代写Derivatives and Risk Management (FINC 650) Summer 2024代做Python语言

Project Outline

Derivatives and Risk Management (FINC 650)

Summer 2024

Title: Applying Binomial Valuation Model for Estimating Option Price

Learning Objectives:

To learn to apply the Binomial Modelling Technique to estimate the theoretical value of the futures option and to evaluate the risk and return of the underlying commodity.

Choosing a futures contract near-money options

You may work with any commodity or interest rate futures contracts, but must choose call option linked to the same futures contract with strike prices near the current futures price.  For example, if you choose to work on December Oil futures contract which is trading at 106 today, then you search for one call or one put with strike price being the closest to 106 (K=105).  Apply the Binomial Model to estimate the theoretical price for the futures option.   This is achieved by first estimating the up and down price for the futures contact with the benchmark option.

It is important that the option used has strike price close to the current futures price (near the money options).  This will be the benchmark option to be used for pricing a second option.

The paper should be divided into 3 sections ( I, II, III) as follows:

Section I: Quantitative Analysis of Risk

1. Calculate the annual historical volatility of the futures contract using the prices of recent months (from last prices of recent days downloaded from Price History in Barchart) with Excel or a statistical software.  First get the standard deviation of the daily returns and then annualize.  

Show calculation procedure and result with Excel table pasted to Section I of the project (one page)

2. Select a benchmark option near the money with at least two months to expiration.  Assume 6% for annual risk free rate.  

Write out the two equations ( one binomial option pricing equation plus one symmetry restriction: Fo = (Fu + Fd)/2, which assumes that today’s futures price Fo is the expected price) you used to solve for Fu and Fd.   Use the pricing equation for call options (in PPT) to solve Fu and Fd  as implied by this benchmark option.   Check your solution for Fd to make sure Fd is below K so that assumption of Cd =0 is valid. (half page).  

3.  Now apply the solved values for Fu and Fd from the benchmark option to pricing a second near-money option with same expiration date but different strike price.

3. Provide information for both options (Commodity type, date of data, market price of futures, K, market price of benchmark and second options, Volume, Expiration Date, Days to Maturity) in a well-organized information summary table with one column for benchmark and one column for second option.  Afterward, set up two additional tables as shown below to summarize your results for the estimated volatility with 6% interest rate.

 Write the volume for the option in a parenthesis next to the strike price.

Summarize data and results with two tables below.  (one page)

   Example of Table Format:

Procedure Table

Ex: December Oil Futures:    Benchmark Option: Dec Call:    K=105 (Volume=18)      Second Option:  Dec Call      K=110 (Volume=21)	Assume annual interest rate =6%
Fo  =
Solve                         Fu=
Solve                         Fd=
Apply the solved Fu and Fd to the second closest to the money option:   Binomial Value of second ption =
Actual Price of second ption =

Result Summary Table

Actual price of second option	Binomial Price of second option	Undervaluation of second ption= (Actual price- Binomial Price)/Actual Price	Black Scholes Price of second option	Historical Volatility  (annualized)	Implied volatility of second option by Barchart	Binomial Volatility= (Fu-Fd)/2/Fo	Binomial Volatility= (Fu-Fd)/2/Fo (annualized by multiplying by root of  252/trading days till expiration)

Section II:  Qualitative Analysis of Risk

1) Evaluate the risk for a speculator speculating on this futures. (half to one page)

2) Find an example of a company that hedges with commodity futures, preferably in the futures that you are working on.  Evaluate the risk for a commodity user who does not hedge with this commodity futures.   (ex: farmers who does not hedge by shorting agriculture futures.  A potato chip company which does not hedge by longing soy oil.   A trucking company which does not hedge by longing gasoline futures.)  If you are evaluating an interest rate futures, then discuss the risk of banks or bond fund managers might face if they do not hedge their interest rate risk.  Evaluate the risk of not hedging for any company (one page)

3 optional :)  This part is optional:  What do you think of the level of risk for this futures contract, as compared to S&P stocks which have 20% annual volatility?  To do this part, you need to estimate beta (market risk) of the futures by regressing daily returns of the futures for the last year or two on the S&P daily returns.  Compare both beta risk and total risk (volatility or standard deviation) of the futures contract to S&P. (optional half page)

Section III: Expected Return Analysis

1) Perform. a market analysis of this commodity.

Ex: What are the exporting nations and the importing nations for this commodity?

What are the main use for this commodity?

Apply your economics knowledge to research on the outlook for demand and supply for this commodity worldwide.

Based on your research, assign a probability to Fu between now and the option expiration period (terminal date).  

Summarize you analysis on the demand and supply outlook and justify the reason for the probability you assigned and whether it is worthwhile to invest in this commodity. (one to two page)

2) Estimate Expected Return.

Ex: Suppose you assign 60% probability of price rising (based on your research).  Then your expected futures price on terminal date or expiration date can be estimated as:

E ( F_T ) = .6 Fu + (1-.6)Fd.

Next, calculate the expected return for futures from today to terminal date :

 E ( r_T)=  ( E( F_T ) – Fo)/Fo

Afterward, you can annualize the expected return using the following equation:

1+ E ( r )  =  ( 1 +  E ( r_T) ) ^ 365/days to exp

  where  E ( r )= expected return of the futures on an annual basis

Show calculation for expected return above.  (half page)

At the end of Section III,  write a brief conclusion and outline what you have learned from this research project . (half page)

This is a solo project in which you work on your own.

Underline keywords in your paper. You may obtain financial information for futures from any source you want, including financial websites such as cmegroup.com or barchart.com which yield many useful financial data.

All the data must be linked to the same date or collected at the same time to be consistent.  Financial information from any source must be referenced.  

(All price data must be gathered on the same date to be consistent. Best time is soon after market close.).

The content and the quality of the paper are more important than the quantity; be concise and organized.  Please refer to rubric table in Sakai for details.

Feel free to consult me if you have any question.