The futures on index XYZ are currently trading at 1000. Consider a portfolio of 100 short at-the-money (ATM) straddles on XYZ futures (ie. you sell 100 class and 100 puts with the same strike price 1000) with maturity 3 months from now. Consider now adding to the portfolio 100 short strangles, with strike prices 750 and 1250, and the same maturity of three months (ie. you also sell 100 call options with strike price 1250 and 100 put options with strike price 750)

a. Draw a diagram of current mark-to-market value and Profit&loss at maturity of the overall portfolio

b. Explain whether the Vega of the overall portfolio is larger than the Vega of the 100 straddles only

c. Explain whether the GRamma of the overall portfolio is larger than the Gramma of the 100 straddles only

d. Use Ito's formula to write down the dynamics of the market value of the overall portfolio, ( Vt) t>=0. What is the sign of the different integrands appearing in the resulting stochastic differential equation?

e. Assume enow that in order to reduce tail risk you purchase 200 strangles with strike prices 650 and 1350, ie. you buy 200 out-of-the-money (OTM) puts with strike price 650, and 200 OTM calls with strike price 1350, all with maturity 3 months from now. Draw a diagram of the current mark-to-market value and Profit & Loss at maturity of the portfolio.

f. Assume that after 2 months and 3 weeks the index is trading at 1350. Use Ito's formula to write down the dynamics of the market value of the overall portfolio (containing long straddles and straddles, as well as the long strangles of the question c above, ( Vt*)t>=0. What is the sign of the different integrands appearing in the resulting stochastic differential equation?

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a Heres a diagram illustrating the current marktomarket value and profitloss at maturity of the over... View the full answer