty in understanding and explanation, since most formulas were derived through complex calculations in the field of stochastic processes.

Black & Scholes model was developed to estimate the European options (fixed date), so criticism of the model argue that it is not suitable for the assessment of real investment projects. Besides the numerous risk factors and the possibility of execution of the project at any time, making it impossible to assess the real options purely analytical way, so you have to use mathematical analysis methods, which include the binomial model, a model based on differential equations and the model of Monte - Carlo.

The formula of Black & Scholes, the price of the call option GCBF ♦ Vol. 11 ♦ No. 1 ♦ 2016 ♦ ISSN 1941-9589 ONLINE & ISSN 2168-0612 USB Flash Drive 171 Global Conference on Business and Finance Proceedings ♦ Volume 11 ♦ Number 1 (, ) = (1 ) − −(−) (2 ) 2 ln � � + ( + 2 )( − ) 1 = �( − ) 2 = 1 − �( − )

–  –  –

This model, in principle, is easy to use, if you program it in MS Excel.

Cox, Ross and Rubinstein first proposed the binomial model in 1979 and it is an effective tool for assessing the investment projects. The advantage of this model is the fact that it is simple, suitable for any consideration of the motion sequences of funds caused by the use of the underlying asset and may be used in the assessment of the American option (n comparison with the European option, American option can be exercised at any time before the mature date). It is characterized by a graphic illustration of the cost of changing the value of the underlying asset, but it’s difficult to take account of more than two stochastic factors.

In evaluating real option binomial model there are built two grids, one - net change in value of the underlying asset, and the second - a grid of calculating the cost of the real option. Also calculated such parameters as discounted cost of the underlying asset at the time of exercising the option at the time of evaluation (S); the price of the option (X); uncertainty σ (the maximum deviation of the natural logarithm of the free cash flows of the underlying asset from the average, the term of the option (T); the risk-free discount rate (rf); loss as a missed dividends (b).

Based on these factors, the factors of uplink are calculated u (up), i.e. the probability of growth in the value of option and the downward movement d (down), i.e. the probability of decrease in the value of option and the risk-free probability (P). When calculating the probability of option value growth u is used as an uncertainty parameter and the square root of the given time interval (δt).

= √ = −√ = 1/ (−)() − = − GCBF ♦ Vol. 11 ♦ No. 1 ♦ 2016 ♦ ISSN 1941-9589 ONLINE & ISSN 2168-0612 USB Flash Drive 172 Global Conference on Business and Finance Proceedings ♦ Volume 11 ♦ Number 1 After calculating these parameters the binomial tree of change in underlying asset value is built. To find the value of the asset values of the upper and lower nodes of the grid at the end of the first period must be multiplied by the original value of asset value, respectively, factors of upward and downward movement.

Figure 2: Binomial tree of three time periods

S0 - the value of the underlying asset at the first period;

Su - the value of the underlying asset in the case of price increase;

Sd - value of the underlying asset in the case of price decrease;

Let C - is the value of the option at the initial time, then Cu - is the price of an option in the case of increase in underlying asset value, and Cd - in the case of decrease in underlying asset value. R - is a compounding factor for the risk-free rate, whereas ( − ) ( − ) + ( − ) ( − ) = If you simplify the expression by adopting the probability of price increase in the underlying asset for p,

and the (1-p) for the probability of price decrease, we get:

–  –  –

= Thus, this formula is used to determine the value of the investment project.

Model Monte - Carlo, in turn, allows option evaluation with the help of computer simulation. Although it does not assess the American option, but provides an opportunity to assess the investment with a large degree of uncertainty, and in the presence of a number of factors affecting the cost of the project in question.

Real options allow bank managers to postpone the investment, if necessary, to achieve the level of confidence in the feasibility and profitability of investments. In addition, evaluation of investment projects with real options is available for any bank, although some banks have more opportunities for their use than others.

This method of assessment is based on the discounted principles, and at the same time it takes into account management flexibility, as the project is regarded as a system of real options, which in the future may be exercised or not exercised. Real option can assist in the assessment of the project at the stage of completion of the payback period. For this purpose the information about the prospects of using probabilistic methods GCBF ♦ Vol. 11 ♦ No. 1 ♦ 2016 ♦ ISSN 1941-9589 ONLINE & ISSN 2168-0612 USB Flash Drive 173 Global Conference on Business and Finance Proceedings ♦ Volume 11 ♦ Number 1 is gathered. Then a mathematical model that shows the optimal sequence of decision-making and implementation for a variety of future options is built.

Optional model previously was used for mining and energy companies, but now they are widely used in other industries. It is also possible to use them in banks.

Project investment is not the main activity of banks, but can become an effective way of placing accumulated funds. Using real options when evaluating the project, the bank protects itself from future risks and loss of profits. In this crisis period the banks are paying more and more attention on risk management and try to tighten the criteria for granting loans and attract deposits as much as possible. Banks see investment in the project as long-term financing and don’t like this type of operations, as they are characterized by numerous of uncertainties and risks. A real option is just a tool for assessing the project in an uncertain situation.

The main area of the project, in which the real option is useful are the projects of launching new products, because in such situations, it is possible to add or eliminate a real option, even though the options can be used almost everywhere. In such cases, real options will help in better definition of project value and understanding the interaction with the risk.

In practice, for example, the company Real Options Valuation, Inc. produces software, training and consulting services in the field of risk analysis. It uses the tools of risk analysis and risk management techniques, such as the analysis of real options; forecasting, optimization, analysis of projects with risk;

identification and quantification of projects. Moreover, there are many companies that operate like the company mentioned above, which uses real options for risk reduction, so this method can be widely applied in practice, not remaining theoretical level.

Thus, banks are encouraged to expand their activity by financing investment projects and at the same time use real options to minimize their risk of loss of invested financial, human and time resources.


[1] Grishina S. A. Option method of evaluation investment effectiveness. – Banking services, 2011, no.

10. S. 6.

[2] Gusev A. A. Real options in the assessment of business and investment. Monografija, M.: ID RIOR, 2009, pp. 118.

[3] Kolesov P.F. The Role of investment activity in enhancement of banks competitiveness - Banking services, 2012, no. 6. pp. 9.

[4] Moskvin V. A. Risk management of investment projects in commercial banks.. M.- Finansy i statistika. 2004, pp. 352.


Ganbat Khaliun, Plekhanov Russian University of Economics, PhD student at Banking Department GCBF ♦ Vol. 11 ♦ No. 1 ♦ 2016 ♦ ISSN 1941-9589 ONLINE & ISSN 2168-0612 USB Flash Drive 174 Global Conference on Business and Finance Proceedings ♦ Volume 11 ♦ Number 1

–  –  –

Most investors know that bond prices move inversely with interest rate fluctuations. These same investors, however, may not fully understand how to assess the interest rate risk of different fixed income investments.

This is particularly timely given the improving U.S. economy and Federal Reserve’s expectation of increasing interest rates in the near future. The simplest measure of interest rate risk for the average investor is something called duration. The Financial Industry Regulatory Authority (FINRA) stated that the one number a bond investor should know is duration. This article will explain what duration is, how to use this measure to evaluate risks, examples of how changes in interest rates will impact bonds or bond funds with different durations, and where investors can find this information.

JEL: M10, G10, M40 KEYWORDS: Duration, Interest Rate Risks, Bonds, Investments


As baby boomers age, the traditional investment advice is to allocate a larger percentage of one’s assets to fixed income as opposed to equities or other investments. Many investors erroneously believe that investments in high quality long-term bonds or bond funds have very minimal risks. This may be true if individual bonds are held to maturity or have a very short maturity. However, if interest rates increase, the value of their bonds or bond funds will decline. This is called interest rate risk and as this article will illustrate interest rate risk generally increases as the maturity of the bond or bond fund increases. Although there may be limited credit risk in a 20-year AA rated bond, investors should still be concerned about interest rate risk. A bond maturing in 20 years may be twice as sensitive (volatile) to changes in interest rates as a 10-year bond. This is a very important point to remember as individuals and some funds are “chasing higher yields” by investing in longer maturity bonds that generally pay a higher rate of interest.

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