Valuation of 3G spectrum license in India: A real option approach

India is about to enter a new technological phase as far as mobile technology is concerned. After almost a decade of existence, Third Generation (3G) mobile technology will be rolled out in India. The licenses for the same were auctioned in April – May 2010 and 3G licenses were allocated to the winners in September 2010. Nine private telecom operators entered the bidding for the license and eventually seven won the licenses. The bidding was intense and eventually the aggregate fees of the license as received by the government were almost twice the expected amount. In the backdrop of experience of 3G auction winners in UK and Germany who paid huge sums to acquire the 3G licenses and later lost their market capitalization as the markets perceived that the price paid for the license was more than the actual value of the license, analysts in India were concerned if the operators had paid too much for the licenses. In this report aggregate value of the 3G licenses is calculated using both traditional discounted cash flow approach and real options approach. We find that the rollout of 3G services gives an internal rate of return of 14.2%over the life of the license. If we assume an internal rate of return of 15% for the telecom operators then the aggregate license value comes out to be INR 594 Billion which is 12% lower than what the operators have paid to acquire the license. We also found out that the value of the license as calculated from the real options methodology is INR 798 Billion which is 17.8% higher than the aggregate value paid by the operators. Hence we see that DCF valuation suggests that the licenses were overvalued while Real Options methodology suggests that the licenses were undervalued. The report discusses the reasons for differences between real option valuation and DCF valuation of the license, the possible challenges that the 3Goperators might face in the short to long term and what are the key enablers for the growth of3G services if they want to extract the maximum mileage out of the 3G technology. The report recommends that in future while allocating telecom licenses or licenses in sectors where high and irreversible investment is required and there is a scope for the licensees to invest in phases or in modules, the government should consider real options methodology for setting the price of the license., or the base price of the licenses in case the government decides to follow an auction methodology3G spectrum, mobile technology, valuation, real options, DCF

Active Hedging Greeks of an Options Portfolio integrating churning and minimization of cost of hedging using Quadratic & Linear Programing

This paper proposes a methodology for active hedging Greeks of an option portfolio integrating churning and minimization of cost of hedging. In the first section, hedging strategy is implemented by taking positions in other available options, while simultaneously minimizing the net premium paid for the hedging and then churning the portfolio to take into account the changed value of Greeks in the new portfolio. In the second section, the paper extends the model to incorporate the transaction cost while hedging the portfolio and churning it in Indian Scenario. Both constant and nonlinear shape of transaction cost has been considered as per the Security Transaction Tax and Brokerage charges in India. A quadratic programming has been presented which has been approximated by a linear programming solution. The prototype software has been developed in MS Excel using Visual Basic.Options Portfolio, Hedging Greeks, Churning of Portfolio, Linear Programing, Transaction Cost

Sum-product estimates for diagonal matrices

Given $d \in \mathbb{N}$, we establish sum-product estimates for finite, non-empty subsets of $\mathbb{R}^d$. This is equivalent to a sum-product result for sets of diagonal matrices. In particular, let $A$ be a finite, non-empty set of $d \times d$ diagonal matrices with real entries. Then for all $\delta_1 < 1/3 + 5/5277$, we have $$|A+A| + |A\cdot A| \gg_{d} |A|^{1 + \delta_{1}/d}.$$ In this setting, the above estimate quantitatively strengthens a result of Chang.Comment: A revised version will appear in Bulletin of the Australian Mathematical Society. 9 page

An Elekes-R\'onyai theorem for sets with few products

Given $d,n \in \mathbb{N}$, we write a polynomial $F \in \mathbb{C}[x_1,\dots,x_n]$ to be degenerate if there exist $P\in \mathbb{C}[y_1, \dots, y_{n-1}]$ and $m_j = x_1^{v_{j,1}}\dots x_n^{v_{j,n}}$ with $v_{j,1}, \dots, v_{j,n} \in \mathbb{Q}$, for every $1 \leq j \leq n-1$, such that $F = P(m_1, \dots, m_{n-1})$. Our main result shows that whenever $F$ is non-degenerate, then for every finite set $A\subseteq \mathbb{C}$ such that $|A\cdot A| \leq K|A|$, one has $$|F(A, \dots, A)| \gg_{d,n} |A|^n 2^{-O_{d,n}((\log 2K)^{3 + o(1)})}.$$ This is sharp up to a factor of $O_{d,n,K}(1)$ since we have the upper bound $|F(A,\dots,A)| \leq |A|^n$ and the fact that for every degenerate $F$ and finite set $A \subseteq \mathbb{C}$ with $|A\cdot A| \leq K|A|$, one has $$|F(A,\dots,A)| \ll K^{O_F(1)}|A|^{n-1}.$$ Our techniques rely on a variety of combinatorial and linear algebraic arguments combined with Freiman type inverse theorems and Schmidt's subspace theorem.Comment: 17 page

Modeling Driving Behavior at Traffic Control Devices

Transportation is a major source of many major air pollutants as well as greenhouse gas emissions. The four common factors responsible for vehicular emissions are vehicle, road characteristics, traffic conditions and driving behavior. The objective of this dissertation was to study driving behavior since it is highly correlated to emissions as shown by previous studies. Understanding driving behavior is likely to help improve emissions estimates. In this dissertation, three levels of analyses of driving behavior were conducted including: (1) exploring driving behavior parameters and assessing their impact on emissions, (2) comparing driving behavior among the three most common traffic control devices, and (3) modeling second-by-second driving behavior of individual drivers. In order to explore these relationships, spatial location, vehicle kinematics, and CO2 emissions were collected along a study road corridor in Urbandale (IA) was. The chosen road corridor comprised of a roundabout, an all-way-stop and a traffic signal along with curve and tangent sections. The traffic during peak and off-peak hours on the corridor was comparable. This was useful for comparing driving behavior across drivers under similar conditions. A single instrumented vehicle was driven over the corridor by four different subject drivers. The vehicle was equipped with a portable emissions measurement device which had engine sensor, tail-pipe sample lines and a GPS. In the first analysis, vehicle kinematic variables were used to derive driving behavior parameters that included gas pedal use and brake pedal use. Two groups of drivers were identified based on these parameters. The study identified gaspad and brakepad as important driving behavior parameters which can explain variation in vehicular emissions. Driving behavior parameters used in previous studies for developing driving cycle were utilized in this study to compare driving behavior between traffic control devices for the second analysis. These parameters characterized speed behavior, speed change behavior and energy gain behavior. A MANOVA model was used for comparing the overall driving behavior between traffic control devices by comparing these parameters. Results showed that driving behavior at the roundabout and all-way-stop differ significantly (p \u3c 0.001) on at least one of driving behavior parameter. Likewise, roundabout and traffic signals also differed in terms of driving behavior (p \u3c 0.001). Driving behavior and emissions are highly correlated. This implies using separate emission factors for different traffic control devices. In the third analysis, speed profiles at roundabout were modeled for the drivers using a fourth degree polynomial regression. Results showed that speed profiles models were significantly different across drivers. This implied that drivers must be treated as random variables in modeling driving behavior and emissions for a given road or driver population. Average speeds of drivers at yield point were simulated based on the model. The maximum difference was found to be about 1.5 mph

Unbounded expansion of polynomials and products

Given $d,s \in \mathbb{N}$, a finite set $A \subseteq \mathbb{Z}$ and polynomials $\varphi_1, \dots, \varphi_{s} \in \mathbb{Z}[x]$ such that $1 \leq deg \varphi_i \leq d$ for every $1 \leq i \leq s$, we prove that $$|A^{(s)}| + |\varphi_1(A) + \dots + \varphi_s(A) | \gg_{s,d} |A|^{\eta_s} ,$$ for some $\eta_s \gg_{d} \log s / \log \log s$. Moreover if $\varphi_i(0) \neq 0$ for every $1 \leq i \leq s$, then $$|A^{(s)}| + |\varphi_1(A) \dots \varphi_s(A) | \gg_{s,d} |A|^{\eta_s}.$$ These generalise and strengthen previous results of Bourgain--Chang, P\'{a}lv\"{o}lgyi--Zhelezov and Hanson--Roche-Newton--Zhelezov. We derive these estimates by proving the corresponding low-energy decompositions. The latter furnish further applications to various problems of a sum-product flavour, including questions concerning large additive and multiplicative Sidon sets in arbitrary sets of integers.Comment: 28 page