Posted: February 12th, 2015

Derivatives Assignment 2

Paper, Order, or Assignment Requirements

Note: Please let the writer that I chose below do the work.

I’ve attached the possible files I got from class to help you with the work.

you might need add an Excel file to the work in order to get the best result.

Use a simple words because my mother tongue isn’t English.

Thank you very much
Appreciate it

The question is:
”
Question 5
Calculate the time value of a call and a put option using Black Scholes. Investigate the effects of changing each of the parameter inputs on the time value of the option. Analyze your results. In what sense is the Black (1976) model equivalent to the Black Scholes (1973) model? Write and implement a VBA project that recalculates the Black Scholes (1973) time and intrinsic values of options using the parameter values you already selected. Also apply a binomial model in VBA and verify your results. Explain how the Cox, Ross and Rubinstein (1979) differs from Black Scholes (1973) given your results. Does your binomial model converge to Black Scholes? Explain the assumptions made in your Binomial approximation. Explain and interpret the code you used to make the calculation. (Is your code consistent with Cox, Ross and Rubinstein (1979)? What limitations are normally encountered in terms of the number of steps possible in Excel for a binomial – how might you overcome these limitations. (Hint: consider the Monte Carlo binomial approach used by Benninga in Lecture 6 of his series or consider using C++.) Explain what alternative you used and why your preference.

Implement the Black Scholes (1973) ‘Greeks’: delta, gamma, theta, vega and rho for your proposed European call and put. Set out the calculations in VBA or C++. Graph your results. How might the Greeks be used to interpret your initial results with regard to the parameter inputs? How could you approximate these (non-analytic Greeks) without explicitly using formulae? What is the effect on the value of your selected option if it were designated as being Asian? How would you approximate Asian option Greeks? Make reference to Benninga’s lecture 6. Set up, in Excel, the delta hedging strategy as proposed by Benninga at the beginning of lecture 6. How effective is this strategy? How might your dynamic replication be improved? How does this approach differ from the static replication proposed by Derman and Taleb (2005)?

Download option price chain data from Yahoo Finance or from Datastream/Eikon for a liquid stock. Estimate the historical volatility for the underlying stock. Estimate the implied volatility of the traded options. Comment on your results. Using the approach outlined in Hull, Chapter 19 (Appendix) to determine the implied risk neutral distribution from the implied volatilities. Set out how Breeden and Litzenberger (1978) employ a series of butterfly trading strategies to accomplish this end? Also, implement an Implied Binomial Rubinstein (1994). How does the volatility smile and/or skewness denote a non-normal distribution of the stock price return? Make reference to Hull Chapter 19. How could the Gram-Charlier approach described by Backus, Foresi and Wu (2004) be used to capture skewness and kurtosis? In what way does Dumas, Fleming and Whaley (1998) deal with volatility skew? Implement both approaches with the option chain data you have collected. Comment on how both approaches perform in terms of pricing? ”

Question 5

Calculate the time value of a call and a put option using Black Scholes. Investigate the effects of changing each of the parameter inputs on the time value of the option. Analyze your results. In what sense is the Black (1976) model equivalent to the Black Scholes (1973) model? Write and implement a VBA project that recalculates the Black Scholes (1973) time and intrinsic values of options using the parameter values you already selected. Also apply a binomial model in VBA and verify your results. Explain how the Cox, Ross and Rubinstein (1979) differs from Black Scholes (1973) given your results. Does your binomial model converge to Black Scholes? Explain the assumptions made in your Binomial approximation. Explain and interpret the code you used to make the calculation. (Is your code consistent with Cox, Ross and Rubinstein (1979)? What limitations are normally encountered in terms of the number of steps possible in Excel for a binomial – how might you overcome these limitations. (Hint: consider the Monte Carlo binomial approach used by Benninga in Lecture 6 of his series or consider using C++.) Explain what alternative you used and why your preference.

Implement the Black Scholes (1973) ‘Greeks’: delta, gamma, theta, vega and rho for your proposed European call and put. Set out the calculations in VBA or C++. Graph your results. How might the Greeks be used to interpret your initial results with regard to the parameter inputs? How could you approximate these (non-analytic Greeks) without explicitly using formulae? What is the effect on the value of your selected option if it were designated as being Asian? How would you approximate Asian option Greeks? Make reference to Benninga’s lecture 6. Set up, in Excel, the delta hedging strategy as proposed by Benninga at the beginning of lecture 6. How effective is this strategy? How might your dynamic replication be improved? How does this approach differ from the static replication proposed by Derman and Taleb (2005)?

Download option price chain data from Yahoo Finance or from Datastream/Eikon for a liquid stock. Estimate the historical volatility for the underlying stock. Estimate the implied volatility of the traded options. Comment on your results. Using the approach outlined in Hull, Chapter 19 (Appendix) to determine the implied risk neutral distribution from the implied volatilities. Also, implement an Implied Binomial Rubinstein (1994). How does the volatility smile and/or skewness denote a non-normal distribution of the stock price return? Make reference to Hull Chapter 19. How could the Gram-Charlier approach described by Backus, Foresi and Wu (2004) be used to capture skewness and kurtosis? In what way does Dumas, Fleming and Whaley (1998) deal with volatility skew? Implement both approaches with the option chain data you have collected. Comment on how both approaches perform in terms of pricing?

Apply macros, userforms and automation of spreadsheets that ease use of your project and serve to promote user-friendliness. Generate graphs and video explanations where appropriate. Interpret your results and illustrate how your work could be useful to a finance practitioner.

Hint :

might you need to look at “Benninga in Lecture 6 “ at YOUTUBE.