# DERIVATIVES MARKETS

DERIVATIVES MARKETS

IMPORTANT INSTRUCTIONS:

? This document provides the instructions of Individual Research Assignment –

PART II. The individual research assignment should be individually and

professionally prepared.

? All analyses and results should be original and based on your own analyses and

findings. Any reference and source of information should be explicitly provided.

? Please complete ALL parts of the Individual Research Assignment, and provide

your discussions and analyses as clear as possible. Summary tables of statistics,

quantitative analyses and qualitative discussions should be included in your

report.

IMPORTANT REQUIREMENTS:

Individual Research Assignments should be your original work, and all parts of

the assignments should be prepared and done all by yourself. No group work

and collaboration will be allowed for individual assignments. Failure to follow

these requirements may result a final grade of an “F”. You must complete the

Individual Research Assignment by yourself and submit your answers to the

following email: mba.finance.sfung@gmail.com by the due date.

IMPORTANT DATES:

? Due date of Individual Research Assignment Part II: Sunday, December 7th,2014

IMPORTANT NOTE ON ELECTRONIC SUBMISSION:

? Please submit electronic files of ALL parts of your assignments (including the

reports, spreadsheet models, references, and other files) to the following email:

mba.finance.sfung@gmail.com2

Question #1 [Option Pricing Models]

The spot price of VXX is $30 (i.e. S0

= $30). The volatility of VXX is 25% (i.e. ? =

0.25). We are valuing the option on VXX with time to maturity of 1 month (i.e. ?t

or T = 1/12). The risk-free rate with continuous compounding is 4% per annum (i.e. r

= 0.04). Assume that there is no dividend for VXX.

Part (a) [Arbitrage Portfolio Approach]

Calculate the value of a 1-month European Call option on VXX with an exercise price

of $29 (i.e. K = $29). Use Arbitrage Portfolio approach with one-step binomial tree.

Note that:

Part (b) [Risk-Neutral Valuation Approach]

Use the Risk-Neutral Valuation approach to calculate the value of option in Part (a).

Part (c) [Black-Scholes-Merton Approach]

Calculate the value of a 1-month European Call option on VXX with an exercise price

of $29 (i.e. K = $29), using the Black-Scholes-Merton option pricing formula and the

assumptions given above (i.e. S0 = $30; ? = 0.25; ?t or T = 1/12; and r = 0.04).

Calculate the value of a 1-month European Put option on VXX with an exercise price

of $29 (i.e. K = $29), using the Black-Scholes-Merton option pricing formula and the

assumptions given above (i.e. S0

= $30; ? = 0.25; ?t or T = 1/12; and r = 0.04).

Part (d) [Implied Volatility]

Assume that the market price of option on VXX = $2. Calculate the Implied Volatility

of this 1-month European Call option on VXX with an exercise price of $29 (i.e. K =

$29). To calculate the Implied Volatility, please use the following assumptions: S0 =

$30; K = $29; ?t or T = 1/12; and r = 0.04. Hint: you may use the

Black-Scholes-Merton option pricing model (e.g., implied volatility model at

Blackboard) to solve the implied volatility.

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Question #2 [Case Study of Real Options]

Prepare a 2-page minimum (1½-spaced paragraphs) case study of Real Option.

Construct a Real Option model in any setting of strategic and dynamic decisions

under risks and uncertainties (e.g. decision to expand/shutdown a project, decision to

make R&D investments, dynamic corporate financing decision, education/career

decisions, and other strategic/dynamic decisions under risks and uncertainties, etc.).

Provide detailed and specific discussions about the nature of the Real Option problem,

the underlying parameters of the Real Option model, and how you apply the Real

Option model for valuation and dynamic decisions under risks and uncertainties. You

analysis should follow the step-by-step Real Option approach below:

Step (1) Real Option Identification.

Identify your Real Option problem. Clearly define the structure of your problem/case

study and explain why it can be framed as a Real Option problem (e.g. discuss the

‘optionality’ of your proposed problem and how Real Option can help to value and

understand your proposed strategic and dynamic decisions under risks and

uncertainties). Importantly, provide explicit discussion and analyses to demonstrate

the major advantages of applying Real Option in your problem/case study.

Step (1.1) Real Option Application.

Identify the major Real Option parameters, which include:

? (i) Type(s) of the Real Option;

? (ii) Underlying asset/risk driver;

? (iii) Exercise/strike price;

? (iv) Volatility (Important variable for Real Options – please provide detailed

explanation and analysis to estimate the volatility of Real Option). Important note:

apply the spreadsheet model of estimating volatility (see Blackboard) with

realistic assumptions and actual data;

? (v) Maturity and exercise strategy;

? (vi) Required risk-free rate of return (suggestion: you may assume 3-4% or other

risk-free rates of returns).

Provide detailed and clear explanations of your Real Option assumptions and

parameters.

Step (2) Real Option Valuation

Construct a Real Option valuation model that can analyze your problem. Please

complete all of the following steps for Real Option Valuation: 4

Step (2.1) ‘Benchmark Case’ with NPV

Start with the NPV method by valuing the project as if there were no option involved,

i.e., the “benchmark case” as if all decisions had to be taken immediately without

flexibility. As an important part of your analyses, demonstrate why your proposed

Real Option model is better than traditional valuation methods such as the NPV

method (see, e.g., the examples of Real Options provided in the lecture).

Step (2.2) Real Option Model

Construct a Real Option model (using the Real Option parameters you identify in Step

(1.1) above) to analyze your problem. To provide valuation of the Real Option, you

can consider the following models:

? Binomial Option Pricing Model, and/or

? Black-Scholes-Merton Model, and/or

? Any other relevant option pricing models (e.g. multi-step binomial model,

trinomial model, stochastic volatility model, jump diffusion model, etc.).

Step (2.3) Sensitivity Analyses [Important Step]

Provide sensitivity analyses and simulations of your estimated Real Option value to

evaluate different possible outcomes/results of your Real Option model. Consider

alternative values/parameters of assumptions used in Step (1.1) above, and perform

sensitivity analyses and robust tests of your Real Option model. For example, you can

perform sensitivity analyses of Real Option value using different values of volatility

assumption (for examining Vega), etc. Note that this is an important step to complete

the Real Option analyses.

Step (3) Interpretation and Conclusions

Summarize the key insights and results obtained from your Real Option model.

Discuss how your Real Option model can provide better valuation and

decision-making for your case study. Provide a conclusion based on the key

findings and learning outcomes from your Real Option analysis. In concluding

section, please summarize:

(i) Key original findings, insights, and implications of your Real Option case.

(ii) Key learning outcomes such as new ideas, concepts, tools/techniques, and

implications you have learnt from your Real Option applications.

5

Important Instructions and Evaluation Criteria:

All analyses and discussions must be original, rigorous, well-organized, concise, and

integrated with frameworks and tables/figures of numerical results. Explain and

present all your assumptions, calculations, and ideas as clear as possible. Summary

tables/figures of numerical results should be provided to support your original

analyses and findings. Please make sure that you provide citations and complete

references of any sources of research, information and data used in your report; e.g.

provide reference of information from different sources of research. Your report may

include an Appendix that contains any additional information used in your analyses.

Individual Research Assignments should be your original work, and all parts of

the assignments should be prepared and done all by yourself. No group work

and collaboration will be allowed for individual assignments. Failure to follow

these requirements may result a final grade of an “F”. You must complete the

Individual Research Assignment by yourself and submit your answers to the

following email: mba.finance.sfung@gmail.com by the due date.

Your Real Option report will be critically evaluated based on the following criteria:

(I) the rigor and completeness of your Real Option case study and analyses, including

the quantitative analyses, Real Option models and sensitivity analyses; (II) the

theoretical applications, original insights and quality of your Real Option study; and

(III) your learning outcomes and demonstrations of successful applications of

derivatives theories, concepts, and techniques.

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